diff --git a/.ipynb_checkpoints/Stochastic quantum dynamics-checkpoint.ipynb b/.ipynb_checkpoints/Stochastic quantum dynamics-checkpoint.ipynb new file mode 100644 index 0000000..07092dc --- /dev/null +++ b/.ipynb_checkpoints/Stochastic quantum dynamics-checkpoint.ipynb @@ -0,0 +1,595 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Info: Nathan Shammah, RIKEN, nathan.shammah@gmail.com\n", + "\n", + "# Open Quantum Dynamics with QuTiP\n", + " \n", + " \n", + " We use QuTiP's solvers to study the open dynamics of a quantum system evolving in time. \n", + " \n", + " \n", + " - #### Lindblad Master Equation\n", + " \n", + " - #### Lindblad Master Equation: Time evolution\n", + " \n", + " - #### Lindblad Master Equation: steady-state solution\n", + " \n", + "- #### Stochastic Dynamics: Quantum Trajectories with Monte Carlo" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from qutip import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define the operators and Hamiltonian\n", + "\n", + "We consider the spin-boson system, which is a prototypical model of light-matter interaction in cavity quantum electrodynamics (cQED): a single two-level system coupled to a single mode of the photonic field. Its Hamiltonian is described by\n", + "\n", + "\\begin{eqnarray}\n", + "H &=& \\omega_c a^\\dagger a + \\frac{\\omega_0}{2}\\sigma_z\n", + "+\\frac{g}{2}\\sigma_x\\left(a+a^\\dagger\\right)+\\frac{\\omega_x}{2}\\sigma_x,\n", + "\\end{eqnarray}\n", + "\n", + "where we added also the possibility of the system of a classical drive onto the system at a frequency $\\omega_x$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# spins\n", + "sx_reduced = sigmax()\n", + "sy_reduced = sigmay()\n", + "sz_reduced = sigmaz()\n", + "sp_reduced = sigmap()\n", + "sm_reduced = sigmam()\n", + "\n", + "# photons\n", + "nph = 4\n", + "a_reduced = destroy(nph)\n", + "\n", + "# tensor space\n", + "sz = tensor(sz_reduced,qeye(nph))\n", + "sx = tensor(sx_reduced,qeye(nph))\n", + "sm = tensor(sm_reduced,qeye(nph))\n", + "sp = sm.dag()\n", + "a = tensor(qeye(2), a_reduced)\n", + "\n", + "# hamiltonians\n", + "wc = 1\n", + "w0 = 0.5*wc\n", + "g = 0.1*w0\n", + "wx = 0.2*w0\n", + "Hcav = wc*a.dag()*a\n", + "Hspin = w0*sz #+ wx*sx\n", + "Hint = g*sx*(a+a.dag())\n", + "HintCheck = g*tensor(sx_reduced,a_reduced+a_reduced.dag())\n", + "H = Hcav + Hspin + Hint\n", + "np.testing.assert_(Hint == HintCheck)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define the initial state" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The initial state of the system is given by \n", + "\\begin{eqnarray}\n", + "\\rho&=&\\rho_\\text{spin}\\otimes\\rho_\\text{phot}\n", + "\\end{eqnarray}\n", + "and in the case of a initially pure state, \n", + "\\begin{eqnarray}\n", + "\\rho&=&|\\psi\\rangle_\\text{spin}\\otimes|\\psi\\rangle_\\text{phot}\n", + "\\end{eqnarray}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# initial state\n", + "psi0_spin = basis(2,0)\n", + "psi0_phot = basis(nph,nph-int(nph/2))\n", + "psi0 = tensor(psi0_spin,psi0_phot)\n", + "rho0 = ket2dm(psi0)\n", + "\n", + "# times at which to calculate the variables\n", + "tlist = np.linspace(0,50,2000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Lindblad master equation: $\\texttt{mesolve}$\n", + "\n", + "We now consider the time evolution of the open quantum system, in which $\\rho$ is dissipatively coupled to a spin and photonic bath,\n", + "\n", + "\\begin{eqnarray}\n", + "\\frac{d}{dt}\\rho =-i\\lbrack H,\\rho\\rbrack+\\gamma\\mathcal{D}_{[\\sigma_-]}\\rho+\\kappa\\mathcal{D}_{[a]}\\rho.\n", + "\\end{eqnarray}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "kappa = 0.3\n", + "gamma = 0.3\n", + "\n", + "my_options = Options(average_states = True, store_states = True)\n", + "results = mesolve(H, psi0, tlist, \n", + " c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], \n", + " options=my_options, progress_bar=True)\n", + "\n", + "# store time evoluted variables\n", + "nph_t = results.expect[0]\n", + "sz_t = results.expect[1]\n", + "rho_t = results.states" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "fs=20\n", + "plt.figure(figsize=(14,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.suptitle(\"Time evolution for spin and photonic excitations of a driven cavity with single two level system, with dissipation\")\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Steady state solver: $\\texttt{steadystate}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "rhoss = steadystate(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "nph_ss= expect(a.dag()*a,rhoss)\n", + "sz_ss= expect(sz,rhoss)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "plt.figure()\n", + "plt.imshow(abs(rhoss.full()))\n", + "plt.show()\n", + "plt.close()\n", + "plt.figure()\n", + "plt.subplot(121)\n", + "plt.imshow(abs(ptrace(rhoss,0).full()))\n", + "plt.xlabel(\"atom\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.imshow(abs(ptrace(rhoss,1).full()))\n", + "plt.xlabel(\"photon\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Liouvillian structure\n", + "\n", + "We can derive thermodynamical properties of the out-of-equilibrium system by studying the spectrum of the Liouvillian." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "L = liouvillian(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "\n", + "# represent the Liouvillian\n", + "plt.figure(figsize=(14,6))\n", + "plt.subplot(121)\n", + "plt.imshow(np.real(L.full()))\n", + "plt.title(\"Real values of the Liouvillian\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.imshow(np.imag(L.full()))\n", + "plt.title(\"Imaginary values of the Liouvillian\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Liouvillian Spectrum, $\\texttt{eigenstates}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "L = liouvillian(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "\n", + "# Plot the Liouvillian spectrum in the complex plane\n", + "eigenvalues_L, eigenvectors_L = L.eigenstates()\n", + "\n", + "\n", + "real_eigenvalues = np.real(eigenvalues_L)\n", + "imag_eigenvalues = np.imag(eigenvalues_L)\n", + "\n", + "plt.figure(figsize=(10,10))\n", + "plt.plot(real_eigenvalues, imag_eigenvalues,\"o\")\n", + "plt.title(\"Real values of the Liouvillian\",fontsize=fs)\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us decipher the spectrum of the Liouvillian:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure(figsize=(10,10))\n", + "plt.plot(real_eigenvalues, imag_eigenvalues,\"o\")\n", + "plt.title(\"Real values of the Liouvillian\")\n", + "plt.axvline(x=0,color=\"red\")\n", + "plt.axhline(y=0,color=\"black\",linestyle=\"dashed\")\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We find symmetries in the Liouvillian spectrum with respect to the real and imaginary axis." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure(figsize=(6,6))\n", + "plt.plot(real_eigenvalues[-1],imag_eigenvalues[-1],\"o\",markersize=20,label=\"$\\lambda_0$\")\n", + "plt.plot(real_eigenvalues[-2],imag_eigenvalues[-2],\"*\",markersize=20,label=\"$\\lambda_1$\")\n", + "plt.plot(real_eigenvalues[-3],imag_eigenvalues[-3],\"s\",markersize=20,label=\"$\\lambda_2$\")\n", + "plt.xlim([-2,2])\n", + "plt.ylim([-2,2])\n", + "plt.legend(fontsize=20)\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Photon counting statistics: $\\texttt{mcsolve}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# set dynamics options\n", + "my_options = Options(average_states = False, store_states = True)\n", + "# solve dynamics\n", + "results_mc = mcsolve(H, psi0, tlist, \n", + " c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], \n", + " options=my_options, progress_bar=True)\n", + "\n", + "# store time evoluted variables\n", + "nph_mc_t = results_mc.expect[0]\n", + "sz_mc_t = results_mc.expect[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The default options for $\\texttt{mcsolve}$ imply solving the dynamics for 500 trajectories. \n", + "\n", + "This option can be controlled by setting a different number in $\\texttt{Options(ntraj=500})$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "rho_mc_t = results_mc.states\n", + "len(rho_mc_t)\n", + "#help(expect)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sz_stoch_t = []\n", + "nph_stoch_t = []\n", + "for i in range(len(rho_mc_t)):\n", + " sz_stoch_t.append(expect(sz,rho_mc_t[i]))\n", + " nph_stoch_t.append(expect(a.dag()*a,rho_mc_t[i]))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure(figsize=(14,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t, label=\"me solve\")\n", + "plt.plot(tlist, sz_mc_t, label=\"mc solve (500 trajectories)\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5, label=\"me solve\")\n", + "plt.plot(tlist, nph_mc_t/nph/0.5, label=\"mc solve (500 trajectories)\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.show()\n", + "plt.close()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Lindblad master equation as the limit of the stochastic evolution: $\\texttt{mesolve}$ and $\\texttt{mcsolve}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# 50 trajectories\n", + "my_options50 = Options(ntraj=50)\n", + "results_mc50 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options50, progress_bar=True)\n", + "nph_mc_t50 = results_mc50.expect[0]\n", + "sz_mc_t50 = results_mc50.expect[1]\n", + "# 100 trajectories\n", + "my_options100 = Options(ntraj=100)\n", + "results_mc100 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options100, progress_bar=True)\n", + "nph_mc_t100 = results_mc100.expect[0]\n", + "sz_mc_t100 = results_mc100.expect[1]\n", + "# 200 trajectories\n", + "my_options200 = Options(ntraj=200)\n", + "results_mc200 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options200, progress_bar=True)\n", + "nph_mc_t200 = results_mc200.expect[0]\n", + "sz_mc_t200 = results_mc200.expect[1]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure(figsize=(16,6))\n", + "# spin excitation\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_mc_t50, label=\"mc solve (50 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t100, label=\"mc solve (100 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t200, label=\"mc solve (200 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t, label=\"mc solve (500 trajectories)\")\n", + "plt.plot(tlist, sz_t, label=\"me solve\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "# photonic excitation\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_mc_t50/nph/0.5, label=\"mc solve (50 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t100/nph/0.5, label=\"mc solve (100 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t200/nph/0.5, label=\"mc solve (200 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t/nph/0.5, label=\"mc solve (500 trajectories)\")\n", + "plt.plot(tlist, nph_t/nph/0.5, label=\"me solve\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.show()\n", + "plt.close()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We observe that progressively, as the number of trajectories is increased, the value given by the average over the trajectories gets closer to the master equation value." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "plt.figure(figsize=(12,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t)\n", + "plt.plot(tlist, sz_mc_t)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle s_z \\rangle$\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5)\n", + "plt.plot(tlist, nph_mc_t/nph/0.5)\n", + "\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle n_{ph} \\rangle$\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting single quantum trajectories\n", + "\n", + "By setting:\n", + "my_options = Options(average_states = False, store_states = True)\n", + "\n", + "we can inspect single quantum trajectories and their behaviour." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure(figsize=(14,5))\n", + "plt.subplot(121)\n", + "for i in range(len(sz_stoch_t)):\n", + " plt.plot(tlist, sz_stoch_t[i],alpha=0.1)\n", + "\n", + "plt.plot(tlist, sz_t,\"b\",linewidth=3)\n", + "plt.plot(tlist, sz_mc_t,\"y\",linewidth=2)\n", + "plt.plot(tlist, sz_stoch_t[4]/nph/0.5,\"g\",linewidth=5)\n", + "plt.plot(tlist, sz_stoch_t[6]/nph/0.5,\"r\",linewidth=5)\n", + "plt.subplot(122)\n", + "for i in range(len(sz_stoch_t)):\n", + " plt.plot(tlist, nph_stoch_t[i]/nph/0.5,alpha=0.1)\n", + "plt.plot(tlist, nph_t/nph/0.5,\"b\",linewidth=3)\n", + "plt.plot(tlist, nph_mc_t/nph/0.5,\"y\",linewidth=2)\n", + "plt.plot(tlist, nph_stoch_t[4]/nph/0.5,\"g\",linewidth=5)\n", + "plt.plot(tlist, nph_stoch_t[6]/nph/0.5,\"r\",linewidth=5)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle X \\rangle$\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We obseverve that the single trajectories can provide information about the phase of the system. In presence of a phase transition the quantum trajectory jumps between possible choices of the degenerate steady state. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "qutip.about()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/.ipynb_checkpoints/sqd-run-checkpoint.ipynb b/.ipynb_checkpoints/sqd-run-checkpoint.ipynb new file mode 100644 index 0000000..4224861 --- /dev/null +++ b/.ipynb_checkpoints/sqd-run-checkpoint.ipynb @@ -0,0 +1,851 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Info: Nathan Shammah, RIKEN, nathan.shammah@gmail.com\n", + "\n", + "# Open Quantum Dynamics with QuTiP\n", + " \n", + " \n", + " We use QuTiP's solvers to study the open dynamics of a quantum system evolving in time. \n", + " \n", + " \n", + " - #### Lindblad Master Equation\n", + " \n", + " - #### Lindblad Master Equation: Time evolution\n", + " \n", + " - #### Lindblad Master Equation: steady-state solution\n", + " \n", + "- #### Stochastic Dynamics: Quantum Trajectories with Monte Carlo" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from qutip import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define the operators and Hamiltonian\n", + "\n", + "We consider the spin-boson system, which is a prototypical model of light-matter interaction in cavity quantum electrodynamics (cQED): a single two-level system coupled to a single mode of the photonic field. Its Hamiltonian is described by\n", + "\n", + "\\begin{eqnarray}\n", + "H &=& \\omega_c a^\\dagger a + \\frac{\\omega_0}{2}\\sigma_z\n", + "+\\frac{g}{2}\\sigma_x\\left(a+a^\\dagger\\right)+\\frac{\\omega_x}{2}\\sigma_x,\n", + "\\end{eqnarray}\n", + "\n", + "where we added also the possibility of the system of a classical drive onto the system at a frequency $\\omega_x$." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# spins\n", + "sx_reduced = sigmax()\n", + "sy_reduced = sigmay()\n", + "sz_reduced = sigmaz()\n", + "sp_reduced = sigmap()\n", + "sm_reduced = sigmam()\n", + "\n", + "# photons\n", + "nph = 4\n", + "a_reduced = destroy(nph)\n", + "\n", + "# tensor space\n", + "sz = tensor(sz_reduced,qeye(nph))\n", + "sx = tensor(sx_reduced,qeye(nph))\n", + "sm = tensor(sm_reduced,qeye(nph))\n", + "sp = sm.dag()\n", + "a = tensor(qeye(2), a_reduced)\n", + "\n", + "# hamiltonians\n", + "wc = 1\n", + "w0 = 0.5*wc\n", + "g = 0.1*w0\n", + "wx = 0.2*w0\n", + "Hcav = wc*a.dag()*a\n", + "Hspin = w0*sz #+ wx*sx\n", + "Hint = g*sx*(a+a.dag())\n", + "HintCheck = g*tensor(sx_reduced,a_reduced+a_reduced.dag())\n", + "H = Hcav + Hspin + Hint\n", + "np.testing.assert_(Hint == HintCheck)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define the initial state" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The initial state of the system is given by \n", + "\\begin{eqnarray}\n", + "\\rho&=&\\rho_\\text{spin}\\otimes\\rho_\\text{phot}\n", + "\\end{eqnarray}\n", + "and in the case of a initially pure state, \n", + "\\begin{eqnarray}\n", + "\\rho&=&|\\psi\\rangle_\\text{spin}\\otimes|\\psi\\rangle_\\text{phot}\n", + "\\end{eqnarray}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# initial state\n", + "psi0_spin = basis(2,0)\n", + "psi0_phot = basis(nph,nph-int(nph/2))\n", + "psi0 = tensor(psi0_spin,psi0_phot)\n", + "rho0 = ket2dm(psi0)\n", + "\n", + "# times at which to calculate the variables\n", + "tlist = np.linspace(0,50,2000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Lindblad master equation: $\\texttt{mesolve}$\n", + "\n", + "We now consider the time evolution of the open quantum system, in which $\\rho$ is dissipatively coupled to a spin and photonic bath,\n", + "\n", + "\\begin{eqnarray}\n", + "\\frac{d}{dt}\\rho =-i\\lbrack H,\\rho\\rbrack+\\gamma\\mathcal{D}_{[\\sigma_-]}\\rho+\\kappa\\mathcal{D}_{[a]}\\rho.\n", + "\\end{eqnarray}" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10.0%. Run time: 0.02s. Est. time left: 00:00:00:00\n", + "20.0%. Run time: 0.04s. Est. time left: 00:00:00:00\n", + "30.0%. Run time: 0.06s. Est. time left: 00:00:00:00\n", + "40.0%. Run time: 0.08s. Est. time left: 00:00:00:00\n", + "50.0%. Run time: 0.10s. Est. time left: 00:00:00:00\n", + "60.0%. Run time: 0.12s. Est. time left: 00:00:00:00\n", + "70.0%. Run time: 0.14s. Est. time left: 00:00:00:00\n", + "80.0%. Run time: 0.16s. Est. time left: 00:00:00:00\n", + "90.0%. Run time: 0.18s. Est. time left: 00:00:00:00\n", + "Total run time: 0.20s\n" + ] + } + ], + "source": [ + "kappa = 0.3\n", + "gamma = 0.3\n", + "\n", + "my_options = Options(average_states = True, store_states = True)\n", + "results = mesolve(H, psi0, tlist, \n", + " c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], \n", + " options=my_options, progress_bar=True)\n", + "\n", + "# store time evoluted variables\n", + "nph_t = results.expect[0]\n", + "sz_t = results.expect[1]\n", + "rho_t = results.states" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fs=20\n", + "plt.figure(figsize=(14,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.suptitle(\"Time evolution for spin and photonic excitations of a driven cavity with single two level system, with dissipation\")\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Steady state solver: $\\texttt{steadystate}$" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "rhoss = steadystate(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "nph_ss= expect(a.dag()*a,rhoss)\n", + "sz_ss= expect(sz,rhoss)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAD8CAYAAABaQGkdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAACldJREFUeJzt3d+LXPUdxvHncZMY409obbFJaLRIQAo1EgISEBr7I1bRXvQiAYXawl4pSguives/IPaiCBK1gqnSRgURq5WqWKFN3cS0NdkoabBkG22UIv7CjUmeXuwEtnFlz2bOmZn99P2CxZ3dw8xnCG/PmbMz5+skAlDTGcMeAEB3CBwojMCBwggcKIzAgcIIHCiMwIHCCBwojMCBwpZ0cafLlqzIWUvP7+KuPyOfTA/kcYBR8ok+0tFMe77tOgn8rKXn68qv/aiLu/6M4/veGMjjoEVnjA3usU4cH9xjDdDO/KHRdhyiA4UROFAYgQOFEThQGIEDhRE4UBiBA4UROFBYo8Btb7b9uu0Dtu/seigA7Zg3cNtjkn4p6RpJl0naavuyrgcD0L8me/ANkg4kOZjkqKRHJd3Q7VgA2tAk8JWSDs26PdX7GYAR1yTwuT6x8pmLqdsetz1he+Lo8Y/7nwxA35oEPiVp9azbqyQdPnWjJPclWZ9k/bKxFW3NB6APTQJ/RdKlti+2vUzSFklPdjsWgDbM+3nwJMds3yLpWUljkh5IsrfzyQD0rdEFH5I8LenpjmcB0DLeyQYURuBAYQQOFEbgQGEEDhRG4EBhBA4URuBAYZ2sbJJPpllxZJHxmWcO7LEyzXJTg8IeHCiMwIHCCBwojMCBwggcKIzAgcIIHCiMwIHCCBworMnKJg/YPmL7tUEMBKA9Tfbgv5K0ueM5AHRg3sCTvCTpPwOYBUDLeA0OFNbap8lsj0sal6TlYmUTYBS0tgefvXTRUg3uo4cAPh+H6EBhTf5M9oikP0laa3vK9o+7HwtAG5qsTbZ1EIMAaB+H6EBhBA4URuBAYQQOFEbgQGEEDhRG4EBhBA4U1snSRVh8WE6oJvbgQGEEDhRG4EBhBA4URuBAYQQOFEbgQGEEDhRG4EBhBA4U1uSii6ttv2B70vZe27cNYjAA/WvyXvRjkn6aZLftcyXtsv1ckn0dzwagT03WJnsrye7e9x9ImpS0suvBAPRvQZ8ms71G0jpJO+f4HUsXASOm8Uk22+dIekzS7UneP/X3LF0EjJ5Ggdteqpm4tyd5vNuRALSlyVl0S7pf0mSSu7sfCUBbmuzBN0q6SdIm23t6X9/reC4ALWiyNtnLkjyAWQC0jHeyAYUROFAYgQOFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQGIEDhRE4UFiTiy4ut/0X23/tLV3080EMBqB/TRY+mJa0KcmHvcsnv2z7d0n+3PFsAPrU5KKLkfRh7+bS3le6HApAO5oufDBme4+kI5KeSzLn0kW2J2xPfKrptucEcBoaBZ7keJLLJa2StMH21+fYhqWLgBGzoLPoSd6T9KKkzZ1MA6BVTc6iX2j7gt73Z0n6lqT9XQ8GoH9NzqJfJOkh22Oa+R/Cb5I81e1YANrQ5Cz63zSzJjiARYZ3sgGFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQWJN3so00nzm4D7Zkuu6n5J49vGdgj/Xdr1w+sMf6f8ceHCiMwIHCCBwojMCBwggcKIzAgcIIHCiMwIHCCBworHHgvWujv2qb67EBi8RC9uC3SZrsahAA7Wu6sskqSddK2tbtOADa1HQPfo+kOySd6HAWAC1rsvDBdZKOJNk1z3asTQaMmCZ78I2Srrf9pqRHJW2y/fCpG7E2GTB65g08yV1JViVZI2mLpOeT3Nj5ZAD6xt/BgcIWdEWXJC9qZnVRAIsAe3CgMAIHCiNwoDACBwojcKAwAgcKI3CgMAIHCutu6aIzxjq769kqLyc0SCwnVBN7cKAwAgcKI3CgMAIHCiNwoDACBwojcKAwAgcKI3CgsEbvZOtdUfUDScclHUuyvsuhALRjIW9V/WaSdzubBEDrOEQHCmsaeCT93vYu2+NdDgSgPU0P0TcmOWz7S5Kes70/yUuzN+iFPy5Jy7Wi5TEBnI5Ge/Akh3v/PSLpCUkb5tiGpYuAEdNk8cGzbZ978ntJ35H0WteDAehfk0P0L0t6wvbJ7X+d5JlOpwLQinkDT3JQ0jcGMAuAlvFnMqAwAgcKI3CgMAIHCiNwoDACBwojcKAwAgcK627pohPHO7trAM2wBwcKI3CgMAIHCiNwoDACBwojcKAwAgcKI3CgMAIHCmsUuO0LbO+wvd/2pO0rux4MQP+avlX1F5KeSfID28skLnwOLAbzBm77PElXSfqhJCU5Kulot2MBaEOTQ/RLJL0j6UHbr9re1rs+OoAR1yTwJZKukHRvknWSPpJ056kb2R63PWF74lNNtzwmgNPRJPApSVNJdvZu79BM8P+DpYuA0TNv4EnelnTI9trej66WtK/TqQC0oulZ9Fslbe+dQT8o6ebuRgLQlkaBJ9kjaX3HswBoGe9kAwojcKAwAgcKI3CgMAIHCiNwoDACBwojcKAwAgcKI3CgMAIHCiNwoDACBwojcKAwAgcKI3CgMAIHCiNwoDACBwqbN3Dba23vmfX1vu3bBzEcgP7Me9HFJK9LulySbI9J+pekJzqeC0ALFnqIfrWkfyT5ZxfDAGhX0+uin7RF0iNz/cL2uKRxSVrO4qPASGi8B+8tenC9pN/O9XuWLgJGz0IO0a+RtDvJv7saBkC7FhL4Vn3O4TmA0dQocNsrJH1b0uPdjgOgTU3XJvtY0hc6ngVAy3gnG1AYgQOFEThQGIEDhRE4UBiBA4UROFAYgQOFOUn7d2q/I2mhHyn9oqR3Wx9mNFR9bjyv4flqkgvn26iTwE+H7Ykk64c9RxeqPjee1+jjEB0ojMCBwkYp8PuGPUCHqj43nteIG5nX4ADaN0p7cAAtG4nAbW+2/brtA7bvHPY8bbC92vYLtidt77V927BnapPtMduv2n5q2LO0yfYFtnfY3t/7t7ty2DP1Y+iH6L1rrb+hmSvGTEl6RdLWJPuGOlifbF8k6aIku22fK2mXpO8v9ud1ku2fSFov6bwk1w17nrbYfkjSH5Ns611odEWS94Y91+kahT34BkkHkhxMclTSo5JuGPJMfUvyVpLdve8/kDQpaeVwp2qH7VWSrpW0bdiztMn2eZKuknS/JCU5upjjlkYj8JWSDs26PaUiIZxke42kdZJ2DneS1twj6Q5JJ4Y9SMsukfSOpAd7Lz+22T572EP1YxQC9xw/K3Nq3/Y5kh6TdHuS94c9T79sXyfpSJJdw56lA0skXSHp3iTrJH0kaVGfExqFwKckrZ51e5Wkw0OapVW2l2om7u1JqlyRdqOk622/qZmXU5tsPzzckVozJWkqyckjrR2aCX7RGoXAX5F0qe2Leyc1tkh6csgz9c22NfNabjLJ3cOepy1J7kqyKskazfxbPZ/kxiGP1Yokb0s6ZHtt70dXS1rUJ0UXujZZ65Ics32LpGcljUl6IMneIY/Vho2SbpL0d9t7ej/7WZKnhzgT5nerpO29nc1BSTcPeZ6+DP3PZAC6MwqH6AA6QuBAYQQOFEbgQGEEDhRG4EBhBA4URuBAYf8F2jJ8yK7fBPoAAAAASUVORK5CYII=\n", + "text/plain": [ + "
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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.imshow(abs(rhoss.full()))\n", + "plt.show()\n", + "plt.close()\n", + "plt.figure()\n", + "plt.subplot(121)\n", + "plt.imshow(abs(ptrace(rhoss,0).full()))\n", + "plt.xlabel(\"atom\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.imshow(abs(ptrace(rhoss,1).full()))\n", + "plt.xlabel(\"photon\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Liouvillian structure\n", + "\n", + "We can derive thermodynamical properties of the out-of-equilibrium system by studying the spectrum of the Liouvillian." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "L = liouvillian(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "\n", + "# represent the Liouvillian\n", + "plt.figure(figsize=(14,6))\n", + "plt.subplot(121)\n", + "plt.imshow(np.real(L.full()))\n", + "plt.title(\"Real values of the Liouvillian\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.imshow(np.imag(L.full()))\n", + "plt.title(\"Imaginary values of the Liouvillian\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Liouvillian Spectrum, $\\texttt{eigenstates}$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "L = liouvillian(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "\n", + "# Plot the Liouvillian spectrum in the complex plane\n", + "eigenvalues_L, eigenvectors_L = L.eigenstates()\n", + "\n", + "\n", + "real_eigenvalues = np.real(eigenvalues_L)\n", + "imag_eigenvalues = np.imag(eigenvalues_L)\n", + "\n", + "plt.figure(figsize=(10,10))\n", + "plt.plot(real_eigenvalues, imag_eigenvalues,\"o\")\n", + "plt.title(\"Real values of the Liouvillian\",fontsize=fs)\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us decipher the spectrum of the Liouvillian:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10,10))\n", + "plt.plot(real_eigenvalues, imag_eigenvalues,\"o\")\n", + "plt.title(\"Real values of the Liouvillian\")\n", + "plt.axvline(x=0,color=\"red\")\n", + "plt.axhline(y=0,color=\"black\",linestyle=\"dashed\")\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We find symmetries in the Liouvillian spectrum with respect to the real and imaginary axis." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(6,6))\n", + "plt.plot(real_eigenvalues[-1],imag_eigenvalues[-1],\"o\",markersize=20,label=\"$\\lambda_0$\")\n", + "plt.plot(real_eigenvalues[-2],imag_eigenvalues[-2],\"*\",markersize=20,label=\"$\\lambda_1$\")\n", + "plt.plot(real_eigenvalues[-3],imag_eigenvalues[-3],\"s\",markersize=20,label=\"$\\lambda_2$\")\n", + "plt.xlim([-2,2])\n", + "plt.ylim([-2,2])\n", + "plt.legend(fontsize=20)\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Photon counting statistics: $\\texttt{mcsolve}$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10.0%. Run time: 4.65s. Est. time left: 00:00:00:41\n", + "20.0%. Run time: 9.36s. Est. time left: 00:00:00:37\n", + "30.0%. Run time: 14.29s. Est. time left: 00:00:00:33\n", + "40.0%. Run time: 19.73s. Est. time left: 00:00:00:29\n", + "50.0%. Run time: 27.13s. Est. time left: 00:00:00:27\n", + "60.0%. Run time: 32.55s. Est. time left: 00:00:00:21\n", + "70.0%. Run time: 37.79s. Est. time left: 00:00:00:16\n", + "80.0%. Run time: 42.91s. Est. time left: 00:00:00:10\n", + "90.0%. Run time: 48.88s. Est. time left: 00:00:00:05\n", + "100.0%. Run time: 54.61s. Est. time left: 00:00:00:00\n", + "Total run time: 54.67s\n" + ] + } + ], + "source": [ + "# set dynamics options\n", + "my_options = Options(average_states = False, store_states = True)\n", + "# solve dynamics\n", + "results_mc = mcsolve(H, psi0, tlist, \n", + " c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], \n", + " options=my_options, progress_bar=True)\n", + "\n", + "# store time evoluted variables\n", + "nph_mc_t = results_mc.expect[0]\n", + "sz_mc_t = results_mc.expect[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The default options for $\\texttt{mcsolve}$ imply solving the dynamics for 500 trajectories. \n", + "\n", + "This option can be controlled by setting a different number in $\\texttt{Options(ntraj=500})$." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "500" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rho_mc_t = results_mc.states\n", + "len(rho_mc_t)\n", + "#help(expect)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "sz_stoch_t = []\n", + "nph_stoch_t = []\n", + "for i in range(len(rho_mc_t)):\n", + " sz_stoch_t.append(expect(sz,rho_mc_t[i]))\n", + " nph_stoch_t.append(expect(a.dag()*a,rho_mc_t[i]))" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(14,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t, label=\"me solve\")\n", + "plt.plot(tlist, sz_mc_t, label=\"mc solve (500 trajectories)\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5, label=\"me solve\")\n", + "plt.plot(tlist, nph_mc_t/nph/0.5, label=\"mc solve (500 trajectories)\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.show()\n", + "plt.close()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Lindblad master equation as the limit of the stochastic evolution: $\\texttt{mesolve}$ and $\\texttt{mcsolve}$" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10.0%. Run time: 0.36s. Est. time left: 00:00:00:03\n", + "20.0%. Run time: 0.53s. Est. time left: 00:00:00:02\n", + "30.0%. Run time: 0.74s. Est. time left: 00:00:00:01\n", + "40.0%. Run time: 0.90s. Est. time left: 00:00:00:01\n", + "50.0%. Run time: 1.09s. Est. time left: 00:00:00:01\n", + "60.0%. Run time: 1.26s. Est. time left: 00:00:00:00\n", + "70.0%. Run time: 1.45s. Est. time left: 00:00:00:00\n", + "80.0%. Run time: 1.63s. Est. time left: 00:00:00:00\n", + "90.0%. Run time: 1.82s. Est. time left: 00:00:00:00\n", + "100.0%. Run time: 2.00s. Est. time left: 00:00:00:00\n", + "Total run time: 2.12s\n", + "10.0%. Run time: 0.40s. Est. time left: 00:00:00:03\n", + "20.0%. Run time: 0.76s. Est. time left: 00:00:00:03\n", + "30.0%. Run time: 1.14s. Est. time left: 00:00:00:02\n", + "40.0%. Run time: 1.52s. Est. time left: 00:00:00:02\n", + "50.0%. Run time: 1.96s. Est. time left: 00:00:00:01\n", + "60.0%. Run time: 2.33s. Est. time left: 00:00:00:01\n", + "70.0%. Run time: 2.72s. Est. time left: 00:00:00:01\n", + "80.0%. Run time: 3.11s. Est. time left: 00:00:00:00\n", + "90.0%. Run time: 3.49s. Est. time left: 00:00:00:00\n", + "100.0%. Run time: 3.99s. Est. time left: 00:00:00:00\n", + "Total run time: 4.05s\n", + "10.0%. Run time: 1.32s. Est. time left: 00:00:00:11\n", + "20.0%. Run time: 2.80s. Est. time left: 00:00:00:11\n", + "30.0%. Run time: 3.91s. Est. time left: 00:00:00:09\n", + "40.0%. Run time: 4.96s. Est. time left: 00:00:00:07\n", + "50.0%. Run time: 5.83s. Est. time left: 00:00:00:05\n", + "60.0%. Run time: 6.61s. Est. time left: 00:00:00:04\n", + "70.0%. Run time: 7.64s. Est. time left: 00:00:00:03\n", + "80.0%. Run time: 8.43s. Est. time left: 00:00:00:02\n", + "90.0%. Run time: 9.18s. Est. time left: 00:00:00:01\n", + "100.0%. Run time: 9.92s. Est. time left: 00:00:00:00\n", + "Total run time: 10.04s\n" + ] + } + ], + "source": [ + "# 50 trajectories\n", + "my_options50 = Options(ntraj=50)\n", + "results_mc50 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options50, progress_bar=True)\n", + "nph_mc_t50 = results_mc50.expect[0]\n", + "sz_mc_t50 = results_mc50.expect[1]\n", + "# 100 trajectories\n", + "my_options100 = Options(ntraj=100)\n", + "results_mc100 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options100, progress_bar=True)\n", + "nph_mc_t100 = results_mc100.expect[0]\n", + "sz_mc_t100 = results_mc100.expect[1]\n", + "# 200 trajectories\n", + "my_options200 = Options(ntraj=200)\n", + "results_mc200 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options200, progress_bar=True)\n", + "nph_mc_t200 = results_mc200.expect[0]\n", + "sz_mc_t200 = results_mc200.expect[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16,6))\n", + "# spin excitation\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_mc_t50, label=\"mc solve (50 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t100, label=\"mc solve (100 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t200, label=\"mc solve (200 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t, label=\"mc solve (500 trajectories)\")\n", + "plt.plot(tlist, sz_t, label=\"me solve\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "# photonic excitation\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_mc_t50/nph/0.5, label=\"mc solve (50 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t100/nph/0.5, label=\"mc solve (100 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t200/nph/0.5, label=\"mc solve (200 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t/nph/0.5, label=\"mc solve (500 trajectories)\")\n", + "plt.plot(tlist, nph_t/nph/0.5, label=\"me solve\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.show()\n", + "plt.close()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We observe that progressively, as the number of trajectories is increased, the value given by the average over the trajectories gets closer to the master equation value." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(12,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t)\n", + "plt.plot(tlist, sz_mc_t)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle s_z \\rangle$\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5)\n", + "plt.plot(tlist, nph_mc_t/nph/0.5)\n", + "\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle n_{ph} \\rangle$\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting single quantum trajectories\n", + "\n", + "By setting:\n", + "my_options = Options(average_states = False, store_states = True)\n", + "\n", + "we can inspect single quantum trajectories and their behaviour." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(14,5))\n", + "plt.subplot(121)\n", + "for i in range(len(sz_stoch_t)):\n", + " plt.plot(tlist, sz_stoch_t[i],alpha=0.1)\n", + "\n", + "plt.plot(tlist, sz_t,\"b\",linewidth=3)\n", + "plt.plot(tlist, sz_mc_t,\"y\",linewidth=2)\n", + "plt.plot(tlist, sz_stoch_t[4]/nph/0.5,\"g\",linewidth=5)\n", + "plt.plot(tlist, sz_stoch_t[6]/nph/0.5,\"r\",linewidth=5)\n", + "plt.subplot(122)\n", + "for i in range(len(sz_stoch_t)):\n", + " plt.plot(tlist, nph_stoch_t[i]/nph/0.5,alpha=0.1)\n", + "plt.plot(tlist, nph_t/nph/0.5,\"b\",linewidth=3)\n", + "plt.plot(tlist, nph_mc_t/nph/0.5,\"y\",linewidth=2)\n", + "plt.plot(tlist, nph_stoch_t[4]/nph/0.5,\"g\",linewidth=5)\n", + "plt.plot(tlist, nph_stoch_t[6]/nph/0.5,\"r\",linewidth=5)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle X \\rangle$\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We obseverve that the single trajectories can provide information about the phase of the system. In presence of a phase transition the quantum trajectory jumps between possible choices of the degenerate steady state. " + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "QuTiP: Quantum Toolbox in Python\n", + "Copyright (c) 2011 and later.\n", + "A. J. Pitchford, P. D. Nation, R. J. Johansson, A. Grimsmo, and C. Granade\n", + "\n", + "QuTiP Version: 4.3.1\n", + "Numpy Version: 1.15.4\n", + "Scipy Version: 1.2.1\n", + "Cython Version: 0.29.8\n", + "Matplotlib Version: 3.0.3\n", + "Python Version: 3.7.3\n", + "Number of CPUs: 2\n", + "BLAS Info: OPENBLAS\n", + "OPENMP Installed: False\n", + "INTEL MKL Ext: False\n", + "Platform Info: Darwin (x86_64)\n", + "Installation path: /miniconda3/lib/python3.7/site-packages/qutip\n", + "==============================================================================\n", + "Please cite QuTiP in your publication.\n", + "==============================================================================\n", + "For your convenience a bibtex file can be easily generated using `qutip.cite()`\n" + ] + } + ], + "source": [ + "qutip.about()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/1.Introduction to QuTiP.ipynb b/1.Introduction to QuTiP.ipynb new file mode 100644 index 0000000..2293a31 --- /dev/null +++ b/1.Introduction to QuTiP.ipynb @@ -0,0 +1,683 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction to QuTiP\n", + "Contact: Nathan Shammah nathan.shammah@gmail.com\n", + "\n", + "You can find this notebook at https://github.com/nathanshammah/interactive-notebooks\n", + "\n", + "**Run this notebook live** at https://mybinder.org/v2/gh/nathanshammah/interactive-notebooks/binder\n", + "\n", + "This notebook has been developed for the interactive lecture on [QuTiP](qutip.org) for the [iTHEMS](https://ithems.riken.jp/en/events/quantum-physics-and-science-with-open-source-software-qutip-the-quantum-toolbox-in-python) Quantum Computing and Information (QCoIn) working group." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from qutip import *" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "qutip.about()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum Objects\n", + "\n", + "### Operators and kets" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Let's define a quantum object. We can start from a simple \n", + "# bosonic destruction operator\n", + "n_max = 2\n", + "a = destroy(n_max)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# in QuTiP, all number (Fock) states are defined on the \"basis\". \n", + "psi0 = basis(n_max)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "psi0 # it's a ket!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a*psi0 # destroing the ground state gives the vacuum" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a.dag()*psi0" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "psi0 = basis(n_max)\n", + "for n in range(1,n_max):\n", + " print(\"n = \",n)\n", + " psi = a.dag()*psi0/np.sqrt(n)\n", + " print(psi)\n", + " psi0 = psi\n", + "psi0 = basis(n_max)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Density matrix" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "rho0 = psi0*psi0.dag()\n", + "rho0" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "rho1 = fock(n_max,1)*fock(n_max,1).dag()\n", + "rho1" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mixed = (rho0 + rho1)/2\n", + "mixed" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# let's define the Schrodinger cat state\n", + "cat = fock(n_max,0)+fock(n_max,1)\n", + "cat = cat \n", + "cat_rho = ket2dm(cat)/2\n", + "cat_rho" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# trace Tr[rho]\n", + "print(cat_rho.tr())\n", + "print(mixed.tr())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# purity Tr[rho*rho]\n", + "print((cat_rho*cat_rho).tr())\n", + "print((mixed*mixed).tr())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hamiltonian" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# We can now build a Hamiltonian, \n", + "# that of the Quantum Harmonic Oscillator \n", + "# exploring its features with QuTiP\n", + "n_max = 6\n", + "a = destroy(n_max)\n", + "\n", + "H = a.dag()*a" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "H" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "E_n , Psi_n = H.eigenstates()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "E_n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Psi_n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "g = .6\n", + "H_driven = a.dag()*a + g*(a + a.dag())\n", + "En_driven , Psin_driven = H_driven.eigenstates()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure()\n", + "plt.plot(E_n,\"o-\",markersize = 10, label=\"QHO\")\n", + "plt.plot(En_driven,\"s--\",markersize = 10, label=\"Driven QHO\")\n", + "\n", + "plt.ylabel(\"energy\")\n", + "plt.xlabel(\"eigenvalue\")\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Open Quantum System: Lindblad Master Equation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\\begin{eqnarray}\n", + "\\dot{\\rho}&=&-i\\lbrack H, \\rho\\rbrack +\\kappa\\left(a\\rho a^\\dagger - a^\\dagger a\\rho- \\rho a^\\dagger a\\right)\\\\\n", + "\\partial_t{\\rho}&=&-i\\lbrack H, \\rho\\rbrack +\\kappa\\mathcal{D}_{[a]}(\\rho)\n", + "\\end{eqnarray}\n", + "\n", + "* Non-unitary dynamics: Non-Hermitian matrix, $\\partial_t{\\rho}=\\mathcal{L}\\rho$\n", + "* Contractive map \n", + "* Linear map" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "rho0 = ket2dm(basis(n_max,n_max-1))\n", + "t = np.linspace(0,30,300)\n", + "kappa = 0.1\n", + "results = mesolve(H,rho0,t,[kappa*a])\n", + "rho_t = results.states\n", + "rho_t[0]\n", + "\n", + "rho_t[-1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us consider a driven, lossy photonic cavity " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results = mesolve(H_driven,rho0,t,c_ops=[kappa*a], e_ops=[a,a.dag()*a])\n", + "at = results.expect[0]\n", + "nt = results.expect[1]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure()\n", + "plt.plot(t,nt,\"-\",markersize = 10, label=\"$\\\\langle a^\\dagger a \\\\rangle$\")\n", + "plt.ylabel(\"photons in cavity\")\n", + "plt.xlabel(\"time\")\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Cavity QED: Qubit in a cavity" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "rho0qubit = ket2dm(basis(2,1))\n", + "rho0_tot = tensor(rho0,rho0qubit)\n", + "Om = 0.5\n", + "Hint_tot = Om*tensor(a+a.dag(),sigmax())\n", + "H0_tot = tensor(H,qeye(2))+tensor(qeye(n_max),sigmaz())\n", + "H_tot=H0_tot+Hint_tot\n", + "t = np.linspace(0,50,300)\n", + "kappa = 0.1\n", + "a_tot = tensor(a,qeye(2))\n", + "sz_tot = tensor(qeye(n_max),sigmaz())\n", + "sm_tot = tensor(qeye(n_max),sigmam())\n", + "results_tot = mesolve(H_tot,rho0_tot,t,\n", + " c_ops=[kappa*a_tot, kappa*sm_tot], \n", + " e_ops= [a_tot.dag()*a_tot,sz_tot])\n", + "nphot_tot_t = results_tot.expect[0]\n", + "sz_tot_t = results_tot.expect[1]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure()\n", + "plt.plot(t,sz_tot_t,\"-\",markersize = 10, \n", + " label=\"$\\\\langle \\sigma_z \\\\rangle (t)$\")\n", + "plt.plot(t,nphot_tot_t,\"--\",markersize = 10, \n", + " label=\"$\\\\langle a^\\dagger a \\\\rangle (t)$\")\n", + "plt.ylabel(\"System excitation\")\n", + "plt.xlabel(\"time\")\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Bloch Sphere\n", + "\n", + "We can visualize a state on the Bloch sphere. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "b = Bloch()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "b.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "b2 = Bloch()\n", + "vec = [0,1,0]\n", + "b2.add_vectors(vec)\n", + "b2.render()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x = (basis(2,0)+(1+0j)*basis(2,1)).unit() \n", + "y = (basis(2,0)+(0+1j)*basis(2,1)).unit()\n", + "z = (basis(2,0)+(0+0j)*basis(2,1)).unit() \n", + "b3 = Bloch() \n", + "b3.add_states([x,y,z])\n", + "b3.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Wigner Function\n", + "\n", + "You can find a Gallery of Wigner functions at qutip.org/tutorials and at R.J. Johansson's http://github.com/jrjohansson/qutip-lectures" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_wigner_2d_3d(psi):\n", + " #fig, axes = plt.subplots(1, 2, subplot_kw={'projection': '3d'}, figsize=(12, 6))\n", + " fig = plt.figure(figsize=(17, 8))\n", + " \n", + " ax = fig.add_subplot(1, 2, 1)\n", + " plot_wigner(psi, fig=fig, ax=ax, alpha_max=6);\n", + "\n", + " ax = fig.add_subplot(1, 2, 2, projection='3d')\n", + " plot_wigner(psi, fig=fig, ax=ax, projection='3d', alpha_max=6);\n", + " \n", + " plt.close(fig)\n", + " return fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Coherent state $|\\psi\\rangle=|\\alpha\\rangle$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "N = 30\n", + "psi = coherent(N, 2.0)\n", + "plot_wigner_2d_3d(psi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Schrödinger Cat state $|\\psi\\rangle=\\frac{1}{\\sqrt{2}}(|\\alpha\\rangle+|-\\alpha\\rangle)$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "N = 30\n", + "psi = (coherent(N, -2.0) + coherent(N, 2.0)) / np.sqrt(2)\n", + "plot_wigner_2d_3d(psi)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Squeezed state" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "psi = squeeze(N, 0.5) * basis(N, 0)\n", + "display(plot_wigner_2d_3d(psi))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "psi = (coherent(N, -2.0) + coherent(N, -1j) + coherent(N, 1j) + coherent(N, 2.0)).unit()\n", + "plot_wigner_2d_3d(psi)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "NN = 8\n", + "\n", + "fig, axes = plt.subplots(NN, 1, figsize=(5, 5 * NN), sharex=True, sharey=True) \n", + "for n in range(NN):\n", + " psi = sum([coherent(N, 2*np.exp(2j * np.pi * m / (n + 2))) for m in range(n + 2)]).unit()\n", + " plot_wigner(psi, fig=fig, ax=axes[n])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum Circuits with QuTiP" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "q = QubitCircuit(3, reverse_states=False)\n", + "q.add_gate(\"TOFFOLI\", controls=[0, 2], targets=[1])\n", + "q.add_gate(\"CNOT\", targets=[1], controls=[0])\n", + "display(\"q\",q.png)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "q.add_gate(\"TOFFOLI\", controls=[0, 2], targets=[1])\n", + "display(\"q updated\",q.png)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "q2 = QubitCircuit(3, reverse_states=False)\n", + "q2.add_gate(\"TOFFOLI\", controls=[0, 2], targets=[1])\n", + "q2.add_gate(\"TOFFOLI\", controls=[0, 2], targets=[1])\n", + "display(\"q2\",q2.png)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "U = gate_sequence_product(q.propagators())\n", + "U" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "qutip.about()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References\n", + "[1] J. Robert Johansson, Paul D. Nation, and Franco Nori, QuTiP: An open-source Python framework for the dynamics of open quantum systems, Comp. Phys. Comm. 183, 1760 (2012); QuTiP 2: A Python framework for the dynamics of open quantum systems, Comp. Phys. Comm. . 184, 1234 (2013).\n", + "\n", + "[2] Nathan Shammah and Shahnawaz Ahmed, The rise of open source in quantum physics research, Nature’s Physics Blog “On your Wavelength”, January 9th, 2019, http://blogs.nature.com/onyourwavelength/2019/01/09/the-rise-of-open-source-in-quantum-physics-research/\n", + "\n", + "[3] Nathan Shammah, Neill Lambert, Franco Nori, and Simone De Liberato, Superradiance with local phase-breaking effects, Phys. Rev. A 96, 023863 (2017); Nathan Shammah, Shahnawaz Ahmed, Neill Lambert, Simone De Liberato, and Franco Nori, Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance, Phys. Rev. A 98, 063815 (2018). \n", + "\n", + "[4] Nathan Shammah, A Guide to Building Your Open-Source Science Library, https://github.com/nathanshammah/opensource/blob/master/README.md" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + }, + "nteract": { + "version": "0.14.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/2.Stochastic quantum dynamics.ipynb b/2.Stochastic quantum dynamics.ipynb new file mode 100644 index 0000000..07092dc --- /dev/null +++ b/2.Stochastic quantum dynamics.ipynb @@ -0,0 +1,595 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Info: Nathan Shammah, RIKEN, nathan.shammah@gmail.com\n", + "\n", + "# Open Quantum Dynamics with QuTiP\n", + " \n", + " \n", + " We use QuTiP's solvers to study the open dynamics of a quantum system evolving in time. \n", + " \n", + " \n", + " - #### Lindblad Master Equation\n", + " \n", + " - #### Lindblad Master Equation: Time evolution\n", + " \n", + " - #### Lindblad Master Equation: steady-state solution\n", + " \n", + "- #### Stochastic Dynamics: Quantum Trajectories with Monte Carlo" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from qutip import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define the operators and Hamiltonian\n", + "\n", + "We consider the spin-boson system, which is a prototypical model of light-matter interaction in cavity quantum electrodynamics (cQED): a single two-level system coupled to a single mode of the photonic field. Its Hamiltonian is described by\n", + "\n", + "\\begin{eqnarray}\n", + "H &=& \\omega_c a^\\dagger a + \\frac{\\omega_0}{2}\\sigma_z\n", + "+\\frac{g}{2}\\sigma_x\\left(a+a^\\dagger\\right)+\\frac{\\omega_x}{2}\\sigma_x,\n", + "\\end{eqnarray}\n", + "\n", + "where we added also the possibility of the system of a classical drive onto the system at a frequency $\\omega_x$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# spins\n", + "sx_reduced = sigmax()\n", + "sy_reduced = sigmay()\n", + "sz_reduced = sigmaz()\n", + "sp_reduced = sigmap()\n", + "sm_reduced = sigmam()\n", + "\n", + "# photons\n", + "nph = 4\n", + "a_reduced = destroy(nph)\n", + "\n", + "# tensor space\n", + "sz = tensor(sz_reduced,qeye(nph))\n", + "sx = tensor(sx_reduced,qeye(nph))\n", + "sm = tensor(sm_reduced,qeye(nph))\n", + "sp = sm.dag()\n", + "a = tensor(qeye(2), a_reduced)\n", + "\n", + "# hamiltonians\n", + "wc = 1\n", + "w0 = 0.5*wc\n", + "g = 0.1*w0\n", + "wx = 0.2*w0\n", + "Hcav = wc*a.dag()*a\n", + "Hspin = w0*sz #+ wx*sx\n", + "Hint = g*sx*(a+a.dag())\n", + "HintCheck = g*tensor(sx_reduced,a_reduced+a_reduced.dag())\n", + "H = Hcav + Hspin + Hint\n", + "np.testing.assert_(Hint == HintCheck)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define the initial state" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The initial state of the system is given by \n", + "\\begin{eqnarray}\n", + "\\rho&=&\\rho_\\text{spin}\\otimes\\rho_\\text{phot}\n", + "\\end{eqnarray}\n", + "and in the case of a initially pure state, \n", + "\\begin{eqnarray}\n", + "\\rho&=&|\\psi\\rangle_\\text{spin}\\otimes|\\psi\\rangle_\\text{phot}\n", + "\\end{eqnarray}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# initial state\n", + "psi0_spin = basis(2,0)\n", + "psi0_phot = basis(nph,nph-int(nph/2))\n", + "psi0 = tensor(psi0_spin,psi0_phot)\n", + "rho0 = ket2dm(psi0)\n", + "\n", + "# times at which to calculate the variables\n", + "tlist = np.linspace(0,50,2000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Lindblad master equation: $\\texttt{mesolve}$\n", + "\n", + "We now consider the time evolution of the open quantum system, in which $\\rho$ is dissipatively coupled to a spin and photonic bath,\n", + "\n", + "\\begin{eqnarray}\n", + "\\frac{d}{dt}\\rho =-i\\lbrack H,\\rho\\rbrack+\\gamma\\mathcal{D}_{[\\sigma_-]}\\rho+\\kappa\\mathcal{D}_{[a]}\\rho.\n", + "\\end{eqnarray}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "kappa = 0.3\n", + "gamma = 0.3\n", + "\n", + "my_options = Options(average_states = True, store_states = True)\n", + "results = mesolve(H, psi0, tlist, \n", + " c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], \n", + " options=my_options, progress_bar=True)\n", + "\n", + "# store time evoluted variables\n", + "nph_t = results.expect[0]\n", + "sz_t = results.expect[1]\n", + "rho_t = results.states" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "fs=20\n", + "plt.figure(figsize=(14,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.suptitle(\"Time evolution for spin and photonic excitations of a driven cavity with single two level system, with dissipation\")\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Steady state solver: $\\texttt{steadystate}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "rhoss = steadystate(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "nph_ss= expect(a.dag()*a,rhoss)\n", + "sz_ss= expect(sz,rhoss)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "plt.figure()\n", + "plt.imshow(abs(rhoss.full()))\n", + "plt.show()\n", + "plt.close()\n", + "plt.figure()\n", + "plt.subplot(121)\n", + "plt.imshow(abs(ptrace(rhoss,0).full()))\n", + "plt.xlabel(\"atom\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.imshow(abs(ptrace(rhoss,1).full()))\n", + "plt.xlabel(\"photon\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Liouvillian structure\n", + "\n", + "We can derive thermodynamical properties of the out-of-equilibrium system by studying the spectrum of the Liouvillian." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "L = liouvillian(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "\n", + "# represent the Liouvillian\n", + "plt.figure(figsize=(14,6))\n", + "plt.subplot(121)\n", + "plt.imshow(np.real(L.full()))\n", + "plt.title(\"Real values of the Liouvillian\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.imshow(np.imag(L.full()))\n", + "plt.title(\"Imaginary values of the Liouvillian\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Liouvillian Spectrum, $\\texttt{eigenstates}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "L = liouvillian(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "\n", + "# Plot the Liouvillian spectrum in the complex plane\n", + "eigenvalues_L, eigenvectors_L = L.eigenstates()\n", + "\n", + "\n", + "real_eigenvalues = np.real(eigenvalues_L)\n", + "imag_eigenvalues = np.imag(eigenvalues_L)\n", + "\n", + "plt.figure(figsize=(10,10))\n", + "plt.plot(real_eigenvalues, imag_eigenvalues,\"o\")\n", + "plt.title(\"Real values of the Liouvillian\",fontsize=fs)\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us decipher the spectrum of the Liouvillian:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure(figsize=(10,10))\n", + "plt.plot(real_eigenvalues, imag_eigenvalues,\"o\")\n", + "plt.title(\"Real values of the Liouvillian\")\n", + "plt.axvline(x=0,color=\"red\")\n", + "plt.axhline(y=0,color=\"black\",linestyle=\"dashed\")\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We find symmetries in the Liouvillian spectrum with respect to the real and imaginary axis." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure(figsize=(6,6))\n", + "plt.plot(real_eigenvalues[-1],imag_eigenvalues[-1],\"o\",markersize=20,label=\"$\\lambda_0$\")\n", + "plt.plot(real_eigenvalues[-2],imag_eigenvalues[-2],\"*\",markersize=20,label=\"$\\lambda_1$\")\n", + "plt.plot(real_eigenvalues[-3],imag_eigenvalues[-3],\"s\",markersize=20,label=\"$\\lambda_2$\")\n", + "plt.xlim([-2,2])\n", + "plt.ylim([-2,2])\n", + "plt.legend(fontsize=20)\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Photon counting statistics: $\\texttt{mcsolve}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# set dynamics options\n", + "my_options = Options(average_states = False, store_states = True)\n", + "# solve dynamics\n", + "results_mc = mcsolve(H, psi0, tlist, \n", + " c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], \n", + " options=my_options, progress_bar=True)\n", + "\n", + "# store time evoluted variables\n", + "nph_mc_t = results_mc.expect[0]\n", + "sz_mc_t = results_mc.expect[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The default options for $\\texttt{mcsolve}$ imply solving the dynamics for 500 trajectories. \n", + "\n", + "This option can be controlled by setting a different number in $\\texttt{Options(ntraj=500})$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "rho_mc_t = results_mc.states\n", + "len(rho_mc_t)\n", + "#help(expect)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sz_stoch_t = []\n", + "nph_stoch_t = []\n", + "for i in range(len(rho_mc_t)):\n", + " sz_stoch_t.append(expect(sz,rho_mc_t[i]))\n", + " nph_stoch_t.append(expect(a.dag()*a,rho_mc_t[i]))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure(figsize=(14,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t, label=\"me solve\")\n", + "plt.plot(tlist, sz_mc_t, label=\"mc solve (500 trajectories)\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5, label=\"me solve\")\n", + "plt.plot(tlist, nph_mc_t/nph/0.5, label=\"mc solve (500 trajectories)\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.show()\n", + "plt.close()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Lindblad master equation as the limit of the stochastic evolution: $\\texttt{mesolve}$ and $\\texttt{mcsolve}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# 50 trajectories\n", + "my_options50 = Options(ntraj=50)\n", + "results_mc50 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options50, progress_bar=True)\n", + "nph_mc_t50 = results_mc50.expect[0]\n", + "sz_mc_t50 = results_mc50.expect[1]\n", + "# 100 trajectories\n", + "my_options100 = Options(ntraj=100)\n", + "results_mc100 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options100, progress_bar=True)\n", + "nph_mc_t100 = results_mc100.expect[0]\n", + "sz_mc_t100 = results_mc100.expect[1]\n", + "# 200 trajectories\n", + "my_options200 = Options(ntraj=200)\n", + "results_mc200 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options200, progress_bar=True)\n", + "nph_mc_t200 = results_mc200.expect[0]\n", + "sz_mc_t200 = results_mc200.expect[1]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure(figsize=(16,6))\n", + "# spin excitation\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_mc_t50, label=\"mc solve (50 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t100, label=\"mc solve (100 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t200, label=\"mc solve (200 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t, label=\"mc solve (500 trajectories)\")\n", + "plt.plot(tlist, sz_t, label=\"me solve\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "# photonic excitation\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_mc_t50/nph/0.5, label=\"mc solve (50 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t100/nph/0.5, label=\"mc solve (100 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t200/nph/0.5, label=\"mc solve (200 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t/nph/0.5, label=\"mc solve (500 trajectories)\")\n", + "plt.plot(tlist, nph_t/nph/0.5, label=\"me solve\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.show()\n", + "plt.close()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We observe that progressively, as the number of trajectories is increased, the value given by the average over the trajectories gets closer to the master equation value." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "plt.figure(figsize=(12,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t)\n", + "plt.plot(tlist, sz_mc_t)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle s_z \\rangle$\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5)\n", + "plt.plot(tlist, nph_mc_t/nph/0.5)\n", + "\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle n_{ph} \\rangle$\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting single quantum trajectories\n", + "\n", + "By setting:\n", + "my_options = Options(average_states = False, store_states = True)\n", + "\n", + "we can inspect single quantum trajectories and their behaviour." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure(figsize=(14,5))\n", + "plt.subplot(121)\n", + "for i in range(len(sz_stoch_t)):\n", + " plt.plot(tlist, sz_stoch_t[i],alpha=0.1)\n", + "\n", + "plt.plot(tlist, sz_t,\"b\",linewidth=3)\n", + "plt.plot(tlist, sz_mc_t,\"y\",linewidth=2)\n", + "plt.plot(tlist, sz_stoch_t[4]/nph/0.5,\"g\",linewidth=5)\n", + "plt.plot(tlist, sz_stoch_t[6]/nph/0.5,\"r\",linewidth=5)\n", + "plt.subplot(122)\n", + "for i in range(len(sz_stoch_t)):\n", + " plt.plot(tlist, nph_stoch_t[i]/nph/0.5,alpha=0.1)\n", + "plt.plot(tlist, nph_t/nph/0.5,\"b\",linewidth=3)\n", + "plt.plot(tlist, nph_mc_t/nph/0.5,\"y\",linewidth=2)\n", + "plt.plot(tlist, nph_stoch_t[4]/nph/0.5,\"g\",linewidth=5)\n", + "plt.plot(tlist, nph_stoch_t[6]/nph/0.5,\"r\",linewidth=5)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle X \\rangle$\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We obseverve that the single trajectories can provide information about the phase of the system. In presence of a phase transition the quantum trajectory jumps between possible choices of the degenerate steady state. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "qutip.about()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Introduction to QuTiP.ipynb b/Introduction to QuTiP.ipynb deleted file mode 100644 index a92acc7..0000000 --- a/Introduction to QuTiP.ipynb +++ /dev/null @@ -1,738 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Introduction to QuTiP\n", - "Contact: Nathan Shammah nathan.shammah@gmail.com" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from qutip import *" - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "QuTiP: Quantum Toolbox in Python\n", - "Copyright (c) 2011 and later.\n", - "A. J. Pitchford, P. D. Nation, R. J. Johansson, A. Grimsmo, and C. Granade\n", - "\n", - "QuTiP Version: 4.3.1\n", - "Numpy Version: 1.15.4\n", - "Scipy Version: 1.2.1\n", - "Cython Version: 0.29.8\n", - "Matplotlib Version: 3.1.0\n", - "Python Version: 3.7.3\n", - "Number of CPUs: 2\n", - "BLAS Info: OPENBLAS\n", - "OPENMP Installed: False\n", - "INTEL MKL Ext: False\n", - "Platform Info: Darwin (x86_64)\n", - "Installation path: /miniconda3/lib/python3.7/site-packages/qutip\n", - "==============================================================================\n", - "Please cite QuTiP in your publication.\n", - "==============================================================================\n", - "For your convenience a bibtex file can be easily generated using `qutip.cite()`\n" - ] - } - ], - "source": [ - "qutip.about()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Quantum Objects\n", - "\n", - "### Operators and kets" - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "metadata": {}, - "outputs": [], - "source": [ - "# Let's define a quantum object. We can start from a simple \n", - "# bosonic destruction operator\n", - "n_max = 2\n", - "a = destroy(n_max)" - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 1.0\\\\0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}" - ], - "text/plain": [ - "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\n", - "Qobj data =\n", - "[[0. 1.]\n", - " [0. 0.]]" - ] - }, - "execution_count": 58, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "a" - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "metadata": {}, - "outputs": [], - "source": [ - "# in QuTiP, all number (Fock) states are defined on the \"basis\". \n", - "psi0 = basis(n_max)" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}" - ], - "text/plain": [ - "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", - "Qobj data =\n", - "[[1.]\n", - " [0.]]" - ] - }, - "execution_count": 60, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "psi0 # it's a ket!" - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}" - ], - "text/plain": [ - "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", - "Qobj data =\n", - "[[0.]\n", - " [0.]]" - ] - }, - "execution_count": 61, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "a*psi0 # destroing the ground state gives the vacuum" - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\1.0\\\\\\end{array}\\right)\\end{equation*}" - ], - "text/plain": [ - "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", - "Qobj data =\n", - "[[0.]\n", - " [1.]]" - ] - }, - "execution_count": 62, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "a.dag()*psi0" - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "n = 1\n", - "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", - "Qobj data =\n", - "[[0.]\n", - " [1.]]\n" - ] - } - ], - "source": [ - "psi0 = basis(n_max)\n", - "for n in range(1,n_max):\n", - " print(\"n = \",n)\n", - " psi = a.dag()*psi0/np.sqrt(n)\n", - " print(psi)\n", - " psi0 = psi\n", - "psi0 = basis(n_max)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Density matrix" - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}" - ], - "text/plain": [ - "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", - "Qobj data =\n", - "[[1. 0.]\n", - " [0. 0.]]" - ] - }, - "execution_count": 64, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "rho0 = psi0*psi0.dag()\n", - "rho0" - ] - }, - { - "cell_type": "code", - "execution_count": 65, - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0\\\\0.0 & 1.0\\\\\\end{array}\\right)\\end{equation*}" - ], - "text/plain": [ - "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", - "Qobj data =\n", - "[[0. 0.]\n", - " [0. 1.]]" - ] - }, - "execution_count": 65, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "rho1 = fock(n_max,1)*fock(n_max,1).dag()\n", - "rho1" - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500 & 0.0\\\\0.0 & 0.500\\\\\\end{array}\\right)\\end{equation*}" - ], - "text/plain": [ - "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", - "Qobj data =\n", - "[[0.5 0. ]\n", - " [0. 0.5]]" - ] - }, - "execution_count": 66, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "mixed = (rho0 + rho1)/2\n", - "mixed" - ] - }, - { - "cell_type": "code", - "execution_count": 78, - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500 & 0.500\\\\0.500 & 0.500\\\\\\end{array}\\right)\\end{equation*}" - ], - "text/plain": [ - "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", - "Qobj data =\n", - "[[0.5 0.5]\n", - " [0.5 0.5]]" - ] - }, - "execution_count": 78, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# let's define the Schrodinger cat state\n", - "cat = fock(n_max,0)+fock(n_max,1)\n", - "cat = cat \n", - "cat_rho = ket2dm(cat)/2\n", - "cat_rho" - ] - }, - { - "cell_type": "code", - "execution_count": 82, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1.0\n", - "1.0\n" - ] - } - ], - "source": [ - "# trace Tr[rho]\n", - "print(cat_rho.tr())\n", - "print(mixed.tr())" - ] - }, - { - "cell_type": "code", - "execution_count": 83, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1.0\n", - "0.5\n" - ] - } - ], - "source": [ - "# purity Tr[rho*rho]\n", - "print((cat_rho*cat_rho).tr())\n", - "print((mixed*mixed).tr())" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Hamiltonian" - ] - }, - { - "cell_type": "code", - "execution_count": 97, - "metadata": {}, - "outputs": [], - "source": [ - "# We can now build a Hamiltonian, \n", - "# that of the Quantum Harmonic Oscillator \n", - "# exploring its features with QuTiP\n", - "n_max = 6\n", - "a = destroy(n_max)\n", - "\n", - "H = a.dag()*a" - ] - }, - { - "cell_type": "code", - "execution_count": 98, - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "Quantum object: dims = [[6], [6]], shape = (6, 6), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 2.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 3.000 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 4.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 5.0\\\\\\end{array}\\right)\\end{equation*}" - ], - "text/plain": [ - "Quantum object: dims = [[6], [6]], shape = (6, 6), type = oper, isherm = True\n", - "Qobj data =\n", - "[[0. 0. 0. 0. 0. 0.]\n", - " [0. 1. 0. 0. 0. 0.]\n", - " [0. 0. 2. 0. 0. 0.]\n", - " [0. 0. 0. 3. 0. 0.]\n", - " [0. 0. 0. 0. 4. 0.]\n", - " [0. 0. 0. 0. 0. 5.]]" - ] - }, - "execution_count": 98, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "H" - ] - }, - { - "cell_type": "code", - "execution_count": 99, - "metadata": {}, - "outputs": [], - "source": [ - "E_n , Psi_n = H.eigenstates()" - ] - }, - { - "cell_type": "code", - "execution_count": 100, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([0., 1., 2., 3., 4., 5.])" - ] - }, - "execution_count": 100, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "E_n" - ] - }, - { - "cell_type": "code", - "execution_count": 101, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", - "Qobj data =\n", - "[[1.]\n", - " [0.]\n", - " [0.]\n", - " [0.]\n", - " [0.]\n", - " [0.]],\n", - " Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", - "Qobj data =\n", - "[[0.]\n", - " [1.]\n", - " [0.]\n", - " [0.]\n", - " [0.]\n", - " [0.]],\n", - " Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", - "Qobj data =\n", - "[[0.]\n", - " [0.]\n", - " [1.]\n", - " [0.]\n", - " [0.]\n", - " [0.]],\n", - " Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", - "Qobj data =\n", - "[[0.]\n", - " [0.]\n", - " [0.]\n", - " [1.]\n", - " [0.]\n", - " [0.]],\n", - " Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", - "Qobj data =\n", - "[[0.]\n", - " [0.]\n", - " [0.]\n", - " [0.]\n", - " [1.]\n", - " [0.]],\n", - " Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", - "Qobj data =\n", - "[[0.]\n", - " [0.]\n", - " [0.]\n", - " [0.]\n", - " [0.]\n", - " [1.]]], dtype=object)" - ] - }, - "execution_count": 101, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "Psi_n" - ] - }, - { - "cell_type": "code", - "execution_count": 120, - "metadata": {}, - "outputs": [], - "source": [ - "g = .6\n", - "H_driven = a.dag()*a + g*(a + a.dag())\n", - "En_driven , Psin_driven = H_driven.eigenstates()" - ] - }, - { - "cell_type": "code", - "execution_count": 137, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure()\n", - "plt.plot(E_n,\"o-\",markersize = 10, label=\"QHO\")\n", - "plt.plot(En_driven,\"s--\",markersize = 10, label=\"Driven QHO\")\n", - "\n", - "plt.ylabel(\"energy\")\n", - "plt.xlabel(\"eigenvalue\")\n", - "plt.legend()\n", - "plt.show()\n", - "plt.close()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Open Quantum System: Lindblad Master Equation" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\\begin{eqnarray}\n", - "\\partial_t{\\rho}&=&-i\\lbrack H, \\rho\\rbrack +\\kappa\\left(a\\rho a^\\dagger - a^\\dagger a\\rho- \\rho a^\\dagger a\\right)\\\\\n", - "\\partial_t{\\rho}&=&-i\\lbrack H, \\rho\\rbrack +\\kappa\\mathcal{D}_{[a]}(\\rho)\n", - "\\end{eqnarray}\n", - "\n", - "* Non-unitary dynamics: Non-Hermitian matrix, $\\partial_t{\\rho}=\\mathcal{L}\\rho$\n", - "* Contractive map \n", - "* Linear map \n", - "* " - ] - }, - { - "cell_type": "code", - "execution_count": 153, - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "Quantum object: dims = [[6], [6]], shape = (6, 6), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.706 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.254 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.037 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.003 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 9.514\\times10^{-05} & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.371\\times10^{-06}\\\\\\end{array}\\right)\\end{equation*}" - ], - "text/plain": [ - "Quantum object: dims = [[6], [6]], shape = (6, 6), type = oper, isherm = True\n", - "Qobj data =\n", - "[[7.06203481e-01 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", - " 0.00000000e+00 0.00000000e+00]\n", - " [0.00000000e+00 2.54400986e-01 0.00000000e+00 0.00000000e+00\n", - " 0.00000000e+00 0.00000000e+00]\n", - " [0.00000000e+00 0.00000000e+00 3.66579057e-02 0.00000000e+00\n", - " 0.00000000e+00 0.00000000e+00]\n", - " [0.00000000e+00 0.00000000e+00 0.00000000e+00 2.64111551e-03\n", - " 0.00000000e+00 0.00000000e+00]\n", - " [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", - " 9.51406810e-05 0.00000000e+00]\n", - " [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", - " 0.00000000e+00 1.37141101e-06]]" - ] - }, - "execution_count": 153, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "rho0 = ket2dm(basis(n_max,n_max-1))\n", - "t = np.linspace(0,30,300)\n", - "kappa = 0.3\n", - "results = mesolve(H,rho0,t,[kappa*a])\n", - "rho_t = results.states\n", - "rho_t[0]\n", - "\n", - "rho_t[-1]" - ] - }, - { - "cell_type": "code", - "execution_count": 154, - "metadata": {}, - "outputs": [], - "source": [ - "results = mesolve(H,rho0,t,c_ops=[kappa*a], e_ops=[a,a.dag()*a])\n", - "at = results.expect[0]\n", - "nt = results.expect[1]" - ] - }, - { - "cell_type": "code", - "execution_count": 156, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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dy2UPf0bV3n1eRxKREBBIwRea2Z1m1s/M8szsL/gOth6Uc67eOTcSyAHGmtmwJp4z3TlX4JwryMzMbFn6CDIiJ417Lh7NirIqrtHqkyISgEAK/jqgFpgBzAS+wncZv4D5h3XeBU5tYT5p5NiB3fjDOcP5YNVWfjlroebIi0izDjrU4pzbDfyypW9sZpnAPufcDv9qlCcCf2x5RGnsvIJelO3ayx1vrCQzpRO/Om2w15FEpIMKaCz9EGUDj5pZNL7/Kcx0zr0cxM+LGNcedxhlu2r453trSYmP5drjDvM6koh0QEEreOfcQmBUsN4/kpkZt00eStXefdz++gpS4mP47pG5XscSkQ4mmHvwEkRRUcbt5+VTXVPPzS8uISk+hrNH5XgdS0Q6kEAu+JEJXAnkNn6+c+6K4MWSQMRGR/H3i0ZxxSOf8bNnFpIYF8PJWtJARPwCmUXzIpAKzAVeaXSTDiA+Nprp3ytgeM9UfvTk53y0eqvXkUSkgwik4BOcc79wzs10zs3afwt6MglYUqcYHrn8cPIyE7nysUKtWyMiQGAF/7KZnR70JNIqaQlxPPb9sXRL7sRlD39K8YYdXkcSEY8FUvA/xlfyX5nZLjOrMrNdwQ4mLdctOZ4nrhxHWkIslzw4n4WlKnmRSBbIcsHJzrko51xn51yK//eU9ggnLdczrTNPXTmO1M6xXPLAfBZv3HnwF4lIWDpgwZvZIP+fo5u6tV9EaamcLgk8deU4kuNjuVglLxKx7EDrmZjZdOfcNDN7p4mHnXPu+LYOU1BQ4AoLC9v6bSPWhm17uGD6PHbX1vHED45gaI9UryOJSBszsyLnXEGTj3WkBatU8G1vfeUeLpj+CXv21fPkD8YxpIdG10TCSXMFH8hBVglhvTMSeGraODrHRnPRA/NYVKrhGpFIoYKPAH0yEpkx7UiSOsVw0f3zKFy3zetIItIOVPARondGAjOvOpLM5E5898FPdcarSAQI5KLb480s0f/zJf6rO/UJfjRpaz3SOjPjqiPpnZ7A5Y98xtvLy7yOJCJBFMge/L3AHjPLB34OlACPBTWVBE1mcieenjaOQd2TmfZYEa8s3Ox1JBEJkkAKvs75ptpMAf7qnPsrkBzcWBJMXRLjePwHRzCqdxrXPbWAZ4tKvY4kIkEQSMFXmdmvgEuAV/xXaIoNbiwJtpT4WB69YizjD+vKz54p5v7313odSUTaWCAFfz5QA3zfObcF6AncHtRU0i4S4mJ44NICzhieze9eXcbvX11GQ0PHOS9CRFonkItubwHubPT7ejQGHzY6xURz94WjyEiKY/r7a6moquFPU0cQG60JViKhLpArOp0D/BHoBpj/5rTgWPiIjvJd47VbcifueGMl23bXcs/Fo0nspCs6ioSyQHbT/gRMds6lajXJ8GVm/Oj4/vzhnOF8sKqCix6Yz7bdtV7HEpFWCKTgy5xzy4KeRDqEC8b25p/fLWD55l1MvfdjSip3ex1JRA5RIAVfaGYzzOxCMztn/y3oycQzJw3J4okfHMG2PbWcfc/HWtpAJEQFUvApwB7gZOBM/21SMEOJ9wpy03n+mvGkdo7logfm81LxJq8jiUgLBTKL5vL2CCIdT9+uiTx39VFc9a8irn/qc9ZX7uba4w7DzLyOJiIBCGQtmhwze97Mys2szMxmmVlOe4QT73VJjONfPxjLWSN7cMcbK7np2YXU1jV4HUtEAhDIEM3DwEtAD3wnOc323ycRolNMNH85fyQ3nNifZ4tK+d5D89muGTYiHV4gBZ/pnHvYOVfnvz0CZAY5l3QwZsYNJw7gL+fns6BkB5P/8SHLt+zyOpaINCOQgt/qXyY42n+7BKgMdjDpmM4elcPTV42jZl8D59zzMXMWazVKkY4qkIK/AvgOsAXYDEwFdOA1go3u3YXZ101gQFYyP3x8AXe+uVJr2Ih0QIEUfC/n3GTnXKZzrptz7iygV7CDSceWlRLP09PGMXVMDne/tYqrHi+iuqbO61gi0kggBf+3AO+TCBMfG83tU0dwy5lDeHt5Oefc8xFrK6q9jiUifgecB29mRwJHAZlmdmOjh1KA6GAHk9BgZlw+vi8Ds5K59skFTP77R9w+dQSnDc/2OppIxGtuDz4OSML3j0Byo9sufOPwzTKzXmb2jpktM7MlZvbjtggsHdNRh3Xl5esncli3JK5+YgG/fXkp++o1X17ES+a7Gl8zTzDr45wrMbNkfMsEB/R/cDPLBrKdcwv8ry0CznLOLT3QawoKClxhYWEL4ktHU1vXwO9eWcqjn5RQ0KcLf79oNN1T472OJRK2zKzIOVfQ1GOBjMEnm9nnwGJgiZkVmdmwg73IObfZObfA/3MVsAzfiVISxuJiorhtyjDuvnAUSzfvYtLfPuDj1Vu9jiUSkQIp+OnAjc65Ps65PsBP/fcFzMxygVHA/CYem2ZmhWZWWFFR0ZK3lQ5scn4PXrx2PGkJcVzy4HzumruSek2lFGlXgRR8onPunf2/OOfeBRID/QAzSwJmATc45/7j1Efn3HTnXIFzriAzUyfIhpP+Wcm8eO14Juf34K65q7jw/nls2vGV17FEIkYgBb/WzG42s1z/7b+BLwN5czOLxVfuTzjnnmtNUAlNiZ1iuOuCUfz5vHwWb9zJaX/9gNeXbPE6lkhECPRM1kzgOeB5/88HPZPVfGvKPggsc87debDnS3g7d0wOL183gV7pnbnqX0Xc/MJi9u6r9zqWSFg76CyaQ35jswnAB8AiYP98uV8751490Gs0iyb81dTVc/ucFTzw4ZcM6p7M3ReOYkBWstexREJWc7NoApkmOQD4GZBLoxOjnHPHt2FGQAUfSd5ZUc7PZhZTVVPHTScP5IoJfYmO0oVERFqqtQVfDNyHbx771/+nds4VtWVIUMFHmq3VNfzquUW8ubSMsbnp/Pk7+fRKT/A6lkhIaW3BFznnxgQl2beo4COPc45ZCzZy20tLaHCOmycN4fzDe+mygCIBOqQTncws3czSgdlmdo2ZZe+/z3+/SKuZGVPH5PDaDRMZkZPGL59bxPcfLaS8aq/X0URC3gH34M3sS8ABTe1KOedcXluH0R58ZGtocDzy8Tr+OGc5CXHR/GbKMCaNyNbevEgzWjVE055U8AKwuryan878guLSnZw4uBu/PWsY2amdvY4l0iG1ai0aM4s3sxvN7Dkzm2VmN5iZVo+SoDmsWxKzrj6K/zp9MB+u3srJd77PE/NLdNUokRYK5ESnx4Ch+C7y8XdgCPCvYIYSiYmO4sqj83j9hqMZnpPKfz2/mAvun6cLioi0QEDTJJ1z+Qe7ry1oiEaa4pzjmcJS/veVpeyta+CGE/tz5cQ8YqMD2T8RCW+tXS74czMb1+jNjgA+aqtwIgdjZnzn8F7MvfEYThjUjT/NWcHkv39EUck2r6OJdGiBFPwRwMdmts7M1gGfAMeY2SIzWxjUdCKNdEuJ595LxnDfJWPYuaeWc+/9hJueKaayusbraCId0gGvydrIqUFPIdICpw7rztEDunL3W6t54IO1vLG0jJtOGciFY3truQORRjRNUkLa6vIqbn5hCZ+srWRETiq/nTKM/F5pXscSaTetHYMX6bAO65bMk1cewV8vGMmWnXs5656P+NVzi9iqYRsRFbyEPjNjysievPXTY7j8qL48U7iB425/l3++t4aaOq05L5FLBS9hIzk+lv85cwhzbjiaw/um83+vLeekO99nzuItdKShSJH2ooKXsHNYtyQeuuxwHrtiLPGxUfzw8SIumD6PxRt3eh1NpF2p4CVsHT0gk1evn8hvzxrGyrIqzvz7h9z0TLEu/C0RQ7NoJCLs/Goff397FY9+XAIGlx2Vy9XH9KNLYpzX0URaRatJivht2LaHu+au4rnPS0nqFMMPj+nH5eNzSYgL5JQQkY5HBS/yLSu2VHH76yuYu6yMzOROXH9Cfy44vJfWt5GQo3nwIt8ysHsyD1xawLM/PJLcjARufmExJ975HrOKSqmrb/A6nkibUMFLRCvITWfmVUfy8GWHkxgXw0+fKVbRS9jQEI2In3OON5eWcdfcVSzdvIvcjASuO74/U0b2IEZDN9JBaQxepAWcc7zhL/plm3fRt2siPzruMBW9dEgqeJFD0NDgeHPZv4s+p0tnph2dx3ljetE5LtrreCKACl6kVRoaHHOXlXHfe2tYsH4HGYlxXD4+l++OyyU1IdbreBLhVPAibcA5x2frtnPvu6t5Z0UFiXHRXHREb74/IY/uqboOvXhDBS/SxpZu2sU/31/D7OJNREcZ54zK4QcT+9I/K9nraBJhVPAiQbJh2x7u/2AtMz7bQE1dAxP7d+WK8X05ZkAmUbq6lLQDFbxIkFVW1/DUp+v517wSynbVkNc1kcvG53Lu6BwSO2kZBAkeFbxIO6mta+C1xZt56KN1FG/YQXJ8DOcX9OLSo3LplZ7gdTwJQyp4EQ8sWL+dhz78ktf8Fxw5flAWF4/rzdH9M3VxcGkzzRW8/u8oEiSje3dh9EVd2LTjKx6fV8LMwg3MXVZGTpfOXDi2N+cV5NAtWbNvJHi0By/STmrrGnhj6RaemLeeT9ZWEhNlnDK0Oxcd0Zsj8zJ0UFYOiSd78Gb2EDAJKHfODQvW54iEiriYKCaN6MGkET1YU1HNU/PX80xRKa8s2kzfromcf3gvzhnVk24p2quXthG0PXgzOxqoBh4LtOC1By+RZu++el5dtJkn56+nsGQ7UQbHDMjkvIJenDC4G51itCSCNM+zg6xmlgu8rIIXObg1FdXMKirluQUb2bJrL2kJsUzJ78HUMb0Y1jMFMw3hyH/q0AVvZtOAaQC9e/ceU1JSErQ8IqGgvsHx4eqtPFO4gTeWllFb18Cg7smcOzqHSfnZZKd29jqidCAduuAb0x68yDft3LOP2Qs38UxRKcUbdmAGY3PTmTyyB6cPy9ZFw0UFLxIOvty6m5e+2MRLxRtZU7GbmCjj6AGZTM7vwUlDsnTGbITSPHiRMNC3ayI/PrE/159wGEs37+KlLzYxu3gTby8vJz42ihMHZ3Fmfg+OGZBJfKwOzkpwZ9E8BRwLdAXKgFuccw829xrtwYu0TEODo7BkOy8Vb+TVRVvYtruWhLhojhvYjVOGdef4Qd1I0p59WNNSBSIRYF99A/PWVjJn8RZeX1LG1uoa4qKjmNi/K6cM685Jg7M0Zh+GVPAiEaa+wbFg/XbmLN7CnMVb2LjjK6KjjHF56ZwytDsnDM6iZ5pm44QDFbxIBHPOsXjjLuYs2cxri7ewtmI3AIO6J3PC4G4cPyiLkb3StABaiFLBi8jXVpdX887yct5aXsZn67ZT3+BIT4zj2IGZnDAoi4kDupISr2vNhgoVvIg0aeeefby/qoK3l5fzzopyduzZR0yUcXhuOscMzGRi/64M7p6ihdA6MBW8iBxUfYPj8/XbeWt5Oe8sL2f5lioAMhLjmNC/KxP7+wo/S4uhdSgqeBFpsbJde/lw1VY+XL2VD1ZVsLW6FoABWUlM7J/JhP5dOaJvOglxmobpJRW8iLRKQ4Nj+ZYqPlhVwYertzL/y23U1jUQFx3FyN5pjMvLYFxeOqN7d9FJVu1MBS8ibWrvvno+/XIbH67eyry1lSzeuJMGh6/we6UxLi+dcXkZjOrdhc5xKvxgUsGLSFDt2ruPwnXbmL92G/PWVrLIX/ix0eYv/AwOz01nZO80zdBpYyp4EWlXVXv3UbhuO/O+rGTe2m0s3riT+gaHGQzMSmZMny5f33qnJ2it+1ZQwYuIp6pr6vhi/Q6KSrZTtH47n5dsp6qmDoCuSXGM7u0r+4LcLgztkapx/BbQapIi4qmkTjFM6N+VCf27Ar4pmavLqykq2U5hyTYWlGznjaVlgG9YZ2D3ZEbkpJGfk8qInDT6d0siJjrKy00ISdqDF5EOYWt1DUUl2/liww4Wlu5gYelOqvb69vLjY6MY1sNX9iNyUhmRk0puRqJOwEJDNCISghoaHOsqd7OwdCfF/sJfsmkne/c1AJAcH8PwnqkM7ZHCkB4pDMlOJS8zkdgI29PXEI2IhJyoKCMvM4m8zCTOGtUTgLr6BlaWVfv28DfuZFHpTh79pITaOl/px8VEMTArmSHZ/tLvkd1Pdx4AAAc6SURBVMKg7skkR+jMHe3Bi0hIq6tvYO3W3SzdtIulm3d9/ee23bVfP6dPRgKDu6cwoHsyA7KSGJCVTN+u4bG3rz14EQlbMdFRDMhKZkBW8td7+s45yqtq/qP031i6hQb/Pm1MlJGXmUj/rGQGdPMVf/+sZHIzEsLmgK4KXkTCjpmRlRJPVko8xw3q9vX9e/fVs6aimlVl1awsq2JlWRWLSnfy6qLN7B/MiIuOIi8zkQFZyfTLTKJvZiJ5XRPJy0wMuXV3QiutiEgrxMdGM7RHKkN7pH7j/q9q61ld/u/SX1lWRVHJdmYv3ETjUezuKfHkZSbSt2ui7/iAv/hzuiR0yAumqOBFJOJ1jotmeE4qw3O+Wfx799WzrnI3ayt2s7aimrVbfT/PLt7ELv8UTvDt9ffOSCCvayK5XRPpnZ5A7/QE+mQk0COts2dj/Sp4EZEDiI+NZlD3FAZ1T/nG/c45tu2u9Rf+v4t/TUU1766ooLa+4evnRhn0SOtMnwxf6fdKT6BP+r//EUhNCN4MHxW8iEgLmRkZSZ3ISOrE4bnp33isocFRVrWXkso9rN+2hw3bfH+WVO7hjSVlVDaa3QOQ2jmWAVlJPPPDo9o8pwpeRKQNRUUZ2amdyU7tzLi8jP94vLqmjg3+wt9f/nUNDU28U+up4EVE2lFSpxgGZ6cwODvl4E9upfCY7CkiIv9BBS8iEqZU8CIiYUoFLyISplTwIiJhSgUvIhKmVPAiImFKBS8iEqY61AU/zKwCKDnEl3cFtrZhHC+Fy7aEy3aAtqUjCpftgNZtSx/nXGZTD3Sogm8NMys80FVNQk24bEu4bAdoWzqicNkOCN62aIhGRCRMqeBFRMJUOBX8dK8DtKFw2ZZw2Q7QtnRE4bIdEKRtCZsxeBER+aZw2oMXEZFGVPAiImEq5AvezE41sxVmttrMful1ntYws3VmtsjMvjCzQq/ztISZPWRm5Wa2uNF96Wb2ppmt8v/ZxcuMgTrAttxqZhv9380XZna6lxkDYWa9zOwdM1tmZkvM7Mf++0Pue2lmW0Lxe4k3s0/NrNi/Lbf57+9rZvP938sMM4tr9WeF8hi8mUUDK4GTgFLgM+BC59xST4MdIjNbBxQ450Lu5A0zOxqoBh5zzg3z3/cnYJtz7g/+f3y7OOd+4WXOQBxgW24Fqp1zd3iZrSXMLBvIds4tMLNkoAg4C7iMEPtemtmW7xB634sBic65ajOLBT4EfgzcCDznnHvazO4Dip1z97bms0J9D34ssNo5t9Y5Vws8DUzxOFNEcs69D2z71t1TgEf9Pz+K7y9kh3eAbQk5zrnNzrkF/p+rgGVAT0Lwe2lmW0KO86n2/xrrvzngeOBZ//1t8r2EesH3BDY0+r2UEP3S/RzwhpkVmdk0r8O0gSzn3Gbw/QUFunmcp7V+ZGYL/UM4HX5YozEzywVGAfMJ8e/lW9sCIfi9mFm0mX0BlANvAmuAHc65Ov9T2qTLQr3grYn7QnfMCcY750YDpwHX+ocKpGO4F+gHjAQ2A3/2Nk7gzCwJmAXc4Jzb5XWe1mhiW0Lye3HO1TvnRgI5+EYiBjf1tNZ+TqgXfCnQq9HvOcAmj7K0mnNuk//PcuB5fF98KCvzj53uH0Mt9zjPIXPOlfn/UjYA9xMi341/jHcW8IRz7jn/3SH5vTS1LaH6veznnNsBvAuMA9LMLMb/UJt0WagX/GdAf//R5zjgAuAljzMdEjNL9B88wswSgZOBxc2/qsN7CbjU//OlwIseZmmV/YXodzYh8N34D+Y9CCxzzt3Z6KGQ+14OtC0h+r1kmlma/+fOwIn4jim8A0z1P61NvpeQnkUD4J8WdRcQDTzknPudx5EOiZnl4dtrB4gBngylbTGzp4Bj8S17WgbcArwAzAR6A+uB85xzHf7g5QG25Vh8wwAOWAdctX8cu6MyswnAB8AioMF/96/xjV2H1PfSzLZcSOh9LyPwHUSNxreTPdM59xt/BzwNpAOfA5c452pa9VmhXvAiItK0UB+iERGRA1DBi4iEKRW8iEiYUsGLiIQpFbyISJhSwUvEMrM0M7vG/3MPM3v2YK8RCSWaJikRy7+mycv7V4wUCTcxB3+KSNj6A9DPv+jTKmCwc26YmV2GbyW/aGAYvvVN4oDvAjXA6c65bWbWD/gHkAnsAa50zi1v/80QaZqGaCSS/RJY41/06aZvPTYMuAjf2ia/A/Y450YBnwDf8z9nOnCdc24M8DPgnnZJLRIg7cGLNO0d/7rjVWa2E5jtv38RMMK/quFRwDO+ZVIA6NT+MUUOTAUv0rTGa4A0NPq9Ad/fmyh863ePbO9gIoHSEI1Esiog+VBe6F+L/EszOw98qx2aWX5bhhNpLRW8RCznXCXwkf/i2rcfwltcDHzfzIqBJehykdLBaJqkiEiY0h68iEiYUsGLiIQpFbyISJhSwYuIhCkVvIhImFLBi4iEKRW8iEiY+n+lJQKmzeHSiAAAAABJRU5ErkJggg==\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure()\n", - "plt.plot(t,nt,\"-\",markersize = 10, label=\"$\\\\langle a^\\dagger a \\\\rangle$\")\n", - "plt.ylabel(\"photons in cavity\")\n", - "plt.xlabel(\"time\")\n", - "plt.legend()\n", - "plt.show()\n", - "plt.close()" - ] - }, - { - "cell_type": "code", - "execution_count": 90, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "QuTiP: Quantum Toolbox in Python\n", - "Copyright (c) 2011 and later.\n", - "A. J. Pitchford, P. D. Nation, R. J. Johansson, A. Grimsmo, and C. Granade\n", - "\n", - "QuTiP Version: 4.3.1\n", - "Numpy Version: 1.15.4\n", - "Scipy Version: 1.2.1\n", - "Cython Version: 0.29.8\n", - "Matplotlib Version: 3.1.0\n", - "Python Version: 3.7.3\n", - "Number of CPUs: 2\n", - "BLAS Info: OPENBLAS\n", - "OPENMP Installed: False\n", - "INTEL MKL Ext: False\n", - "Platform Info: Darwin (x86_64)\n", - "Installation path: /miniconda3/lib/python3.7/site-packages/qutip\n", - "==============================================================================\n", - "Please cite QuTiP in your publication.\n", - "==============================================================================\n", - "For your convenience a bibtex file can be easily generated using `qutip.cite()`\n" - ] - } - ], - "source": [ - "qutip.about()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/environment.yml b/environment.yml index 5d317bc..8689261 100644 --- a/environment.yml +++ b/environment.yml @@ -7,5 +7,6 @@ dependencies: - cython==0.29.8 - numpy==1.16.4 - scipy==1.2.1 -- matplotlib=3.1.0 -- qutip==4.3.1 +- matplotlib=3.0.3 +- qutip==4.4.0 +- imagemagick=7.0.8_49 diff --git a/0.overview_ensembles_piqs.ipynb b/extra-notebooks/3.overview_ensembles_piqs.ipynb similarity index 100% rename from 0.overview_ensembles_piqs.ipynb rename to extra-notebooks/3.overview_ensembles_piqs.ipynb diff --git a/extra-notebooks/4.dicke-model-wigner-time.ipynb b/extra-notebooks/4.dicke-model-wigner-time.ipynb new file mode 100644 index 0000000..9ffc021 --- /dev/null +++ b/extra-notebooks/4.dicke-model-wigner-time.ipynb @@ -0,0 +1,758 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# Liouvillian of one cavity and $N$ spins, open Dicke model\n", + "\n", + "We consider a system of $N$ two-level systems (TLSs) coupled to a cavity mode, such that it can emit and absorb two photons at a time. This is known as the two-photon Dicke model.\n", + "\n", + "\n", + "\n", + "\\begin{eqnarray}\n", + "H&=&\\frac{\\omega_{0}}{N}J_z + \\omega_{c}a^\\dagger a + g\\left((a^\\dagger)^2 + (a)^2\\right)\\left(J_{+} + J_{-}\\right)\n", + "\\end{eqnarray}\n", + "\n", + "and it is an extension to $N>1$ of the two-photon Rabi model [1-4]. Note the normalization in $N$ of the atomic bare energy term. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each TLS has identical frequency $\\omega_{0}$. The light matter coupling can be in the ultrastrong coupling (USC) regime, $g/omega_{0}>0.1$.\n", + "\n", + "If we study this model as an open quantum system, the cavity can leak photons and the TLSs are subject to local processes. For example the system can be incoherently pumped at a rate $\\gamma_\\text{P}$, the TLSs are subject to dephaisng at a rate $\\gamma_\\text{D}$, and local incoherent emission occurs at a rate $\\gamma_\\text{E}$. The dynamics of the coupled light-matter system is governed by\n", + "\n", + "\\begin{eqnarray}\\dot{\\rho} &=& \n", + "-i\\lbrack H,\\rho \\rbrack\n", + "+\\frac{\\kappa}{2}\\mathcal{L}_{a}[\\rho]\n", + "+\\frac{\\gamma_\\text{CE}}{2}\\mathcal{L}_{J_{-}}[\\rho] \n", + "+\\sum_{n=1}^{N}\\left(\\frac{\\gamma_\\text{P}}{2}\\mathcal{L}_{J_{+,n}}[\\rho] \n", + "+\\frac{\\gamma_\\text{E}}{2}\\mathcal{L}_{J_{+,n}}[\\rho]\n", + "+\\frac{\\gamma_\\text{D}}{2}\\mathcal{L}_{J_{+,n}}[\\rho]\\right)\n", + "\\end{eqnarray}\n", + "\n", + "When only the dissipation of the cavity is present, beyond a critical value of the coupling $g$, the steady state of the system becomes superradiant. This is visible by looking at the Wigner function of the photonic part of the density matrix, which displays two displaced lobes in the $x$ and $p$ plane. \n", + "\n", + "As it has been shown in Ref. [5], the presence of dephasing suppresses the superradiant phase transition, while the presence of local emission restores it [6].\n", + "\n", + "In order to study this system using QuTiP [7] and $PIQS$ [8], we will first build the TLS Liouvillian, then we will build the photonic Liouvillian and finally we will build the light-matter interaction. The total dynamics of the system is thus defined in a Liouvillian space that has both TLS and photonic degrees of freedom. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1) Piqs method" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from time import clock\n", + "import matplotlib.pyplot as plt\n", + "from scipy.io import mmwrite\n", + "import matplotlib as mpl\n", + "from matplotlib import cm\n", + "\n", + "from qutip import *\n", + "from qutip.piqs import *" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "gt/gc 0.5477225575051662\n", + "g/gc 1.6\n", + "g/gt 2.9211869733608857\n", + "g 0.8\n", + "1-phot Dicke model for hint\n" + ] + } + ], + "source": [ + "#spin parameters\n", + "N = 3\n", + "ntls = N\n", + "system = Dicke(N = ntls)\n", + "nds = num_dicke_states(ntls)\n", + "[jx, jy, jz] = jspin(N)\n", + "jp = jspin(N, \"+\")\n", + "jm = jspin(N, \"-\")\n", + "w0 = 0.1 # bare frequency\n", + "wx = 0. # coherent driving\n", + "system.hamiltonian = w0 * jz + wx * jx \n", + "\n", + "gE = 0.001\n", + "gCE = 0.0\n", + "system.collective_emission = gCE\n", + "system.emission = gE\n", + "\n", + "liouv = system.liouvillian() \n", + "#photon parameters\n", + "wc = 1.\n", + "nphot = 2*N+3\n", + "kappa = 0.01\n", + "pump = 0.\n", + "a = destroy(nphot)\n", + "c_ops_phot = [np.sqrt(kappa) * a, np.sqrt(pump) * a.dag()]\n", + "liouv_phot = liouvillian(wc * a.dag()*a , c_ops_phot)\n", + "#spin-photon parameters\n", + "#w_int = 1.6/np.sqrt(ntls)\n", + "w_int = wc*.8\n", + "g = w_int\n", + "gc = wc/2.0#wc/(4*ntls)\n", + "gt = np.sqrt(wc*w0*N/4)\n", + "print('gt/gc',gt/gc)\n", + "print('g/gc', g/gc)\n", + "print('g/gt', g/gt)\n", + "print(\"g \",g)\n", + "Dicke_true = True\n", + "jc_true = False\n", + "if Dicke_true == True:\n", + " h_int = w_int * tensor((a + a.dag()), jx) # standard Dicke Hamiltonian\n", + " print(\"1-phot Dicke model for hint\")\n", + "if jc_true == True:\n", + " h_int = w_int * (tensor(a, jp)+tensor(a.dag(), jm)) # standard JC Hamiltonian\n", + " print(\"1-phot Jaynes-Cummings model for hint\")" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "64 6 27 81\n" + ] + } + ], + "source": [ + "print(4**N,num_dicke_states(N),N**3,N**4)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(2916, 2916)\n" + ] + } + ], + "source": [ + "#identity super-operators\n", + "id_tls = to_super(qeye(nds))\n", + "id_phot =to_super(qeye(nphot))\n", + "#total liouvillian\n", + "liouv_tot = super_tensor(liouv_phot, id_tls) + super_tensor(id_phot, liouv)\n", + "#strong coupling light-matter interaction\n", + "liouv_h_int = -1j* spre(h_int) + 1j* spost(h_int)\n", + "liouv_tot_int = liouv_tot + liouv_h_int\n", + "print(liouv_tot_int.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "#solve using qutip\n", + "jz_tot = tensor(qeye(nphot), jz)\n", + "jpjm_tot = tensor(qeye(nphot), jp*jm)\n", + "jm_tot = tensor(qeye(nphot), jm)\n", + "jp_tot = tensor(qeye(nphot), jp)\n", + "adag_tot = tensor(a.dag(), qeye(nds))\n", + "a_tot = tensor(a, qeye(nds))\n", + "adag_a_tot = tensor(a.dag()*a, qeye(nds))\n", + "adag2_a2_tot = tensor(a.dag()**2*a**2, qeye(nds))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "steadystate time 0.06966300000000003\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:1: DeprecationWarning: time.clock has been deprecated in Python 3.3 and will be removed from Python 3.8: use time.perf_counter or time.process_time instead\n", + " \"\"\"Entry point for launching an IPython kernel.\n", + "/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:5: DeprecationWarning: time.clock has been deprecated in Python 3.3 and will be removed from Python 3.8: use time.perf_counter or time.process_time instead\n", + " \"\"\"\n" + ] + }, + { + "data": { + "text/plain": [ + "0.8152236523395088" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "clock_t0 = clock()\n", + "rho_ss = steadystate(liouv_tot_int,method='direct')\n", + "#steadystate 'method': direct,eigen,power,iterative-gmres,iterative-lgmres,svd\n", + "\n", + "clock_tf = clock()\n", + "dt_clock = clock_tf - clock_t0\n", + "print(\"steadystate time \",dt_clock)\n", + "jzt_ss = expect(jz_tot, rho_ss)\n", + "jpjmt_ss = expect(jpjm_tot, rho_ss)\n", + "adagat_ss = expect(adag_a_tot, rho_ss)\n", + "rhoss_phot = Qobj(rho_ss[:nphot,:nphot])\n", + "rhoss_spin = Qobj(rho_ss[-rho_ss.shape[0]:,-rho_ss.shape[0]:])\n", + "rhoss_phot1 = rho_ss.ptrace(0)\n", + "rhoss_spin1 = rho_ss.ptrace(1)\n", + "adagat_ss" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Eigenvalues of the Liouvillian" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "eigs, eigv = liouv_tot_int.eigenstates()\n", + "re_eigs = np.real(eigs)\n", + "im_eigs = np.imag(eigs)\n", + "plt.figure(figsize=(10,8))\n", + "plt.plot(re_eigs,im_eigs,'.')\n", + "plt.axvline(x=0,color=\"red\")\n", + "#plt.xlim([-1,0.1])\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The spectrum of the Liouvillian shows the eigenvalues $\\lambda$ in the complex plane. \n", + "All Liouvillians have a symmetry around the horizontal axis and take only real negative values, $\\text{Re}[\\lambda]<0$ (left of the red line). " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Wigner function of the steady state $\\rho_\\text{ss}$" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#psi = (basis(10, 0) + basis(10, 3) + basis(10, 9)).unit()\n", + "psi = rho_ss.ptrace(0)\n", + "xvec = np.linspace(-8, 8, 100)\n", + "W = wigner(psi, xvec, xvec)\n", + "wmap = wigner_cmap(W) # Generate Wigner colormap\n", + "nrm = mpl.colors.Normalize(-W.max(), W.max())\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(13, 6))\n", + "label_size = 15\n", + "plt.rc('text', usetex = True)\n", + "plt.rc('xtick', labelsize=label_size) \n", + "plt.rc('ytick', labelsize=label_size)\n", + "# first subplot\n", + "plt1 = axes[0].contourf(xvec, xvec, W, 100, cmap=cm.RdBu, norm=nrm)\n", + "axes[0].set_title(r\"Wigner Function (Standard Colormap)\", fontsize=label_size);\n", + "max_cb =np.max(W)\n", + "min_cb =np.min(W)\n", + "cb1 = fig.colorbar(plt1, ax=axes[0],ticks=[min_cb, max_cb])\n", + "# Wigner colormap option\n", + "wigner_map = False\n", + "if wigner_map == True:\n", + " plt2 = axes[0].contourf(xvec, xvec, W, 100, cmap=wmap) \n", + " cb2 = fig.colorbar(plt2, ax=axes[1], ticks=[0, max_cb])\n", + " axes[0].set_title(r\"Wigner Function (Wigner Colormap)\", fontsize=label_size);\n", + "axes[0].set_xlabel(r\"$x$\", fontsize=label_size)\n", + "axes[0].set_ylabel(r\"$p$\", fontsize=label_size)\n", + "\n", + "# plot its fock-state distribution\n", + "# second subplot\n", + "axes[1].set_title(r\"Steady-state intra-cavity photon population\", fontsize=label_size);\n", + "axes[1].bar(np.arange(0, nphot), \n", + " np.real(psi.diag()), color=\"blue\", \n", + " alpha=0.8,\n", + " label =r\"Fock state, $P_{n}=\\mathrm{Tr}[\\rho_\\mathrm{ss},|n\\rangle \\langle n |]$\")\n", + "axes[1].axvline(x=nphot,color=\"red\",\n", + " label =r\"Hilbert-space photon cut-off, $n_{ph}$\")\n", + "nph_ss=(psi*(a.dag()*a)).tr()\n", + "axes[1].axhline(y=nph_ss,\n", + " linestyle='dashed',\n", + " color=\"orange\",\n", + " linewidth = 4,\n", + " label =r\"Mean photon number, $\\langle a^\\dagger a \\rangle={}$\".format(np.round(nph_ss,2)))\n", + "axes[1].set_ylim(0, 1)\n", + "nmaxphot_bar = nphot+1\n", + "axes[1].set_xlim(0, nmaxphot_bar)\n", + "axes[1].set_xlabel(r\"$n$\", fontsize=label_size)\n", + "axes[1].set_ylabel(r\"$P_n$\", fontsize=label_size)\n", + "# saving plot options\n", + "fig.tight_layout()\n", + "fname = 'cs_wigner_2phot_N{}.pdf'.format(N)\n", + "plt.legend(fontsize=label_size*0.9,loc=2)\n", + "savefile = False\n", + "if savefile == True:\n", + " plt.savefig(fname, bbox_inches='tight')\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " ## Steady-state correlations: $g^{(2)}(\\tau)$ for $\\rho_\\text{ss}$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:9: DeprecationWarning: time.clock has been deprecated in Python 3.3 and will be removed from Python 3.8: use time.perf_counter or time.process_time instead\n", + " if __name__ == '__main__':\n", + "/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:14: DeprecationWarning: time.clock has been deprecated in Python 3.3 and will be removed from Python 3.8: use time.perf_counter or time.process_time instead\n", + " \n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "integration time (s): 2.420608999999999\n" + ] + } + ], + "source": [ + "# time integration parameters\n", + "nt = 1001\n", + "tmax = 400 \n", + "t = np.linspace(0, tmax, nt)\n", + "\n", + "B = adag_a_tot\n", + "rhoB = a_tot * rho_ss * adag_tot\n", + "\n", + "clock_t0 = clock()\n", + "opts = Options(store_states = True, nsteps = 1000, atol = 1e-6)\n", + "result3 = mesolve(liouv_tot_int, rhoB, t, [], e_ops = B, options = opts)\n", + "nt_bos = result3.states\n", + "g2t_bos = result3.expect[0]\n", + "clock_tf = clock()\n", + "dt_clock = clock_tf - clock_t0\n", + "print(\"integration time (s): \",dt_clock)\n", + "\n", + "g2_norm, G2 = coherence_function_g2(liouv_tot_int, None, t, [], a_tot)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Time evolution" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# initial tensor state\n", + "excited_ = dicke(N, N/2, N/2)\n", + "ground_ = dicke(N, N/2, -N/2)\n", + "rho0_tls = ground_\n", + "ground_phot = ket2dm(basis(nphot, 0))\n", + "rho0 = tensor(ground_phot, rho0_tls)\n", + "# solution of the master equation\n", + "opts = Options(store_states = True, nsteps = 10000, atol = 1e-6)\n", + "result4 = mesolve(liouv_tot_int, rho0, t, [], e_ops = [jz_tot, adag_a_tot, jpjm_tot], options = opts)\n", + "rhot_tot = result4.states\n", + "jzt_tot = result4.expect[0]\n", + "adagat_tot = result4.expect[1]\n", + "jpjmt_tot = result4.expect[2]" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "jmax = (0.5 * N)\n", + "j2max = (0.5 * N + 1) * (0.5 * N)\n", + "\n", + "plt.rc('text', usetex = True)\n", + "label_size = 20\n", + "label_size2 = 20\n", + "label_size3 = 20\n", + "\n", + "fig1 = plt.figure()\n", + "plt.plot(t, np.real(g2t_bos)/adagat_ss**2, '-', label = 'g2 nat')\n", + "plt.plot(t, np.real(g2_norm), '--', label = 'g2 qutip')\n", + "plt.plot(t, 0 * t + 1, '--', label = '')\n", + "#plt.ylim([-1,1])\n", + "plt.xlabel(r'$\\tau$', fontsize = label_size3)\n", + "plt.ylabel(r'$Re(g^{(2)}(\\tau))$', fontsize = label_size3)\n", + "#plt.xticks([0,(tmax/2)/td0,tmax/td0])\n", + "#plt.yticks([0.85,1])\n", + "plt.rc('xtick', labelsize=label_size) \n", + "plt.rc('ytick', labelsize=label_size)\n", + "fname = 'sssr_g2t_N{}.pdf'.format(N)\n", + "plt.savefig(fname, bbox_inches='tight') \n", + "plt.show()\n", + "plt.close()\n", + "# Imag(g2) should be zero\n", + "plt.figure()\n", + "plt.plot(t, np.imag(g2t_bos))\n", + "plt.plot(t, np.imag(g2_norm), '--')\n", + "plt.xlabel(r'$\\tau$', fontsize = label_size3)\n", + "plt.ylabel(r'$Im(g^{(2)}(\\tau))$', fontsize = label_size3)\n", + "plt.ylim([-0.5, 0.5])\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The imaginary part of the $g^{(2)}(\\tau)$ should be always zero. The real part quantifies the photon statistics, such as bunching and anti-bunching in the system. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3) Plots -- Operators time evolutions" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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mjE/bBUBbqZJhmP5TWFg4aIQIYDEaEOgFR4qRdEb+TmA4efIkNm3a5DTbxhULFy5EfHy8T9sF2K7fxFXFGWZ4MSTCdEKITADZAGoAmADUEFGfX/W9Pc7X2ItRVFSU38N08rzeiN3WrVt92iaJfvJva2sr4uLi/HIdhrGHiLTxSqb/eBNyH/RiJIQwASghojzdtvVCiBoickyO7+dx/qC3MJ2/nVF/zi/Ht3yFXMcJYDFiAkdUVBQaGhqQlJTEguQDiAgNDQ2Iiory6LhBL0YAigDYJ8mXAigBUOCH43xOb2G6QIwZeYL+G09TUxNSU1N91jZ7MWKYQDBu3DgcPnzYpkYk0z+ioqIwbtw4j44ZCmKUD0dRqQDgmBzvm+N8jt4ZdXZ2IiwszO9jRnKtJE/Pr9/fn2LU0tICAKiqqkJsbCzS0tJ8dh2G0RMeHo6JEycGuxnDnkEtRkIIA5SxHps0LCIyCyEghDA5C7l5e5y/0LuftrY2v2bT6cWkq6vL44Kpesfi65VonTkjOU+B074ZZmgz2LPpjIAiIi5ed5x23L/j/ILeGbW3tzuE6Xbt2oXHH3/cJ+e3FyNPnZFejPQJB77AXow4o45hhg+DXYy8LYbk8XFCiEIhRIUQosLXsWW9+5FipE9guOaaa3Drrbdi+/btHp/7o48+QlhYGLZt2wbAdumI/oqRr8d17MXo2LFjPj2/r2lubh6Qk4cZZjAy2MUoYBBRGRFlE1G2XBLcVzgTI70zqqysBKDUbfMUWbbomWeeAeDbMJ0/xailpQVNTU3a84HokubNm4fJkycHuxkMMyQYEmKkjgEF7Dhfow+jdXR02IjR/v37tdf0N2d3kZV0jx8/DkARoOjoaO33gRyma25u9tu1+ovVasWuXbtQW1vLa0MxjA8Y7GIkkwxs6pvrRMZVEoK3x/mMpqYm7du+/c1MH6bbuXOnzTGeIrPSZPmerq4uxMTEaNcdyGG606dP++1a/aWurs7p7wzDeMegFiM1AaEGjmNARgBmVxlx3h7nK+rr62E0GnH//fcDsHVGAGyc0Z49e7Tt3tRusxejzs5OTYwGcphuIDqjv/71r/jHP/4BADbjWQN9bIthBgODWoxUNkMp6aMnU93uj+P6zYkTJwBAK2LozBlJMZILZSUkJHiVSi3F6NSpUyAiWCwWxMbGAnAM09mLojP8GaazLwc00JzRbbfdhquvvhpEZONS6+vrg9gqhhkaDAUxKoZjxYQidTsAJfwmhKgWQhR6clygcOaMZJhOugOj0ejVzV/exPfs2YPdu3cDgI0z0ouROy5JLwq1tbWIj4/HunXrPG6X5IUXXsDRo0cBKM4oIiIC4eHhaGlpGVDOqKOjQ/v91KlTNi7VbHY1QyB4PPvss0hOTh6Qa1YxjDMGvRipIbdiIUSJECJfCLEKSs05+1Cb0cvj/E5vzqi5uRkRERGIjY31yh1IZwQAM2fOBACXYTpnA/FWqxULFy7En//8ZwC2YrRjxw6cOXMG1157LQDg8OHDmDx5Mqqqqtxqm9lsxrXXXotzzz0XgCJGUVFR2nsdSM5ICiagOFu9M5Ji1N7errneQHP8+HF88skn2vP77rsPDQ0NeO+994LSHobxlEEvRgBARJVEVExEG4horX3lbSIyE9EIIirz5Dh/IW/6sqpAbwkM3d3diI6ORkxMjFfuQC9GElfOyJkY7d69G++//z7uuOMOAD2iEBMTo914Ozo6cODAAbz44ovYt28fHnvsMbfaJjP8Dh48CKBHjGJiYhzEyFtn1NjY6Fb4sS/0bTl27JhTMZo2bRrOPvvsfl8LAB588EH85S9/cXv/8ePHY/78+Q7V2L/55hsAymfNV/PjiMjGGba1tXm8vpW+okZXVxf+9a9/+cVhNjQ04P333+/XOerr6/02tcAf64L5ijNnzti871OnTvn1S+GQEKPBhj7kA/SewAAoRQejo6O9dkbp6ekYOXKkts3VmJEzMZKhspAQ5aMi25CUlGQzcJ+Zmalllblb+ViKkaQ3MWptbQUR4fXXX3f7H/jYsWOYOHEifvKTn7i1f2/oQ4YNDQ1obGzUQopmsxldXV2ora1FXV2dNs7nLXV1dVi9ejVuv/127bPx97//HS+99JLLY+Tfcc+ePejq6tL+FocOHQKgiFtqaqpHiyi64g9/+AOSk5Px0UcfgYhw/vnnY8KECVoCymOPPYZ7771X2//w4cM2grBhwwakpqbi008/BQA88MADuOqqq3DnnXc6vB9P2bNnD2699Vbts3X77bdj4cKF+Ne//gUA2LZtG+69916nX9IA5W/71FNPaZ/zrVu3YvTo0bj++uu1dv3+97/H008/3WdbrFYrDh8+rD0vLy+HyWTCG2+8AQDYuHEjDAYDrr76agBAdXU1brrpJrz99tsAFJEvLy/X2mKxWPDRRx9pbTebzXjooYfw1VdfAQC+++47XHPNNVrYvKOjA59++ikOHTqEjo4OG9f+3//+F/fcc4/2OXn99dcxZ84cvPzyywCU8WyDwYAFCxagvb0dn3/+OcaOHYsJEyZo4X5fI7jml+dkZ2eTnEzqDbP/PBtfffUVomOiMSdnDmpra3Hg3weAbQDCgUn3TsLYsWPxwQcfAAAioyIxuWUyYvbE4N///Tfy1zmuZ39z9s1YdtYyHDp1CNdsvEbbvmPHDnR3d+PO79+J+666D0gCRi4fibq6Opxzzjlobm5GTU0N8CFw5KMjqAupwx3v3KEd39TUhB07dkC8J2CtteLq31yNl46/ZCOOMbExaH2lFYZ2A8xGM0bmj9RqyklKLyvF1OSpeHPPm3j404cBKAv77dq1CwBw8NGDWLVyFT6o/wCnp55GVHQUQkJCcLJO+TZfuqgU8zPnY+bPZ8KwwIBzzjnH5vxv//xtxITH4IltT2Ddt8o/47Fjx7B3714AgPlRM44cOYKbX7gZzaObkZCQoB0bHR6N//z8PwCAP3zwB2zZvwWAEo4TQmB6+nQsj1uOH/zgB8AiYMqiKWhubkZ9Qz1AQLoxHf9Z8R9MmjQJuBiYfclsm/NPSZqCsh8qprzwzULsbdhr0/ZZo2bh0YsfBQBc/erV2Fm7Ezt27AAAzJkzBwsnLUTJ4hIAwBX/vAJN7U1ob29HaGgowsPDsWD8Aty/SMnMzHw4ExGxEfjss88AAPHx8bjnp/eg9LpS7Nu3D6nFqZg2bZrN9ZfOXIpbcm5Ba1crLv3HpbDnunOuw2wxG6NMo/DTV3+Kzz77DB0dHUhNTcWECRPwxeNfAN8C/2/j/8PfzH/TPrfz5s1DZGQkjr5yFN+99R1e++g1PLLvEVR+WYnm081ITVXacvifh1H9bjWiJ0Yj+3fZOH36NHbu3IkJEyZg/PjxeGDRA/h+2vex9dBW/GbLb2zaZrVaMf/MfNy+7HbsbNmJ/L/m45T5FFJTUzFlyhRs3boVltcs+MG8H+DGkhux7M/L0N3VjYkTJ2L8+PGoqalByOsh2LRuE77q+gq3vXAb6urqMHbsWEyaNAlVVVU48dcTQCvwUPlDeOqzp1BdXQ0AOOussxAdHY0HZj6AC869AL97/Xd4peoVjBo1CuHh4fh217eoP1mPv13wN9xwww2YcNUEHIw6iOjoaOTk5KCiogKtp1qBfwCbNm3CNc9cg7rYOogQgazMLOzbtw/mo2ZceOJCbNmyBXN+MweVdZVINCRi1jmz8O2336K+ph4JmxPw+eefY/7/Nx8N4coXobFjx6KxqRFth9qAN4GIiAh0LumEcbIRCQkJ2ljiaDEaW+/ZinPOOQenc09DJArMnj0bO3fuhJWssOy34Nqx1+KLL75ATU4NrJFWLDm2BG+99ZbD58QdhBDbicg+cQwAO6OgYG/57b8QSBcC1WCEhoQiIjzCK2dktVoRGhqK+LielVlDQkO01/TXdjVmpKejvQOhoaE9bQQwc4YyFiXDLO5OAtU7wm5Lt1Z9IiQ0BFaLFZZui+YQ29vbtTCT3jH1ht7NbNy4Eeeddx4+/PBD7N27F52dnaiqquq1rVVVVdi9ezeIyOZccn5WeJjiYDs7O7UbFOBeIojcT++i3n77bWzdutUma7K9vd02XNmqhCs///xzbZHDltaeb/ntHe3a9cPDw9He0Y7m5mateoc3GZmffvopZs+ejd/97nfo7OzUnH1TU5PN+XZ+s9PmM9rc3Awiwnd7v1PO89mnICKcaVacrdlshsViQU11DebNm4e2tjY0NjaitrYWVqvV6YRii8ViEzarPViLNWvW4IYbbsCZM2dwyqy050TdCRw/fhwWiwUTTROxZcsWfPD+B+juUs538uRJtLe349ChQ6g9UIs//elP6Ozs1DIjj584rl1r/vz5AIB3y9/FgdoDSDQkIjY2Ft988w22bduGvLw8GAwGPPTQQ6ipqcE333yD06dPo/6kcq7f//73+Oqrr3Dw4EHEx8ejra0N+/btQ2trK2bOnIm0tDQsWbIEdSfqMHXqVISFhqGiogJmsxmjRo3CBx98gNzcXFRur0R4eDhOmU/h6x1fo76+HpMnT1a+ME2fjoaGBsycORPJyck4cuQIrBYrLlxwIR555BHcfPPNmDVrFsynzDhw4ABGjBiByZMna9EDi8WCxYsXIzQ0FJWVlejq6sI5Z5+D7Oxs/P3vf8fevXsxd85czJo1Cy+++KLHnyG3ICJ+ePjIysqi/vD2228TAJo6dSoREf32t78lANrjb3/7GxERRUVFEQCaPXs2/fznP6eMjAyPr5WZmUmXXXYZVVVVaee/7bbbCAC99dZbdP/992vbq6urHY7/5z//SQAoJCSEiIiWL19OY8eOpfPPP58AUGhoKFmtVpv2n3feeW617S9/+Yt2zMmTJ+niiy+mOXPm0KJFi+i8886j888/n2bOnEkA6LHHHqONGzcSAIqMjHTr/LNmzaIFCxZQUlKSdp1LLrmEANAvfvELAkB/+MMfiIjIarXS/fffTzt37iQiIovFoh1TV1dHZWVl2vPi4mJasGABzZ8/n3Jycujiiy+mxx9/XHv9ySefdKt92dnZBIA++eQTeuutt2z6UD6eeOIJ2rJli/a8vLycjh8/rj1vaGigL7/8Unv+29/+ll577TUCQD/60Y+0zxMAKigoIABUX19Pt912G1155ZXU1tbWZzvlcTExMfTcc88RALr++usJAH3/+98no9FI6enpVFBQQC+88ILWlgcffJD27NmjPb/++utp165dBIAyMzMJAD3//PPaZ9FoNNKsWbMIAF111VUEgC6//HL65S9/Sb/97W/pxIkT9OMf/1h73Wq1kslksrkeAHruuedICEEAKCkpSft/A0CTJ0/W9rvxxhtJCEHnnnsuJScn06uvvkoA6M477yQAdNNNNxEA+ve//00XXHCB9nn/9ttvqaqqihYvXkz33HMPvfLKK1RUVER//OMf6emnn9auNWLECFq/fj0BoMTERAoLC6OjR4/S+PHjCQClpaVRR0cHvfbaa5SUlET33XcfERGVl5fTtGnTaM2aNUREdM011xAAmjNnDrW1tdH8+fMJAM2bN486Oztpw4YNFBsbS3fddZf2Wd67dy91dnY6/C2PHz9OX3zxBVksFiIiWrlyJcXGxtKGDRuIiGjjxo00atQo7dpdXV303HPP0X//+1+3PtN9AaCCXNxXg35jH4yP/oqRvKlKMSouLra5Ab3wwgtERBQfH6/9w9900000evRoj681depUWrp0KR08eFA7/+rVqwkAbdy40UYI9+zZ43D8s88+ayNGV111FU2ePJmWLFmi/cMR9dywvve979HMmTPdatuaNWtsrr1gwQK64IIL6Ic//CHNnj2bzjnnHLrooosIAD300EPaTTU8PNzlOS0WC+3evZuIiGJjY+n222/XbipnnXWW1vcXXnghAaDbb7+diIgaGxu1thARnThxQnu+e/duevjhhwkARUVFUWFhIZ199tl0+eWXU15eHs2bN49+9atfUVhYGAGge++9t8/3brVatS8bd911F40fP57OPvtsmj59OgGg3NxcioyMpDvvvNNGCJ977jn69NNPtedffPEFbdq0SXt+3XXX0RNPPEEA6IEHHtDeq8FgoPLycgJA9913n7b/888/74DtG10AACAASURBVLJ9FouFrFYrpaSk0LRp0wgAJSQkUEREBH377bfaOa644gq68sorafLkyXTHHXdQdHQ0paSk0A033KAJY2xsLM2dO5fWrVuniSwAmjZtGoWFhVFzczMtX76cAFB0dDQ1NDTQLbfcoolgSEiIdj0pNE8++SQBoDVr1lBoaCgBoLi4OOrs7NQ+j8XFxdTR0UHJycmaMH/33XfauS666CJNhNLS0ighIYFaW1spNTVVe7/t7e30wQcf0JQpU+iRRx7p829bVFREISEh9Mwzz5DVaqWsrCxNQImI3n33XVq4cCG9++67fZ6LSBGETz/9lFpbW4mIqK6ujkpLS+nkyZPaPlJcBjq9iRGH6YKAfRjHWQIDAC1E1d9sutjYWC1pAXCdTeds0Nh+oLe1tRUxMTFafTtZ++6ll15CTU0NcnJy3M6K0od0GhoanCYwyMX7WltbtQw2feiwq6vLpv9uvfVWTJ8+HZWVlWhpacGYMWNw9913Y8mSJfjLX/6CjIwMANDGNWToz37iqv491NfXa6Gy8ePHo6mpCY2NjTAajTAYDGhqakJ1dTWmTJmClJQUh8QMZ5w4cUIb8H/44Ydx8OBB/PrXv8aKFSsAAFOmTIHJZEJ1dTW+++477bi6ujotKQGAljQBACNGjMCRI0dw5MgRhIaGIjs7W3uvCxcuRE5ODgAl7TshIQGJiYla7P+xxx7DlVdeCbNZGVszmUzIyMjAe++9h5MnT2LVqlWYPn06Tp8+jXPPPRfTp0/X+nLJkiU455xzsG/fPrz//vuYPXs2ZsyYgT179mhjgj/+8Y9RVVWFb7/9FkIIXHXVVYiIiEBVVRVycnIQFxeHe++9F/n5+Xj++edhNBrx+OOPo6mpCWfOnME777yD0NBQpKam4siRIzAajbj55psRERGBlStX4uKLLwYAXHLJJQgPD8fzzz+PDz74AH/84x8RERGBjz/+GK+88gquv/56TJo0SRs3W758OS655BIkJCTg0KFDuPTSSxEdHY0bb7wRgJIAERkZiQsuuAB79uzRskp746mnnkJbWxuWL18OIQTWrVuHhx9+WMsyzcvLw3vvvYe8vLw+zwUo94F58+Zp/3MpKSkoLCxEcnKyto8+bD5YGdSL6w1W7LPpnKV263/2N5suNjZWEyDAs9Ru+2tKMZLnSExMBKD8w0ycOBEGg8FtMdILXWNjI9ra2jBy5EhNjFpbW2E0GhEREYG2tjatrfpsvdGjR2POnDlaBpLMJPrPf/6jvZ6RkYF33nkHgGMqrcwwshcj/VhIQ0MDmpubERsbi6SkJDQ2NmpiFBYWBrPZjOrqamRkZCAkJMQtMZIJCueffz4++ugjAMpNPSoqCidPnsSvf/1rXHfddaiurgYRYcaMGdi/fz/q6uq0z4Vsv/w8zZ49G0eOHMGhQ4cwduxYm9VLlyxZgsTERGRkZKC6uho33ngjmpubsWHDBlRXV+MXv/iFdg6z2awNcOfm5gIAFi5ciNDQUCxfvhz/8z//AyEE3nrrLbz55pu48cYb8c4774CI8NVXX+G2225De3s7Xn31VezatQvjxo3D3Llz8eKLL+I///kPpkyZAoPBgHnz5uHDDz/EZZddBgBIS0vTqpJI5JedvLw8bN++HcnJyRg9ejRWr16Nu+66C0uXLoXBYMCjjz6K0aNH4ze/URIcYmJicMEFF2jnmTp1KqZOnao9f+ONN/Dpp5/iqquughACJSUlePLJJ/H73/8eAPC///u/yM/Px+zZs/v8WzojIiJC+91kMuFXv/qVV+cZTrAYBQF3nZH8GR0djejoaHR2dsJisSA0NLTX8//973/Hnj178Mc//hGtra2IjY1FZGSk9ronk17ljU6f2u1MjCQGgwEtLS3KAL/upukMvRjZOyNZgSEhIUETYtlPMoEgJCQEDQ0NmvDo++zDDz8EoIiRnri4OCQkJGhORwqHXoy6urpsxKi+vl5ry4gRI3DgwAG0trYiKSkJISEhaGpqQnNzM3Jzc9HW1qYJ3LPPPouDBw9qNQifeuop1NTU4MEHH9QK4N5555346KOPMGvWLC39/oEHHgAATJo0Ce+99x66urowbdo0tLa24sSJE7BarYiMjERXVxeOHz+O7u5uhIeHY8aMGaioqMCoUaOQlpaG9PR07T0sWbIEgHKTfeyxx3DnnXfi888/x7PPPouLL74YERERGD9+PJ5++mm0trbiJz/5CUaMGIFnnnkG48aNQ3p6OtLT07F06VJERUUBUOZVSYcxa9Ys7Vpz587FsWPHUF9fj48//hgzZszQsiu/+OIL/OxnPwMAPPnkk9i4cSN++ctf9vo5kegzKO+44w5Mnz4dF110kdZX7qRbSyZPnmyz/MfKlSuxcuVK7XlYWBgyMzPdPh/Tf1iMgoC8qcpv+O44I3nzb2trQ1xcXK/nv+666wAA99xzDzo6OhAbG2vjJjwJ00mxslgsICLNrdiH6STy+alTp2zCCM5oaWnRnFRjY6MmRkajUZtUmZCQYOOU9MfqhVQJR/fU8vvyyy8BOIoR0COwSUlJTp2RfZZYQ0MDTp8+jfj4eBiNRk38UlJSQETo7OxEZ2cnMjIytBtwe3s7brrpJgBAYWEhRowYgZtvvhkAcPnll2PHjh0YPXo0Lr/8crzyyitOJ8tmZWWhtbUVVVVV+NGPfoSjR4+irq4OHR0dmDBhAk6dOoUTJ07AYrFg5MiRGDduHE6fPo1du3bhoosuQlhYGP72t79pc80A4Gc/+5kmBomJiTAajdi3bx/uuOMOzJo1S5tPs2LFCsycORO1tbVYvny51iYpRPakpaUhJSUFJ0+exJIlS7Q5RAcOHMDll19uk+qflZUFAJgxYwZmzJjh9Hx9ERYWpqTaM0MGFqMgIMVI3kDddUaAe2IkkTdkfYgO6HEz7oTp5A2fSCmy2tLS0qczApQxl77EqLW1FaNHj8bp06dtnNGYMWO0fdLS0hAdHY22tjabqgctLS02adGtra02S2LIsSBnYlRSUoLi4mJce+21ePTRR9HV1WVzrlOnTtmkU8swXUJCAlJTU7W/28SJE236b+rUqaitrcXx48ehn4dWVVVlcxP/8MMPsXPnTk2ArrzySqf9s3jxYu33Sy+9FLt378bBgwdx+vRpjBs3DtHR0Th+/DiICCNHjsTYsWMBKKG78ePHAwBuuOEGp+cGlDlI5eXl+OSTT7BixQp0d3drYpSbm4vQ0FC8++67Lo/XI4TA119/jebmZiQlJdmExGbOnIkxY8YgLS0Nhw4d0lwaw+gZ/KNegxA5AC9van05I5nAAPRdo03vFmQoSJ+8ACiOAHAvTKd/vbOz0yFMFx8fb7O/Xoz6oqWlBXFxcRgxYoSNM9ILiMlk0pyRvRjpr9HU1ORQ7iYiIgIjRoxwuO7tt9+O1tZWTJkyBURKmRy9Mzp16pTmjGJiYrQEhvj4eKSlpWn7ZWRk2Jx/+vTpGDVqFNrb27UxLEBJMpDiFBoaiq+//hq7du3C9773vV77Z+TIkfj444/xj3/8AxdeeCFGjlQmKx85cgRpaWlITU3F8ePHUVdXZyNGAGza2RuZmZn4xS9+gaioKMTFxWHnzp04duxYn6FgZ4wePRpTpkwBAJvxqgsvvBCAUs1gy5YtWo1EhtHDzigI2DshdxMYgL5rtOm/0bsjRu46I/m7FCP5TV8/UAt4LkaxsbEwGo2aM4qOjtbCOABw9tln24hReHg4urq60NLSYpOMIMdtAEUgm5ubMWrUKJeliUJCQjTRO3r0qI0YnT59WhOjiRMnas5owoQJmDBhgrbfhAkTbEoijR07FqNGjQIAvPLKKzCZTDhw4AAOHDiA/fv3Y8yYMfje976H119/HR0dHW7VsTvvvPNw3nnnAYAmPkIIjBs3DkSEqqoqhISEYOrUqTZidNZZZ/V5bmd4e5w9YWFh2LhxI06ePKkJ1Lhx4zBu3DifnJ8ZerAzCgL2zshVmE5+O/XEGenHOmSRTFdiZL/Sa29jRvJ3KUZSuPojRjK5IikpCfX19ejo6EBkZCTGjRuHTZs24euvv9YyAaUYyZuZvRg1Nzdrzkg6DmchOj3y5n3kyBGnziguLg4jR47UnFFCQgIuuugiRERE4NZbb4UQQhsEj4yMhBBCS0Xfu3cvFixYgLFjx6K2thbbtm1DTk4OZs6cqaV09+WM7Bk5ciSICFarVRO+48eP48SJE9qYkUQv6MHiiiuu0FLVGaYv2BkFAXedkdzPfsyoN/TOSIqR/ZiRFAxXzuivf/0r0tLScMUVV9iIUXt7O9rb2xETE4OcnByEhobixz/+sdNzu7NEuhx/IiKlPh56hFM/XhIdHY26ujo0NTVh6tSp2L9/v4MYnTlzxkaMtm7dCqPRZtUQB/Ri1NDQgAkTJqC2tlYTo8TERCQnJ2PHjh1obm5GfHw8EhISUF9fr7UzOTkZb7zxhjYQL50RoLia7777Dl9//TX27NmDq6++2sa92Nfv6wspdIDiMtra2rS/T0pKCmJiYrB+/XoQkdvjigwzUGBnFAScOSN96rW9GOmz6fpyRlKMYmJitJuzvHEuWLDA5vxyzEgKXXd3NxobG3HbbbdpIqMXI/04Sl5eHrq6ujB37lyb68sxFLPZDCLCli1btPdpjwzTJSUlaRM57YVTbquvr0dXV5f27b+1tdVGjFpaWrT3K9vU10TAkSNHIjQ0VAvTmUwmAD1huoSEBCQnJ9skMABKGFB/7h/+8IfaBFC9O5k/fz7S09Px9ddfAwBycnI0NzRmzBibv7k76IVu3LhxNs9l0kd+fj4KCuzXjGSYgQ+LURBw5oyciZF0Kp44I/m6vLECPWL09ttva5Wow8LCNGekT/WWs/klejGSoTe5v7PxmNjYWISHh6OhoQHPPfcccnNz8c9//tNpW2WYzmg0anOOXImRXNzOVZhOOqOYmBgsXboUl112GdasWeOynwAlDDpq1CgtTCf7TDojg8GA5ORkLYRon6zhDIPBgAsvvBDTpk3D5MmTbf4OWVlZyMrKwiOPPOKyT3pD76SmTZtmk6TgbsICwwxUOEwXBOxTu/sSI0+ckZxDk56e7jBmpBc1mQjQ1dVl44zsz68XIxl6k/s7QwiB0aNH49ixY5pYyEQKe2SYTn+TdyVGMpzYmxjV1dUhNTUVsbGxePPNN122UU9aWhr27t2LhoYGjB07FjExMZoYJSUlaeNrAJxm5jlj06ZNAJS+0E/UlKnu7pSUcUZqairmzp2LlJQUREdH26RP6xMrGGYwws4oCHgapvPEGenFSGKfwCCvIcN0UgD6EiPpjJydT8+YMWNw9OhRLWRoX2pHXqujowNxcXE2YzvOzq0XP70YNTc3a33V0tKipTh7wrx587B161YQEcaOHYuEhASHMSNJX2NQksjISO3vmZeXh0suuQQbNmzwqF2u+OyzzzShTUlJ0bbr/94MMxhhMQoC7joj6Qb0YuSJM5I4cxvOnFFXV5dbYuTsfHqkGEkR0ovRs88+i3379mlhubi4OBv34coZSWQCgHRGUnzOnDmjZZV5giwnI8+dmJiI06dPw2w2O4iRvp3uEhcXh7ffftsnq83aI4TAgQMHsGvXLrdX12WYgQqLURCQzkj+tHdGslq3szCdr5yRszEjV85IimN/xaiyshI33XQTbrnlFk2M5JiRpC8xSklJQUREhCZGiYmJiImJsQnTecLChQu132fPno3ExESbMSP9WIy7ziiQTJgwweOsPIYZiPCYURCQzkhf+NOZM5LbPHFGcg6LXozs5wLJazgL09mLXWdnJ+Li4tDU1ORRmM5sNuPgwYMAesSoqqoKgFKRQC9G+nCTfa07wDZMN2LECK2Q6pkzZxAXF4fY2FhtnpGnzkg6lz179mDMmDFISEjQ6r8lJiba9CMnCTCM/2BnFAT0jkj+dCZGMkQks99iY2P7nEwqnZGsTSaPtyc8PFyb9NpXAoOcs+KJMwJ6lmeQdd+kKJ05c0ZLPoiLi7Npqz5dWaK/XmKisuSzXozi4uJw6NAhWCwWj50RoKyBI5MKEhMTNRGVrkviqdAxDOM+LEZBwF1nJOfLyEoMMs24N6QYyTkxrtCPGelTu/ViJCtSeytGgCKEDQ0NsFqtWts7OztdhumcOSP99UJCQmzESC4cWF1dDaD/gpGYmKiJpywC+91332lVqBmG8Q8cpgsC9s7IXoyk+PzpT39CXl6eJkpyAmZvSDGSoTlXIbWIiAht6QN9mE4/B6q7uxudnZ2aQ/NGjKZOnYqqqiqYzWZNjBobG7VMO7m8xTXXXIP9+/c7dXH215NiJKsixMXF4bPPPgNg6wi9QS/iUhgnTZqESZMm9eu8DMP0DotRENCLkHzubDZ+ZGQkrrjiCu15cnKyQ2Vqezo6OhAREQEhBI4cOeJyln9cXBzOnDnjEKbTlyaSYtUfZzR9+nRUVVWhvr5eEyOr1Yra2lqtHYCyIKCrSg32y1TExsZqFRji4+NtBLe/YqR3afbXZRjGf3CYLgg4c0Yyg643xo8fry0HLenu7rapR9fR0aFV1B4zZozLdGSZNdZbardMcPBUjPShNlmZuqGhwSbEaF+LDnA+tgXYLkcgj5HOKC4uTps0GxYW1mdx1L7Qj1n1tR4TwzC+g8UoCNiPGVksFrfEaNKkSTh58qRNEsPKlSuRmJioCZysfN0XcnJnZ2cnIiIiEBoa6pDA4MwZhYSEOM3O06MXFb0YNTQ0aM5DipE7BT1ldYHLL78cALTsudbWVsTHx2vZeOPGjfNqHR49ejHj5Q4YJnCwGAUBZwkM7txEZZFNuYIrADz//PMAoK2r464Y6Z1ReHi4ll3Xmxg1NTUhJibGrQmW+fn5SE1N1RZSk85IVrd25oxcER4ejurqaq2eW0xMjFZDLy4uThMjX6Re6wXInVp0DMP4BhajIOBtmE4mMsjBeqBnjGP//v0AlHlG7oqRXLI6NjZWmwTbmxgBfYfoJOvWrcORI0c0pyFXU7UXI3fPZzKZtHBibGyslsihd0bOMvE8RS4u52lFbYZh+gcnMAQBb8N0RqMRU6ZMwRdffKFtk2ngjY2NANx3Rvqln+Pj4xEWFuYw6bW9vR0Wi8UrMRJCIDQ0VMt22717Nzo7OzFp0iRERETg9OnTiI6O7nOZB2fo3VRcXJxWjFSf7OEtYWFh+Pjjj3mCK8MEGBajICCdkfzd3TAdoISi5GRSoCeVW1ZecFeMfvCDH2i/x8XFOQ3TyblAUjSsVqtbYTU9QghMmDABFRUVAJRyPiNHjsThw4e9Lq9jL0Zz585FXV2dV7XjnCGX+WYYJnBwmC4I2M/lkc7oiSeewMcff9zrsQaDwSaBQYqR/qc7YqSfHKp3RnoxklUSIiIitKQFd52RnrPOOgs7duwAoIiRrJLgbbaaXozkuE5KSopXLothmIEB//cGAb0zslgsmjO6+eab+/xWbjAYtBVXgZ7K3546I6DnRh4XF6eNGbW1tWmhPylG4eHh/RKjX/7yl9rvs2fP1uYC6WvSeYK9M2IYZvDjlRgJIRKEELOEEOlCiN7rzjAO6J2RxWJxe8wIUBIP9M5IZrZ56owA28F6fZhOTvZsbm7WXu+PGM2dOxebNm1CSUkJxowZoxUf9aUzYhhmcOPWHVAIsQJAAYBsAASgBkCT+rJJCDFC3fYygA1EdMD3TR06uHJG7pCYmIjW1lYtJVuKkTfO6NVXX8WDDz6IOXPm2CQwJCYmor6+XnNG/RUjAFi8eDEWL14MAMjIyADg/ZIM+pI97IwYZmjgUoxUx/MbALMBrAdQQESnXO2vHrMIwN2qOJUS0Xu+bOxQwd4ZuZvaDfSIQXt7uxZOk8/lT1mBoS9GjRqFRx99FABsUrvlJFNfipGe6667Dl9++SXuvvtur47XV+b2RTo3wzDBx+kdUAgxG0AhgLVEtN/dkxHRFgBb1HOsEEJkEtH/+aSlQ4j+hOmk0LS3tyM+Pt6m8oL86c0cGXtnBPguTGdPXFwcnnnmGa+P15fsYWfEMEMDhzugEGIiABMR3dyfExPR00KIRCHElUT0an/ONdToT5hOipEUH7ksuDdhOj1ySYlAiFF/6W/9OYZhBh4OYqQ6IbfdUG+oYT0WIjv0zqirqwtE5LYzkkLT3t4Oq9WKrq4u7TnQP2fU2toKq9Wqhb70YiRDggNBjGJjY/Hwww/bhCkZhhnceDTpVQgxi4i+8ldjhgt6ZyQdjjfOSLoi/Xn6I0ay+rczZyQZCGIEAL/61a+C3QSGYXyIp6ndRfYb1FDcXUKIWT5q05BH74ykoHjjjKQAyedA/8J09mKkT2CQDozHaBiG8Qe9ipEQYp8QYpsQ4gEhxEXO9iGiU0T0EIAkV/swtjhzRt4kMNiLkQzbeeuMpBNy5ozktXheD8Mw/qAvZ1QAJTtuMYDNAApVcVojhLhIP+FVzaTjPFs3cOaMfBGmk8/7G6aTY0Z6ZyTFiJ0RwzD+oNev40T0JQBt8RwhxLsAygHkASgGQEKISgAVALar2zlhoQ/644x6C9PJUJ23YTpZsduZM5JCx86IYRh/4OmYUQ0RPUREi4koBEAOgHUAkqC4pwd93cChiK+ckV6M9M/dnfSqRy+G9mIUERHBYsQwjF/xdAmJ9fonRFQJoNJ3zRke+MsZyefehukksbGxCA0NtXFGo0ePRmNjI6dTMwzjFzxyRuq4ENNP9M5IhtY8TWDQO6GwsDCfilFMTAwiIiJsxozeeOMN/PznP8fZZ5/t8bkZhmH6wkGMhBAThRBX+uLkanXvm3xxrqGEL8J07e3t2rGJiYk24uTtmJEkOjoaERER2vIUkZGRMJlMePHFF70KATIMw/SFgxjJCgxCiCeFEOnenlit9L2aiLwvQjZEsVqt2s3fF2G6hIQEtLe3awvjeTMx1ZkzknBojmEYf+M0TKdm0d0NYKUQYpMQ4iZ31i1S1zh6SgixCUA1Ea32cXuHBBaLRbvZ+yKBITEx0adiFB0drYleZGSktkwFwzCMv3D5dVytK3c3AAghfgLgGSFEJpT1jMwAGtVdMwDI9YwqoCwd8aXjGRmJP5xRbW1tv8TIPkwXHR1tcz2GYRh/4tYdkIheAfCKfC6ESARggipKfa1zxNiid0ae1qYLCQlBeHi4jTPydZguKiqKxYhhmIDiaWo3AM01sfvxkv44I0ARC/sEhv6KkRSf6OhoCCFYjBiGCSieTnplfIAzZ+SJGMnyPPoxIyLSyvl4I0byGNkuFiOGYQIJi1EQsFqtXicwAD3OSB+mA4DGRmUYTwqJJ9gfw2LEMEwg8SpMBwDqXCQjp257jsVi0W723jijmJgYfPHFF2hpaQEAGI1GAMDJkycBKBUUPEU6I5k5J9vH84oYhgkEHi+uB2AlgCwALyubRAWAbVCy6HjhPTdwNmbkiTNKSEhARUUFvvnmGwA9teRqa2thNBq9mhfkKkwnz80wDONP+hQjdX5REYBlAKoBlBHRSt0uDwkhZkOZkyRFqoyITvujwUMBvTOSlbI9cUayMgKgiIg815tvvonp06d71SZ5DilG0l2xGDEMEwhc3gHVuUVFUOYQlRJRtqt91XlFK9XjVgB4TwjRoB7HS0rYYbFYNCciQ22eiJGsGQcowqQf15EhO0+R7ZHnSk5OBtAzHsUwDONPnN4BhRBPAWgCUKSWB3IbInoawNNCiIkAioQQy4hoWf+bOnSwWq2aE5Hp2J6E6erq6rTf29rabLLnnn76aa/aJBfNk2HDlJQUALYujGEYxl84FSO7MJxXqCJ2d3/PMxTprzM677zz8NZbb2nP09LStN+9DdOde+65GD16NO655x4APeE6LgXEMEwg8DqbTo8QIp2IDvjiXMOB/jqjl156CZs2bUJBQQEAID09HUD/lgSPiorC0aNHteeXXnopFi9ejDVr1nh9ToZhGHfx1TyjJllIVQiR6G5h1eGKPoHBGzGKj4/HnDlztOeJiYkoKSnBJ5984rM2pqenY9OmTRgzZozPzskwDOMKnzgjKEkOGUKIbUR0SgixHsqqsEt8dP4hhZz0KoTQkhH0Sza4w6hRowAA9913HwBg1apVPm0jwzBMIPGVGJUT0WTVFUlHlOSjcw85LBYLQkNDERkZqZXw8VSMIiIi0N3d7ZGjYhiGGaj4KkxXJoSYpRZQFVAmxS7y0bmHHFarVROj5uZmAN6V3WEhYhhmqOBSjDxZ5ZWIHgKwX/39lPo75wS7wGKxICQkBJGRkejq6gLguTNiGIYZSvTmjEo8OZF+TSM1rZtzgl2gd0YSFiOGYYYzvYlRgRDiX0KIH3uTGccL7rlGOiODwaBt4+rYDMMMZ/oaM1oMZYXXJiHEd0KIJ70VJ38ghMgUQhQKIXLlTzeOMQghVgkhTOrvJiFEiTvH+gKr1QpAGe8ZPXq0bBOP/zAMM6zpLZtuAxEtFUKYAOSqj2VQ6tWREKIGwGYA7xLRRv831Ra1XSVElKfbtl4IUUNENb0caoQSgpRhSDOAFUS02X+t7UEvRjI9W6Z5MwzDDFd6c0aNAEBENURURkRLicgIIAPAzVCWHV8G4BUhRIMQYqH/m2tDEYBSu22lcG+sKw/q3CgiGkFEG3zdOFdYLBYAQEhIiOaMvFnygWEYZijhUoxc1acjov1OxOkZAJuFEBP81E5n5AOotNtWoW7vEyIy9+Gg/IIzZySrMDAMwwxX+j3PSBWnYgA5ANb2v0l9I4QwADBBdW+6tpjV102BaIc3OHNGUqAYhmGGK76qwAAiqlRXfQ0ERvWaZhevmwD05npMQgjpoIwAGvsK1QkhCgEUAsD48eM9a60OZ86IYRhmuNNvMRJCXAmgRl1yPFATXQ197+ISORamiY+a+IDeBImIygCUAUB2drbX79OZM2IYhhnu+KIc0FoAW1RRGvBzi9SxojK7ze4mPvQbdkYMwzCO+CJMlwVgKRR3IxHDoAAAC71JREFU5PES4x6O7zTqQ3NCCEMvoTpPqIESuvPV+Vyid0bx8fEAgIsvvtifl2QYhhnw9FuM1EoLXq11LecKeXDINihOTI4HGaHME5Lnk+E7l+NFQohVRGSfaCETIUxwzNDzKVKMQkNDIYTA8ePHkZiY6M9LMgzDDHh8lsDgDWpqdYEXx5nVSbf2Y0dGAC5TtqX4CSE22O1jVH/6PdVbhulCQpQIaWpqqr8vyTAMM+BxOmYkhLhLCHFRf08uhJglhPh1f8/jgs0Asu22ZarbnaIKUJETscoFUOnvEB1g64wYhmEYBVcJDBsALFXr0a3xZDkJIUSCKmYVUKokbOl/M51SDEdXVaRul20xCCGq1bRsSaN+nEoN7RUBWOGndtqgT2BgGIZhFJyG6dQlIFYCgBDiJ1AWzyMApa6SFNT9iqCkd68nInvX4lPUUF2xEKIEyliSrFVn73qMdsdtEELkq/OMkqCE+goCVY1Bn8DAMAzDKPQ5ZkREr0CpPzcRQJEQYi2Acijp0GYoorUISnisSBWygEBElegl4UANu41wsj1gtejsYWfEMAzjiNsJDKrI3A3gbiHEIgC/geKCyojobj+1b8jBzohhGMYRr7LpiGgL/DcWNKRhZ8QwDOMIfz0PMOyMGIZhHOE7YoBhZ8QwDOMIi1GAYWfEMAzjCN8RAwxPemUYhnGExSjA2JcDYhiGYViMAg47I4ZhGEdYjAIMJzAwDMM4wmIUYDiBgWEYxhG+IwYYdkYMwzCOsBgFGHZGDMMwjvAdMcCwM2IYhnGExSjAsDNiGIZxhO+IAYadEcMwjCMsRgGGnRHDMIwjfEcMMFKMwsK8Wr2DYRhmSMJiFGC6u7sBcJiOYRhGD4tRgOFyQAzDMI6wGAUYFiOGYRhHWIwCDIsRwzCMIyxGAYbFiGEYxhEWowAjExg4m45hGKYHFqMAw86IYRjGERajAMNixDAM4wiLUYBhMWIYhnGExSjAsBgxDMM4wmIUYLgcEMMwjCMsRgGGywExDMM4wmIUYDhMxzAM4wiLUYBhMWIYhnGExSjA8HpGDMMwjvAdMcBYLBaEhIRACBHspjAMwwwYWIwCTHd3N2fSMQzD2MFiFGAsFguPFzEMw9jBYhRgWIwYhmEcYTEKMCxGDMMwjrAYBRgWI4ZhGEdYjAKMxWLhBAaGYRg7WIwCTHd3NzsjhmEYO1iMAgyH6RiGYRxhMQowLEYMwzCOsBgFGBYjhmEYR1iMAgwnMDAMwzjCYhRgOIGBYRjGERajAMNhOoZhGEdYjAIMixHDMIwjLEYBhsWIYRjGERajAMNixDAM4wiLUYDh9YwYhmEcYTEKMOyMGIZhHGExCjAsRgzDMI6wGAUYFiOGYRhHWIwCDIsRwzCMIyxGAYbLATEMwzjCYhRguBwQwzCMIyxGAYbDdAzDMI6wGAUYFiOGYRhHWIwCDIsRwzCMIyxGAYbFiGEYxhEWowDD5YAYhmEcYTEKMOyMGIZhHGExCjAsRgzDMI6wGAUYFiOGYRhHWIwCTFdXF48ZMQzD2MFiFGDa2toQExMT7GYwDMMMKFiMAggRoa2tDdHR0cFuCsMwzIBiSMSLhBD5AMxEtNnN/TMBZAOoAWACUOPusf2ho6MDRMTOiGEYxo5BL0ZCiFwATwMocHN/E4ASIsrTbVsvhKghoho/NROAEqIDwGLEMAxjx6AN0wkhTEKIUijOptGDQ4sAlNptKwVQ4qu2uaK1tRUAOEzHMAxjx6AVIyKqIaIiIirz8NB8AJV22yrU7X5FihE7I4ZhGFsGrRh5gxDCACdOiojM6usmf15fhunYGTEMw9gyrMQIgBHoER8nuBQjIUShEKJCCFFx8uRJry7OzohhGMY5w02MDN4eSERlRJRNRNkpKSlenWPGjBn48MMPMXfuXG+bwTAMMyQZ9Nl0g4mEhAScf/75wW4GwzDMgCPoYuThOE1jLyE2T65p8MV5GIZhGN8QVDGSc348OGQbgLX9uKScR2QEoImRmtigf51hGIYJIEEVI3WSqVuTVX10PbMQogaOY0dGKBUcWIwYhmGCwHBLYACAzVBKAenJVLczDMMwQWCoiJERTjLlhBAGIUS1EKJQt7kYjm6sSN3OMAzDBIGgJzB4izrOsxrK3CADgBIhRB6AciLaoNvVqD9ODdUVCyFKoIxByVp1HKJjGIYJEoNWjNRsuF7djLrPCCfbK+FYEohhGIYJEoKIgt2GQYcQ4iSA2n6cIhlAvY+aMxzg/vIM7i/P4P7yjP701wQiclo1gMUoCAghKojIPomCcQH3l2dwf3kG95dn+Ku/hkoCA8MwDDOIYTFiGIZhgg6LUXDwdA2m4Q73l2dwf3kG95dn+KW/eMyIYRiGCTrsjBiGYZigw2LEMAzDBJ1BO+l1sCGEyIRSE68GStWHGiIatvXwhBD5UIrTOvSBO301nPpT7SsTgAz1Z6ldlRHuMx1CiFwAeQAaoPTZdiIqs9uH+8sJamWbEiIqstvu//4iIn74+aH+Ycrttq0HYAp224LUH7kAmgDketNXw6k/AeQDyNQ9NwCoBlDIfebys5Vrt207gFXcX271XymA9XbbAtJfHKYLDEVQ/sh6SuHZWk6DHiGESQhRCuWD2+hiN3f6ajj1p4mU8lUAtBJXJbB9/9xnPRQ52bbZbjv3lxPU9eWMTl4KTH8FW4mHwwPKN1mT3TaD0v3Bb18Q+8SZM+qzr4ZLf6rvaTsAg912EwCSfcB9ZvOe1kMJM+m3lUAJ1fFnrPe+K1Qf9s4oIP3FzsjPqDFYBydA6rLnHi67PqRxp6+GU3+q78mkPpzCfWYLERUQkX0B5XwALwPcX65Qx9nWOdkesP5iMfI/RqDnD+OEIffB7gfu9NWw6k8iGkG6MJ1KLnpWJuY+6wV1LbNKIlqrbuL+co7BxfsNWH9xNp3/cVj0j3GJO33F/anE59eov3OfOUHNQMwDFLeke4n7yw4hRD7ZZWfqCFh/sRgxzCBC/abfqPumzzhBvbluUFd73g5ghROHOexRQ2yuHE1A4TBdgFD/6IwbuNNXw7E/1dh7ERHlOXmN+8wJauioFMAW/XbuL42l5MZcoED0F4uR/5HLmdukTOr+cLzceQ/u9NVw7s8SAIvstnGf9c1mAAZ1kJ77S0WdpFrRx24B6y8O0/kZIjILIWrgGFc1omcQmoH7fTUc+1Odn1VsP0jMfdaD6hy3A1jkIiRn4P6yIRtAhhBimW5bJgCTEKIEwDYi2hCo/mIxCgybofzh9f8gmep2xhZ3+mpY9ac6TlSi/6eW3/LVbdxnCgbYflOXyGwu+d65vwCQXYkkABBCrAKQY5ceH5j+CvZEq+HwgPJPYl8qoxxDvLRIH33SBCDfm74aTv0JZY5MofqPLR+5UOrTcZ859tcqOE4SLoduIiz3V6/9VwLHSa8B6S9ezyhAqPHZZQC2QfmmVklDvOiiPWoMeTWU958P5RvsZigf4g26/frsq+HQn2p/Nbl4uYaIMnT7cp+pqE4yA30XSuX+UlFDnMUAlkIRljIoX3gq1df93l8sRgzDMEzQ4Ww6hmEYJuiwGDEMwzBBh8WIYRiGCTosRgzDMEzQYTFiGIZhgg6LEcMwDBN0WIwYhmGYoMNixDBDCCFEphCiOtjtYBhPYTFimKHFMgyQ9WkYxhNYjBhmaJGLIVTMkxk+sBgxzNAiE0qBSoYZVLAYMcwgRwiRK4QoFUJIESpQn2cGtWEM4wFcKJVhhgjqWjTLiCgr2G1hGE9hZ8QwQ4c88HgRM0hhMWKYoUMueLyIGaSwGDHMEEA3PlQR1IYwjJewGDHM0CAXysqaZkBbJZZhBg0sRgwzNMiBrSsqDFZDGMYbWIwYZuiwHVBSvcGJDMwgg8WIYYYGawDkCSHyAYCIKoPcHobxCJ5nxDAMwwQddkYMwzBM0GExYhiGYYIOixHDMAwTdFiMGIZhmKDDYsQwDMMEHRYjhmEYJuiwGDEMwzBBh8WIYRiGCTosRgzDMEzQYTFiGIZhgs7/D4q5gJRzxgBQAAAAAElFTkSuQmCC\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "jmax = (N/2)\n", + "j2max = N/2*(N/2+1)\n", + "\n", + "label_size = 20\n", + "label_size3 = 20\n", + "\n", + "fig1 = plt.figure(1)\n", + "plt.rc('text', usetex = True)\n", + "plt.plot(t, jzt_tot/jmax, 'k-', label='PIQS')\n", + "plt.plot(t, t*0+jzt_ss/jmax, 'g--', label = 'steady state')\n", + "#plt.ylim([-1,-1+0.3])\n", + "plt.title(r'$\\langle J_{z}\\rangle(t)$, Total inversion', fontsize = label_size)\n", + "plt.xlabel(r'$t$', fontsize = label_size3)\n", + "plt.ylabel(r'$\\langle J_{z}\\rangle(t)$', fontsize = label_size3)\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()\n", + "\n", + "fig2 = plt.figure(2)\n", + "plt.plot(t, jpjmt_tot/j2max, 'k-', label='PIQS')\n", + "plt.plot(t, t*0+jpjmt_ss/j2max, 'g--', label = 'steady state')\n", + "plt.ylim([0,2])\n", + "plt.title(r'$\\langle J_{+}J_{-}\\rangle(t)$, Light emission', fontsize = label_size)\n", + "plt.xlabel(r'$t$', fontsize = label_size3)\n", + "plt.ylabel(r'$\\langle J_{+}J_{-}\\rangle(t)$', fontsize = label_size3)\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()\n", + "\n", + "fig3 = plt.figure(3)\n", + "plt.plot(t, adagat_tot, 'k-', label='PIQS')\n", + "plt.plot(t, t*0 + adagat_ss, 'g--', label = 'steady state')\n", + "#plt.ylim([0, 2*np.max(adagat_tot)])\n", + "plt.title(r'$\\langle a^\\dagger a\\rangle(t)$, Cavity photons', fontsize = label_size)\n", + "plt.xlabel(r'$t$', fontsize = label_size3)\n", + "plt.ylabel(r'$\\langle a^\\dagger a\\rangle(t)$', fontsize = label_size3)\n", + "\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# Here we study the time evolution of the Wigner function and of the photons in the Fock state basis \n", + "## Sampling Time integrations\n", + "nt_sample = 10\n", + "tlist = np.linspace(0, tmax/1, nt_sample) \n", + "result5 = mesolve(liouv_tot_int, rho0, tlist, [], options = opts)\n", + "rhot_tot = result5.states\n", + "rhocav_list=[]\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "xvec = np.linspace(-5,5,200)\n", + "fig, axes = plt.subplots(2, len(rhot_tot),\n", + " figsize=(3*len(rhot_tot), nt_sample))\n", + "for idx, rhot in enumerate(rhot_tot):\n", + " # trace out the cavity density matrix\n", + " rhot_cavity = ptrace(rhot, 0)\n", + " rhocav_list.append(np.real(rhot_cavity.full()))\n", + " # calculate its wigner function\n", + " W = wigner(rhot_cavity, xvec, xvec,method='laguerre')\n", + " # Wigner method:‘iterative’, ‘laguerre’, ‘fft’\n", + " # plot its wigner function\n", + " wlim = abs(W).max()\n", + " axes[0,idx].contourf(xvec, xvec, W, 100, \n", + " norm=mpl.colors.Normalize(-wlim,wlim), \n", + " cmap=plt.get_cmap('RdBu'))\n", + " axes[0,idx].set_title(r'$t = %.1f$' % t[idx], fontsize=label_size) \n", + " # plot its fock-state distribution\n", + " axes[1,idx].bar(np.arange(0, nphot), \n", + " np.real(rhot_cavity.diag()), color=\"blue\", alpha=0.8)\n", + " axes[1,idx].set_ylim(0, 1)\n", + " nmaxphot_bar = 10\n", + " axes[1,idx].set_xlim(0, nmaxphot_bar)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "QuTiP: Quantum Toolbox in Python\n", + "Copyright (c) 2011 and later.\n", + "A. J. Pitchford, P. D. Nation, R. J. Johansson, A. Grimsmo, and C. Granade\n", + "\n", + "QuTiP Version: 4.3.1\n", + "Numpy Version: 1.15.4\n", + "Scipy Version: 1.2.1\n", + "Cython Version: 0.29.8\n", + "Matplotlib Version: 3.1.0\n", + "Python Version: 3.7.3\n", + "Number of CPUs: 2\n", + "BLAS Info: OPENBLAS\n", + "OPENMP Installed: False\n", + "INTEL MKL Ext: False\n", + "Platform Info: Darwin (x86_64)\n", + "Installation path: /miniconda3/lib/python3.7/site-packages/qutip\n", + "==============================================================================\n", + "Please cite QuTiP in your publication.\n", + "==============================================================================\n", + "For your convenience a bibtex file can be easily generated using `qutip.cite()`\n" + ] + } + ], + "source": [ + "qutip.about()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "[1] N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, https://arxiv.org/abs/1805.05129\n", + "\n", + "[2] P. Kirton and J. Keeling, *Phys. Rev. Lett.* **118**, 123602 (2017)\n", + "\n", + "[3] E.G. Dalla Torre *et al.*, *Phys Rev. A* **94**, 061802(R) (2016)\n", + "\n", + "[4] J. R. Johansson, P. D. Nation, and F. Nori, *Comp. Phys. Comm.* **183**, 1760 (2012) http://qutip.org" + ] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + }, + "nteract": { + "version": "0.14.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/intro-run.ipynb b/intro-run.ipynb new file mode 100644 index 0000000..bf806a5 --- /dev/null +++ b/intro-run.ipynb @@ -0,0 +1,1284 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction to QuTiP\n", + "Contact: Nathan Shammah nathan.shammah@gmail.com\n", + "\n", + "You can find this notebook at https://github.com/nathanshammah/interactive-notebooks\n", + "\n", + "**Run this notebook live** at https://mybinder.org/v2/gh/nathanshammah/interactive-notebooks/binder\n", + "\n", + "This notebook has been developed for the interactive lecture on [QuTiP](qutip.org) for the [iTHEMS](https://ithems.riken.jp/en/events/quantum-physics-and-science-with-open-source-software-qutip-the-quantum-toolbox-in-python) Quantum Computing and Information (QCoIn) working group." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from qutip import *" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "QuTiP: Quantum Toolbox in Python\n", + "Copyright (c) 2011 and later.\n", + "A. J. Pitchford, P. D. Nation, R. J. Johansson, A. Grimsmo, and C. Granade\n", + "\n", + "QuTiP Version: 4.3.1\n", + "Numpy Version: 1.15.4\n", + "Scipy Version: 1.2.1\n", + "Cython Version: 0.29.8\n", + "Matplotlib Version: 3.1.0\n", + "Python Version: 3.7.3\n", + "Number of CPUs: 2\n", + "BLAS Info: OPENBLAS\n", + "OPENMP Installed: False\n", + "INTEL MKL Ext: False\n", + "Platform Info: Darwin (x86_64)\n", + "Installation path: /miniconda3/lib/python3.7/site-packages/qutip\n", + "==============================================================================\n", + "Please cite QuTiP in your publication.\n", + "==============================================================================\n", + "For your convenience a bibtex file can be easily generated using `qutip.cite()`\n" + ] + } + ], + "source": [ + "qutip.about()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum Objects\n", + "\n", + "### Operators and kets" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Let's define a quantum object. We can start from a simple \n", + "# bosonic destruction operator\n", + "n_max = 2\n", + "a = destroy(n_max)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 1.0\\\\0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}" + ], + "text/plain": [ + "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\n", + "Qobj data =\n", + "[[0. 1.]\n", + " [0. 0.]]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# in QuTiP, all number (Fock) states are defined on the \"basis\". \n", + "psi0 = basis(n_max)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}" + ], + "text/plain": [ + "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", + "Qobj data =\n", + "[[1.]\n", + " [0.]]" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "psi0 # it's a ket!" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}" + ], + "text/plain": [ + "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", + "Qobj data =\n", + "[[0.]\n", + " [0.]]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a*psi0 # destroing the ground state gives the vacuum" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\1.0\\\\\\end{array}\\right)\\end{equation*}" + ], + "text/plain": [ + "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", + "Qobj data =\n", + "[[0.]\n", + " [1.]]" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.dag()*psi0" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "n = 1\n", + "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", + "Qobj data =\n", + "[[0.]\n", + " [1.]]\n" + ] + } + ], + "source": [ + "psi0 = basis(n_max)\n", + "for n in range(1,n_max):\n", + " print(\"n = \",n)\n", + " psi = a.dag()*psi0/np.sqrt(n)\n", + " print(psi)\n", + " psi0 = psi\n", + "psi0 = basis(n_max)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Density matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}" + ], + "text/plain": [ + "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", + "Qobj data =\n", + "[[1. 0.]\n", + " [0. 0.]]" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rho0 = psi0*psi0.dag()\n", + "rho0" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0\\\\0.0 & 1.0\\\\\\end{array}\\right)\\end{equation*}" + ], + "text/plain": [ + "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", + "Qobj data =\n", + "[[0. 0.]\n", + " [0. 1.]]" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rho1 = fock(n_max,1)*fock(n_max,1).dag()\n", + "rho1" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500 & 0.0\\\\0.0 & 0.500\\\\\\end{array}\\right)\\end{equation*}" + ], + "text/plain": [ + "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", + "Qobj data =\n", + "[[0.5 0. ]\n", + " [0. 0.5]]" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mixed = (rho0 + rho1)/2\n", + "mixed" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500 & 0.500\\\\0.500 & 0.500\\\\\\end{array}\\right)\\end{equation*}" + ], + "text/plain": [ + "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", + "Qobj data =\n", + "[[0.5 0.5]\n", + " [0.5 0.5]]" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# let's define the Schrodinger cat state\n", + "cat = fock(n_max,0)+fock(n_max,1)\n", + "cat = cat \n", + "cat_rho = ket2dm(cat)/2\n", + "cat_rho" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0\n", + "1.0\n" + ] + } + ], + "source": [ + "# trace Tr[rho]\n", + "print(cat_rho.tr())\n", + "print(mixed.tr())" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0\n", + "0.5\n" + ] + } + ], + "source": [ + "# purity Tr[rho*rho]\n", + "print((cat_rho*cat_rho).tr())\n", + "print((mixed*mixed).tr())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hamiltonian" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "# We can now build a Hamiltonian, \n", + "# that of the Quantum Harmonic Oscillator \n", + "# exploring its features with QuTiP\n", + "n_max = 6\n", + "a = destroy(n_max)\n", + "\n", + "H = a.dag()*a" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "Quantum object: dims = [[6], [6]], shape = (6, 6), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 2.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 3.000 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 4.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 5.0\\\\\\end{array}\\right)\\end{equation*}" + ], + "text/plain": [ + "Quantum object: dims = [[6], [6]], shape = (6, 6), type = oper, isherm = True\n", + "Qobj data =\n", + "[[0. 0. 0. 0. 0. 0.]\n", + " [0. 1. 0. 0. 0. 0.]\n", + " [0. 0. 2. 0. 0. 0.]\n", + " [0. 0. 0. 3. 0. 0.]\n", + " [0. 0. 0. 0. 4. 0.]\n", + " [0. 0. 0. 0. 0. 5.]]" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "H" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "E_n , Psi_n = H.eigenstates()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0., 1., 2., 3., 4., 5.])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "E_n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", + "Qobj data =\n", + "[[1.]\n", + " [0.]\n", + " [0.]\n", + " [0.]\n", + " [0.]\n", + " [0.]],\n", + " Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", + "Qobj data =\n", + "[[0.]\n", + " [1.]\n", + " [0.]\n", + " [0.]\n", + " [0.]\n", + " [0.]],\n", + " Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", + "Qobj data =\n", + "[[0.]\n", + " [0.]\n", + " [1.]\n", + " [0.]\n", + " [0.]\n", + " [0.]],\n", + " Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", + "Qobj data =\n", + "[[0.]\n", + " [0.]\n", + " [0.]\n", + " [1.]\n", + " [0.]\n", + " [0.]],\n", + " Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", + "Qobj data =\n", + "[[0.]\n", + " [0.]\n", + " [0.]\n", + " [0.]\n", + " [1.]\n", + " [0.]],\n", + " Quantum object: dims = [[6], [1]], shape = (6, 1), type = ket\n", + "Qobj data =\n", + "[[0.]\n", + " [0.]\n", + " [0.]\n", + " [0.]\n", + " [0.]\n", + " [1.]]], dtype=object)" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Psi_n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "g = .6\n", + "H_driven = a.dag()*a + g*(a + a.dag())\n", + "En_driven , Psin_driven = H_driven.eigenstates()" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(E_n,\"o-\",markersize = 10, label=\"QHO\")\n", + "plt.plot(En_driven,\"s--\",markersize = 10, label=\"Driven QHO\")\n", + "\n", + "plt.ylabel(\"energy\")\n", + "plt.xlabel(\"eigenvalue\")\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Open Quantum System: Lindblad Master Equation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\\begin{eqnarray}\n", + "\\dot{\\rho}&=&-i\\lbrack H, \\rho\\rbrack +\\kappa\\left(a\\rho a^\\dagger - a^\\dagger a\\rho- \\rho a^\\dagger a\\right)\\\\\n", + "\\partial_t{\\rho}&=&-i\\lbrack H, \\rho\\rbrack +\\kappa\\mathcal{D}_{[a]}(\\rho)\n", + "\\end{eqnarray}\n", + "\n", + "* Non-unitary dynamics: Non-Hermitian matrix, $\\partial_t{\\rho}=\\mathcal{L}\\rho$\n", + "* Contractive map \n", + "* Linear map" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "Quantum object: dims = [[6], [6]], shape = (6, 6), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.001 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.017 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.096 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.273 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.390 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.223\\\\\\end{array}\\right)\\end{equation*}" + ], + "text/plain": [ + "Quantum object: dims = [[6], [6]], shape = (6, 6), type = oper, isherm = True\n", + "Qobj data =\n", + "[[0.00116956 0. 0. 0. 0. 0. ]\n", + " [0. 0.01671479 0. 0. 0. 0. ]\n", + " [0. 0. 0.09555111 0. 0. 0. ]\n", + " [0. 0. 0. 0.27311433 0. 0. ]\n", + " [0. 0. 0. 0. 0.39031997 0. ]\n", + " [0. 0. 0. 0. 0. 0.22313024]]" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rho0 = ket2dm(basis(n_max,n_max-1))\n", + "t = np.linspace(0,30,300)\n", + "kappa = 0.1\n", + "results = mesolve(H,rho0,t,[kappa*a])\n", + "rho_t = results.states\n", + "rho_t[0]\n", + "\n", + "rho_t[-1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us consider a driven, lossy photonic cavity " + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "results = mesolve(H_driven,rho0,t,c_ops=[kappa*a], e_ops=[a,a.dag()*a])\n", + "at = results.expect[0]\n", + "nt = results.expect[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(t,nt,\"-\",markersize = 10, label=\"$\\\\langle a^\\dagger a \\\\rangle$\")\n", + "plt.ylabel(\"photons in cavity\")\n", + "plt.xlabel(\"time\")\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Cavity QED: Qubit in a cavity" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "rho0qubit = ket2dm(basis(2,1))\n", + "rho0_tot = tensor(rho0,rho0qubit)\n", + "Om = 0.5\n", + "Hint_tot = Om*tensor(a+a.dag(),sigmax())\n", + "H0_tot = tensor(H,qeye(2))+tensor(qeye(n_max),sigmaz())\n", + "H_tot=H0_tot+Hint_tot\n", + "t = np.linspace(0,50,300)\n", + "kappa = 0.1\n", + "a_tot = tensor(a,qeye(2))\n", + "sz_tot = tensor(qeye(n_max),sigmaz())\n", + "sm_tot = tensor(qeye(n_max),sigmam())\n", + "results_tot = mesolve(H_tot,rho0_tot,t,\n", + " c_ops=[kappa*a_tot, kappa*sm_tot], \n", + " e_ops= [a_tot.dag()*a_tot,sz_tot])\n", + "nphot_tot_t = results_tot.expect[0]\n", + "sz_tot_t = results_tot.expect[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(t,sz_tot_t,\"-\",markersize = 10, \n", + " label=\"$\\\\langle \\sigma_z \\\\rangle (t)$\")\n", + "plt.plot(t,nphot_tot_t,\"--\",markersize = 10, \n", + " label=\"$\\\\langle a^\\dagger a \\\\rangle (t)$\")\n", + "plt.ylabel(\"System excitation\")\n", + "plt.xlabel(\"time\")\n", + "plt.legend()\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Bloch Sphere\n", + "\n", + "We can visualize a state on the Bloch sphere. " + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "b = Bloch()" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "b2 = Bloch()\n", + "vec = [0,1,0]\n", + "b2.add_vectors(vec)\n", + "b2.render()" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = (basis(2,0)+(1+0j)*basis(2,1)).unit() \n", + "y = (basis(2,0)+(0+1j)*basis(2,1)).unit()\n", + "z = (basis(2,0)+(0+0j)*basis(2,1)).unit() \n", + "b3 = Bloch() \n", + "b3.add_states([x,y,z])\n", + "b3.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Wigner Function\n", + "\n", + "You can find a Gallery of Wigner functions at qutip.org/tutorials and at R.J. Johansson's http://github.com/jrjohansson/qutip-lectures" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_wigner_2d_3d(psi):\n", + " #fig, axes = plt.subplots(1, 2, subplot_kw={'projection': '3d'}, figsize=(12, 6))\n", + " fig = plt.figure(figsize=(17, 8))\n", + " \n", + " ax = fig.add_subplot(1, 2, 1)\n", + " plot_wigner(psi, fig=fig, ax=ax, alpha_max=6);\n", + "\n", + " ax = fig.add_subplot(1, 2, 2, projection='3d')\n", + " plot_wigner(psi, fig=fig, ax=ax, projection='3d', alpha_max=6);\n", + " \n", + " plt.close(fig)\n", + " return fig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Coherent state $|\\psi\\rangle=|\\alpha\\rangle$" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "N = 30\n", + "psi = coherent(N, 2.0)\n", + "plot_wigner_2d_3d(psi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Schrödinger Cat state $|\\psi\\rangle=\\frac{1}{\\sqrt{2}}(|\\alpha\\rangle+|-\\alpha\\rangle)$" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\n", + "psi = (coherent(N, -2.0) + coherent(N, 2.0)) / np.sqrt(2)\n", + "plot_wigner_2d_3d(psi)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Squeezed state" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "psi = squeeze(N, 0.5) * basis(N, 0)\n", + "display(plot_wigner_2d_3d(psi))" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "psi = (coherent(N, -2.0) + coherent(N, -1j) + coherent(N, 1j) + coherent(N, 2.0)).unit()\n", + "plot_wigner_2d_3d(psi)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "NN = 8\n", + "\n", + "fig, axes = plt.subplots(NN, 1, figsize=(5, 5 * NN), sharex=True, sharey=True) \n", + "for n in range(NN):\n", + " psi = sum([coherent(N, 2*np.exp(2j * np.pi * m / (n + 2))) for m in range(n + 2)]).unit()\n", + " plot_wigner(psi, fig=fig, ax=axes[n])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum Circuits with QuTiP" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'q'" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "q = QubitCircuit(3, reverse_states=False)\n", + "q.add_gate(\"TOFFOLI\", controls=[0, 2], targets=[1])\n", + "q.add_gate(\"CNOT\", targets=[1], controls=[0])\n", + "display(\"q\",q.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'q updated'" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "q.add_gate(\"TOFFOLI\", controls=[0, 2], targets=[1])\n", + "display(\"q updated\",q.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'q2'" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "q2 = QubitCircuit(3, reverse_states=False)\n", + "q2.add_gate(\"TOFFOLI\", controls=[0, 2], targets=[1])\n", + "q2.add_gate(\"TOFFOLI\", controls=[0, 2], targets=[1])\n", + "display(\"q2\",q2.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0 & 0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}" + ], + "text/plain": [ + "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = True\n", + "Qobj data =\n", + "[[1. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 1. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 1. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 1. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 1. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 1.]\n", + " [0. 0. 0. 0. 1. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 1. 0. 0.]]" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "U = gate_sequence_product(q.propagators())\n", + "U" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " ### Time evolution of a dissipative system: Wigner function study" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "xvec = np.linspace(-5,5,200)\n", + "fig, axes = plt.subplots(2, len(rhot_tot),\n", + " figsize=(3*len(rhot_tot), nt_sample))\n", + "for idx, rhot in enumerate(rhot_tot):\n", + " # trace out the cavity density matrix\n", + " rhot_cavity = ptrace(rhot, 0)\n", + " rhocav_list.append(np.real(rhot_cavity.full()))\n", + " # calculate its wigner function\n", + " W = wigner(rhot_cavity, xvec, xvec,method='laguerre')\n", + " # Wigner method:‘iterative’, ‘laguerre’, ‘fft’\n", + " # plot its wigner function\n", + " wlim = abs(W).max()\n", + " axes[0,idx].contourf(xvec, xvec, W, 100, \n", + " norm=mpl.colors.Normalize(-wlim,wlim), \n", + " cmap=plt.get_cmap('RdBu'))\n", + " axes[0,idx].set_title(r'$t = %.1f$' % t[idx], fontsize=label_size) \n", + " # plot its fock-state distribution\n", + " axes[1,idx].bar(np.arange(0, nphot), \n", + " np.real(rhot_cavity.diag()), color=\"blue\", alpha=0.8)\n", + " axes[1,idx].set_ylim(0, 1)\n", + " nmaxphot_bar = 10\n", + " axes[1,idx].set_xlim(0, nmaxphot_bar)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "QuTiP: Quantum Toolbox in Python\n", + "Copyright (c) 2011 and later.\n", + "A. J. Pitchford, P. D. Nation, R. J. Johansson, A. Grimsmo, and C. Granade\n", + "\n", + "QuTiP Version: 4.3.1\n", + "Numpy Version: 1.15.4\n", + "Scipy Version: 1.2.1\n", + "Cython Version: 0.29.8\n", + "Matplotlib Version: 3.1.0\n", + "Python Version: 3.7.3\n", + "Number of CPUs: 2\n", + "BLAS Info: OPENBLAS\n", + "OPENMP Installed: False\n", + "INTEL MKL Ext: False\n", + "Platform Info: Darwin (x86_64)\n", + "Installation path: /miniconda3/lib/python3.7/site-packages/qutip\n", + "==============================================================================\n", + "Please cite QuTiP in your publication.\n", + "==============================================================================\n", + "For your convenience a bibtex file can be easily generated using `qutip.cite()`\n" + ] + } + ], + "source": [ + "qutip.about()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References\n", + "[1] J. Robert Johansson, Paul D. Nation, and Franco Nori, QuTiP: An open-source Python framework for the dynamics of open quantum systems, Comp. Phys. Comm. 183, 1760 (2012); QuTiP 2: A Python framework for the dynamics of open quantum systems, Comp. Phys. Comm. . 184, 1234 (2013).\n", + "\n", + "[2] Nathan Shammah and Shahnawaz Ahmed, The rise of open source in quantum physics research, Nature’s Physics Blog “On your Wavelength”, January 9th, 2019, http://blogs.nature.com/onyourwavelength/2019/01/09/the-rise-of-open-source-in-quantum-physics-research/\n", + "\n", + "[3] Nathan Shammah, Neill Lambert, Franco Nori, and Simone De Liberato, Superradiance with local phase-breaking effects, Phys. Rev. A 96, 023863 (2017); Nathan Shammah, Shahnawaz Ahmed, Neill Lambert, Simone De Liberato, and Franco Nori, Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance, Phys. Rev. A 98, 063815 (2018). \n", + "\n", + "[4] Nathan Shammah, A Guide to Building Your Open-Source Science Library, https://github.com/nathanshammah/opensource/blob/master/README.md" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + }, + "nteract": { + "version": "0.14.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/slides/2019-ictp-1-lecture-physics.pdf b/slides/2019-ictp-1-lecture-physics.pdf new file mode 100644 index 0000000..dd2b813 Binary files /dev/null and b/slides/2019-ictp-1-lecture-physics.pdf differ diff --git a/slides/2019-ictp-2-lecture-qutip.pdf b/slides/2019-ictp-2-lecture-qutip.pdf new file mode 100644 index 0000000..0942926 Binary files /dev/null and b/slides/2019-ictp-2-lecture-qutip.pdf differ diff --git a/slides/2019-ictp-3-lab-qutip-dyn.pdf b/slides/2019-ictp-3-lab-qutip-dyn.pdf new file mode 100644 index 0000000..d6df6dc Binary files /dev/null and b/slides/2019-ictp-3-lab-qutip-dyn.pdf differ diff --git a/slides/2019-ictp-4-lab-oss.pdf b/slides/2019-ictp-4-lab-oss.pdf new file mode 100644 index 0000000..6d539e9 Binary files /dev/null and b/slides/2019-ictp-4-lab-oss.pdf differ diff --git a/slides/2019-ictp-5-lab-interactive.pdf b/slides/2019-ictp-5-lab-interactive.pdf new file mode 100644 index 0000000..9381f6b Binary files /dev/null and b/slides/2019-ictp-5-lab-interactive.pdf differ diff --git a/sqd-run.ipynb b/sqd-run.ipynb new file mode 100644 index 0000000..4224861 --- /dev/null +++ b/sqd-run.ipynb @@ -0,0 +1,851 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Info: Nathan Shammah, RIKEN, nathan.shammah@gmail.com\n", + "\n", + "# Open Quantum Dynamics with QuTiP\n", + " \n", + " \n", + " We use QuTiP's solvers to study the open dynamics of a quantum system evolving in time. \n", + " \n", + " \n", + " - #### Lindblad Master Equation\n", + " \n", + " - #### Lindblad Master Equation: Time evolution\n", + " \n", + " - #### Lindblad Master Equation: steady-state solution\n", + " \n", + "- #### Stochastic Dynamics: Quantum Trajectories with Monte Carlo" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from qutip import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define the operators and Hamiltonian\n", + "\n", + "We consider the spin-boson system, which is a prototypical model of light-matter interaction in cavity quantum electrodynamics (cQED): a single two-level system coupled to a single mode of the photonic field. Its Hamiltonian is described by\n", + "\n", + "\\begin{eqnarray}\n", + "H &=& \\omega_c a^\\dagger a + \\frac{\\omega_0}{2}\\sigma_z\n", + "+\\frac{g}{2}\\sigma_x\\left(a+a^\\dagger\\right)+\\frac{\\omega_x}{2}\\sigma_x,\n", + "\\end{eqnarray}\n", + "\n", + "where we added also the possibility of the system of a classical drive onto the system at a frequency $\\omega_x$." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# spins\n", + "sx_reduced = sigmax()\n", + "sy_reduced = sigmay()\n", + "sz_reduced = sigmaz()\n", + "sp_reduced = sigmap()\n", + "sm_reduced = sigmam()\n", + "\n", + "# photons\n", + "nph = 4\n", + "a_reduced = destroy(nph)\n", + "\n", + "# tensor space\n", + "sz = tensor(sz_reduced,qeye(nph))\n", + "sx = tensor(sx_reduced,qeye(nph))\n", + "sm = tensor(sm_reduced,qeye(nph))\n", + "sp = sm.dag()\n", + "a = tensor(qeye(2), a_reduced)\n", + "\n", + "# hamiltonians\n", + "wc = 1\n", + "w0 = 0.5*wc\n", + "g = 0.1*w0\n", + "wx = 0.2*w0\n", + "Hcav = wc*a.dag()*a\n", + "Hspin = w0*sz #+ wx*sx\n", + "Hint = g*sx*(a+a.dag())\n", + "HintCheck = g*tensor(sx_reduced,a_reduced+a_reduced.dag())\n", + "H = Hcav + Hspin + Hint\n", + "np.testing.assert_(Hint == HintCheck)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define the initial state" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The initial state of the system is given by \n", + "\\begin{eqnarray}\n", + "\\rho&=&\\rho_\\text{spin}\\otimes\\rho_\\text{phot}\n", + "\\end{eqnarray}\n", + "and in the case of a initially pure state, \n", + "\\begin{eqnarray}\n", + "\\rho&=&|\\psi\\rangle_\\text{spin}\\otimes|\\psi\\rangle_\\text{phot}\n", + "\\end{eqnarray}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# initial state\n", + "psi0_spin = basis(2,0)\n", + "psi0_phot = basis(nph,nph-int(nph/2))\n", + "psi0 = tensor(psi0_spin,psi0_phot)\n", + "rho0 = ket2dm(psi0)\n", + "\n", + "# times at which to calculate the variables\n", + "tlist = np.linspace(0,50,2000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Lindblad master equation: $\\texttt{mesolve}$\n", + "\n", + "We now consider the time evolution of the open quantum system, in which $\\rho$ is dissipatively coupled to a spin and photonic bath,\n", + "\n", + "\\begin{eqnarray}\n", + "\\frac{d}{dt}\\rho =-i\\lbrack H,\\rho\\rbrack+\\gamma\\mathcal{D}_{[\\sigma_-]}\\rho+\\kappa\\mathcal{D}_{[a]}\\rho.\n", + "\\end{eqnarray}" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10.0%. Run time: 0.02s. Est. time left: 00:00:00:00\n", + "20.0%. Run time: 0.04s. Est. time left: 00:00:00:00\n", + "30.0%. Run time: 0.06s. Est. time left: 00:00:00:00\n", + "40.0%. Run time: 0.08s. Est. time left: 00:00:00:00\n", + "50.0%. Run time: 0.10s. Est. time left: 00:00:00:00\n", + "60.0%. Run time: 0.12s. Est. time left: 00:00:00:00\n", + "70.0%. Run time: 0.14s. Est. time left: 00:00:00:00\n", + "80.0%. Run time: 0.16s. Est. time left: 00:00:00:00\n", + "90.0%. Run time: 0.18s. Est. time left: 00:00:00:00\n", + "Total run time: 0.20s\n" + ] + } + ], + "source": [ + "kappa = 0.3\n", + "gamma = 0.3\n", + "\n", + "my_options = Options(average_states = True, store_states = True)\n", + "results = mesolve(H, psi0, tlist, \n", + " c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], \n", + " options=my_options, progress_bar=True)\n", + "\n", + "# store time evoluted variables\n", + "nph_t = results.expect[0]\n", + "sz_t = results.expect[1]\n", + "rho_t = results.states" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fs=20\n", + "plt.figure(figsize=(14,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.suptitle(\"Time evolution for spin and photonic excitations of a driven cavity with single two level system, with dissipation\")\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Steady state solver: $\\texttt{steadystate}$" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "rhoss = steadystate(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "nph_ss= expect(a.dag()*a,rhoss)\n", + "sz_ss= expect(sz,rhoss)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.imshow(abs(rhoss.full()))\n", + "plt.show()\n", + "plt.close()\n", + "plt.figure()\n", + "plt.subplot(121)\n", + "plt.imshow(abs(ptrace(rhoss,0).full()))\n", + "plt.xlabel(\"atom\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.imshow(abs(ptrace(rhoss,1).full()))\n", + "plt.xlabel(\"photon\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Liouvillian structure\n", + "\n", + "We can derive thermodynamical properties of the out-of-equilibrium system by studying the spectrum of the Liouvillian." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Q+jtSb/xy5YRmWJ3nMTgUTvSqvtv1TgI3a+vJpCTJzP5WIXdgtcL+t0yh18wVxrEfom33v8ox7snE+reYWb95bTVK78dm9kqFoGEnSf+jMO5+jcLFh8kK39167ckf+qjDvymc8J+pMOnGKxTGfC9092SQUsccbT1Jq/TAJq8GW5j84Q6F9v12hYtdaxWHMCnkjeVoGwdyrP87hePSXynk91wgabOZfU/S+XVO3Kt1fbsYpY6dDZ1HZNau9/FmhX3xFDO7MF7UOFbhvbi8NmjOoclz2dTnW7pdHDTBRkUcEvLfZjZTYWz63JjgtrFqsTUK4+8mlHzZ4xQ+nLnufnr1EzEBur+gpaxvSPpHhXGCV6r+AXWqQqDx35Le7u4vVD23nWLUXJKr/n6Q+nJVGtzxda4AF1fgvljSuyzMQHSIpDcpXNH5gpltcPev9fMSlXW+QtKixPO71yzXLSr1uczdP9jRmgRrJE0wsxHV+4wkxc9mF4WDYUVluEgj+4cUhj5corD/fsXMXiPpIEm3uPtTA618gy5RGBM8Ne5/LzGzryrOrgK0WvwufVLhRPzQ2mG8MdG8VuV7t5vCBaTq5YcpnJA8XvtPLfLB+PrvjcOIq9d9kmqGMFXrp3f6WwrB0xlm9imVTAxPqD5J+3uFHo23Sfq1F5PsP67QK3O0u8+rfsLMLlRoy8vo69jXV7tY+lgfTza/oNAO7qpw9fzdCsnhB8aE8r6SbqvbxZRubRelAZxHZDSQ97HR/UPu/qyZ3aAQfL9ZIY+nrUOo1L5z2YJBk7NRy93vUxhPtqfCFYRqP5e0U2LsXD37xsebEs+18qTlG4rjU2MEepLCzWe+W7NcpT631p40KuxItV3gfVktaa/awtjATSkurp/Hx9c3sA5J4Qqhuy9w988obJsUrvL15974OCNRzx1jPTcpJHk1ozJ8olVXr3+p8Hk2/F5lcq/Cd3564rnpCtv9q6qyyhCo1P4xTqELtiAOmbhD0uvMbH+1/4Aqhe/IA4lAYzs1MfYWKGEXhROOnyUCjbHaOmyjWuUYl9o3j1DeC4NZ2rfYNs1WGJYxU+Eka73C8KFGXudZhZzGiQoXqk5WeD9Sx5N9FXpv5yWea2Rb6h77FIbF1WrqWB9zfL7l7icqHDv/RGFUQ18eUugtm2Lp6e4rUzL/KvFco7ZIL50XtMKAzyMyqHt+UVNeqm1Uev+omBMfT7MwDe7bJN3n7n3NlNlK7TqXLRi0wUb0jwonoR+q+TJeFh//3dL3hRhj287FvzQ+zqhZ7pUKU/y1RNVJ2hEKY+peLunaREBRrz67KiT0NeKXkiaZ2Vtqyj+uMAtUrS8pdLldZmaFk00L85y/vurvw81st8TrVMo2Jp6rdXVc5zlmtm/Nc5coTKt7dT9XgcqoDFVIJQ43LCbHXSNpqpldFK94bsPCnP77tGJ9JVwVH//ZzF66u3j8vZIU+1IvUxyf/qCkI83s1VXLD5P0efUd1M6Jj2coBJZPK0wx3S5LJe1X/f22MBbmEwo5TkAuKxWOa4fF4ELSS0MYvqAQjNT6Rnz8mG1736CRCjlvOS2NjzOqC2OOXbMTRsxSOFH9kkJi+LWpxPkS5sTH98SfzUoHLUsVem8Pri40szPU2KQplWFe760+bpvZXpIK9w9p9Fhv4Z5Dx8RjUvUyIxR6bqR+2sY4HPYahaFGn6pdl8JEOC8o9DQ3q6Vtoxo8j8jspwqB21FmdkJNPU5QuBD3W22bT1XZP95Xs/xBCuduSR7u//awQg9DJUl+TnPVb8jS+DijurDV57Ipg24YVTV3fzwOmThXYWjRhbH8djO7QGG60ofjGMnfK3xp91aI8O5SyDGQpNsUpmj7YNyZ7lX40h2r0OvQqi+gFK7WvElbG5jU1Zt7FL4g/9fMfhbruptClPyQGrtr9r8qHIRvsTCL1yqF2Rn2UUgknlG9sLs/aGZ/pXDiusjMvq/wRRyh8D68XmEM4Kviv/ylpPeb2U8U3sPVCldtZirkmFyufrj7UjM7TyGQ+lXsinxK4XOapnBC/NE+XqKshxSGKrzbzJ5XGGftkr7p7o8O8DU/oDAN4acUZsy6S2FowUSFZMHXKpyM/76B17zA6t8E74vunryS5e7XmtlxCnOwLzKzb2vrGPJ9JN1QOxuHpM8qBCA/jUmMmxSumI1QSMZP3ohSYQjFWoX8oRGSrkgEzTldpjAU8V4zu0mhYTtSIdC4TWH/A1rO3V80sy8qjMG/38xuUZic4GiFE8kfa+tV58r//MTMZikkUC+q2mdnKgzfWKGtQzda7d8kvVfSf8b1Pq5wVf2tCj0KpW8wV8vdl5nZdxVyNaTGh1BVXuenZrZEYYjRCEm3xRP8WpcrtGd3xXZijcKV5qMUcrhOSPxPan2/sJDgPl3SL83sDoU2dqbCJCepK9qNHOu3VxgGvdTMfiHpUYVE9jfHZW+t7ZWt4wKFNvcDFhKtf6yt99nYQWHK4EbalnpuV3jvvxXPl56V9Ki7DyiQGcB5RBmvsjo3oJW0zN2TN5l0dzez0xRyq66P39cHFWagOl5hQpD3+Laz0N2iEDScZGZ7KtybZ5K23tvrxD7q+Q2Fi6QXKQTN1/axbKu181x2W97AXMvd+KPEnOk1z++mkBi6QdJuNc8dpXAwXaEwvvsphWlvP68w1rt62b0UriI8rvBFW6QQwAxXYo5nNXCfjZr/G61wgHRJ9/ex3ASFRmKpwgng7xQClNFqYM7l+Nw7FGYa2KRwBeM6haBrjurPJX1QfP5RhaBhlULC0VclvbFqudcpJAn/Oi7zrMLO/nVJf9bge/MWheTF1XGdSyT9i2ruldLf9vazjtcqHFjXKDTuL32G/b1maj+I5SMVGqKfaevc58vies6TtHPJus2r7O99/BxfvWziNbZTuDnPfIUrZxsVZvt4v6rmEa/5nzPi/v6cwjj0ryqM8U6uo+r/ZlfV67A6yyTf00b24dSyVcsvVPju/1Fh7PdBqvPdrPf5xefmqM53gZ/e+lGizVD/95Tpa99I7avDFXIhHlA45v1B4Qpz3eNq/G7+ncKJznMK7dKXFRJY1ykkVlcv39D3IT5Xb9//Xwq96qvjuu5SONGaoZp7BsTl+/zu1yx7XHyNe5r83D5edTz5iz6WO1ZhmM46haTWHyoEDY0eP3ZUGIq9Mn4ev1EIBuvuKyp5rFc4qf6IwrS9yxTa3qdivc+WNLKB92VHhavSD8f1PaNw4vyWsvtriXUMUzi/eEQhCN7m+zCQfS4+V+o8op+6VfbRvn4W1ix7ceJ19lf4jj4Rt/EJhVEV+9dZ714KCdaV85p7FCbAqbuO+H+TFHr7XCForrddhfe0kX24j2Vbdi6rfo6b1T8W/wEAAHQZM9tP4arvde5+Un/LdxsLU8F+QtKZ3v9kIAAGocGeswEAQNczs1fECQyqy0Zr61DTm9tfq+ZYuCnb2QpXf9sy7TWA7jOoczYAAOgR5ymMAZ+nMITjFQo32dtTYbjNf3auao2xcEPDQxVyHHaT9CHfdvp5AEMIwQYAAJ33I4UJF96ikJO3WWH41BcVbvrVS2Oe36kw5fWTChOxXNb34gAGM3I2AAAAAGTRVM6Gmb3VzB4ysyVxKlkAALoG7RQAdNaAezbijb1+qzAv9HKFab9OcvcH6v3P8HGjfcSuyTu5d7XRI54vlG18YWQHagJgsHlh5TPavHaj9b8kGjWQdmrY2DE+fMKEek+3TqrpZS8A0IU2r1qlLes3DPgI1UzOxuGSlrj7I5JkZtcpzKdd9yA+YtcdNfmzZzWxys44bOJjhbIFK1L39AGAxiz98KxOV2Ewa7idGj5hgiaef172ilniFn3O/JDoNanTT0bnDzorPtfv/Zf71MyhbQ9J1Wfhy2PZNszsLDObb2bzN69lMgoAQNs03E5tWb+hbZUDgKGgmWCjVDzr7rPcfaq7Tx0+bnQTqwMAoCENt1PDxo5pQ7UAYOhoZhjVcoXbnlfsKWlFoy+ycc32hbLR458deK0ySA2ZOmHfhYWyG5dMaUd1AADltKSdGruseF1u/aTEOKiE1HApKT1kyrYklhtWajVAZzSSe8TwqiGrmZ6NeyTtZ2b7mNlISe+WdGtrqgUAQNNopwCgwwbcs+Hum83sA5J+IGmYpKvcfVHLagYAQBNopwCg85q6g7i7f0/S91pUFwAAWop2CgA6i4n2AAAAAGTRVM9GK6SSwTct26FQNmrSunZUp7RUMvg5B8wrlF2xeEb+ygAAskklg+/xk2LZ428oXr+rd++MssngJI2j59RLBOeeHEMWPRsAAAAAsiDYAAAAAJAFwQYAAACALAg2AAAAAGTR8QTxlFQy+Iv3jy+UbXfQmnZUpzSSwQFgaEglg+8/e3Wh7KEzd0r+P8ngGHLK3m2cpPFBh54NAAAAAFkQbAAAAADIgmADAAAAQBYEGwAAAACy6MoE8ZRUMvjwu4pJ45K0+ajuShyvddjEx5LlC1bs1eaaAAD6Y8WbhSfvDJ5KBk9NeCJJm5btUHxNksEx1JA0PiTQswEAAAAgC4INAAAAAFkQbAAAAADIgmADAAAAQBYEGwAAAACy6JnZqFLqzTo15rZxhbINM9fmrk5p9WadOmHfhYWyG5dMyV0dAECFF2efSs08ZVsS/5qYTSo16xSAPjBD1aBDzwYAAACALAg2AAAAAGRBsAEAAAAgC4INAAAAAFn0dIJ4Palk8J2/OaZQ9vSpG9pRndJSyeDnHDCvUHbF4hn5KwMAQ5EVE8LLJoOXXa6escuK1//WT3oxsSQwxJA03tPo2QAAAACQBcEGAAAAgCwINgAAAABkQbABAAAAIItBmSCekkoGn3j5yELZivOeb0d1SiMZHAA6K0cyeEoqGXzincWM1xXTU5mxwBBD0njPoGcDAAAAQBYEGwAAAACyINgAAAAAkAXBBgAAAIAshkyCeEoqGXzjmu0LZaPHP9uO6jTlhH0XFspSdyQHADSv2WTwslLJ4KMmrSuUbVq2Q0vXa3VuXF57d3VkVG8eABKe60u8N6l9tt7+jTw4bAAAAADIgmADAAAAQBYEGwAAAACyINgAAAAAkMWQThBPSSWDpxLvUgl6nZRKBr/04FsKZR+777h2VAcAkEk7ksHrJYLnuHM66qiXCM5dshtSdv8maTwfejYAAAAAZEGwAQAAACALgg0AAAAAWRBsAAAAAMii3wRxM7tK0rGSVrr7n8WyCZKulzRZ0lJJJ7r76nzV7KxUMviL940vlG138Jp2VKe0VDL4DYfNLpSduODMdlQHALKgnUobu6x4PXH9pGIWbDJZNpEILqWTwUkab7NUMjhJ4w1paFIEEsebVqZnY46kt9aUXSDpdnffT9Lt8W8AADphjminAKAr9RtsuPudklbVFB8naW78fa6k41tcLwAASqGdAoDuNdCcjd3c/QlJio+71lvQzM4ys/lmNn/z2o0DXB0AAA0ZUDu1Zf2GtlUQAIaC7Ani7j7L3ae6+9Th40bnXh0AAA2pbqeGjR3T6eoAwKAy0DuIP2lmu7v7E2a2u6SVraxUL0glgw+/q5g0vvmo7koaJxkcwBAx5NupVDL4xDuLWcMrphezi+sleJMM3qVIGm9avURw7jbevIH2bNwq6bT4+2mSbmlNdQAAaAnaKQDoAv0GG2b2H5LulrS/mS03szMkfVrSm83sYUlvjn8DANB2tFMA0L36HUbl7ifVeeqYFtcFAICG0U4BQPfiDuIAAAAAshhogjgSUsngY24bVyjbMHNtO6rTlBP2XVgou3HJlA7UBADQn7J3RE4lg0+ftqhQdufdBybXQzJ4DyFpvCXKfrdIGq+Png0AAAAAWRBsAAAAAMiCYAMAAABAFgQbAAAAALIgQTyzVDL4hKvHJpdddcr63NUpLZUMfunB6Xtifey+43JXBwAQlU5YLXm371Qy+KhJ65Lr3rRsh/6qh25G0nhLkDTeGHo2AAAAAGRBsAEAAAAgC4INAAAAAFkQbAAAAADIgmADAAAAQBbMRtUB9Wadmnj5yELZivOez12d0urNOnXDYbMLZScuODN3dQBgSGpm5qmyyzHr1BDCDFUtwQxV9dGzAQAAACALgg0AAAAAWRBsAAAAAMiCYAMAAAC6rQhHAAAbQElEQVRAFiSId5FUMvjeF71QKHv0khHtqE5pJIMDQGc1kwzerLHLitct108aglmwgwlJ4y1B0nhAzwYAAACALAg2AAAAAGRBsAEAAAAgC4INAAAAAFmQIN7lUsngqTu7jpq0rh3Vaco5B8wrlF2xeEbb6wEAQ0GOZPCUVDL49GmLCmV33n1gS9dbNvkWLZJIBh+Kyc7NGopJ43wtAQAAAGRBsAEAAAAgC4INAAAAAFkQbAAAAADIggTxHpRKBn/xvvGFsu0OXtOO6pSWSga/4bDZhTLuSA4AvS2VDJ5qu1ITnqSUTqpN3DVdal+y/FDTSJL+YEp4brXBnjROzwYAAACALAg2AAAAAGRBsAEAAAAgC4INAAAAAFmQID5IpJLBh/9PMWl88+u7K2k8lQy+aNo1hbID7z65HdUBAGRSNhk8pWwyeL1E8EaWRXPqJTEPpoTndhhMSeP0bAAAAADIgmADAAAAQBYEGwAAAACyINgAAAAAkAUJ4oNYKhl8zG3jCmUbZq5tR3VKIxkcAIauscuK10HXTypmwaYSvLmDePcaTAnPndKrd2ynZwMAAABAFgQbAAAAALIg2AAAAACQBcEGAAAAgCz6TRA3s70kfUPSKyS9KGmWu3/BzCZIul7SZElLJZ3o7qvzVRWtkEoG3/mbYwplT5+6oR3Vaco5B8wrlF2xeEbb6wGgs2inekPZ5NZUMvjnjr26UHb+d04pvh6J4D2FpPHm9cId28v0bGyWdL67HyDpCEnvN7NXS7pA0u3uvp+k2+PfAAC0G+0UAHSpfoMNd3/C3X8Vf18nabGkPSQdJ2luXGyupONzVRIAgHpopwCgezWUs2FmkyW9RtIvJO3m7k9I4UAvadc6/3OWmc03s/mb125srrYAAPSh2XZqy/ruH0IKAL2kdLBhZmMl3STpPHcvfRc4d5/l7lPdferwcaMHUkcAAPrVinZq2NhiDhsAYOBK3UHczEYoHMCvcfdvxeInzWx3d3/CzHaXtDJXJZFXKhl84uUjC2Urznu+HdUpLZUMfsNhswtlJy44sw21AdBJtFPdpXTib+KO36kk71Qy+PRpiwpld959YJnqoYuRNN4a3fQ+9tuzYWYm6WuSFrv756ueulXSafH30yTd0vrqAQDQN9opAOheZXo2jpR0qqT7zWxhLPt7SZ+WdIOZnSFpmaR35qkiAAB9op0CgC7Vb7Dh7ndJsjpPH9Pa6gAA0BjaKQDoXtxBHAAAAEAWpRLEMfSkksH3vuiF5LKPXjIid3VKSyWDL5p2TaHswLtPbkd1AGBIaiYZvOxyqWTwUZPWJeuzadkOyXL0hm5Kdu5lnXof6dkAAAAAkAXBBgAAAIAsCDYAAAAAZEGwAQAAACALgg0AAAAAWTAbFUqrN+vU3mevLC575a65q1MaM08BQOc1M/NUWcw6NXQwQ1VrlH0fm0HPBgAAAIAsCDYAAAAAZEGwAQAAACALgg0AAAAAWZAgjqalksFfvH98oWy7g9a0ozoAgB7RTDJ4sz537NWFsvO/c0pL19GO5FtsRdJ4a7T6/WGXBwAAAJAFwQYAAACALAg2AAAAAGRBsAEAAAAgCxLEkUUqGXz4XcWk8c1HkTQOAGi/VDL49GmLCmV33n1gqdcrnZzc4rumo28kjXcePRsAAAAAsiDYAAAAAJAFwQYAAACALAg2AAAAAGRBgjjaJpUMPua2cYWyDTPXtqM6AABsI5UM/rK91hfKnntsbKGsmWRwksbbq5E7u5M43jx6NgAAAABkQbABAAAAIAuCDQAAAABZEGwAAAAAyIIEcXRUKhl8wtXFxLtVpxQT9AAAyC2VDF4WyeC9o14iOHcbbx49GwAAAACyINgAAAAAkAXBBgAAAIAsCDYAAAAAZEGCOLpOKhl84uUjC2Urznu+HdUBAAwRjdxZutbv3nVloexPrj+7+Hokg/eUsvsESeP10bMBAAAAIAuCDQAAAABZEGwAAAAAyIJgAwAAAEAWJIijJ6SSwfe+6IVC2aOXjGhHdQAAPa504m/JO36nksE/d+zVhbLzv3NKmeqhi5E03hh6NgAAAABkQbABAAAAIAuCDQAAAABZEGwAAAAAyKLfBHEzGyXpTkkvi8vf6O6fMLN9JF0naYKkX0k61d25pTPaJpUMvvfZK4vLXblrO6oDoENopzAQzSSDl10ulQw+fdqiQtmddx+YqiJ6CEnj9ZXp2XhO0hvd/RBJUyS91cyOkPQZSZe5+36SVks6I181AQCoi3YKALpUv8GGB+vjnyPij0t6o6QbY/lcScdnqSEAAH2gnQKA7lUqZ8PMhpnZQkkrJf1I0u8kPePum+MiyyXtUed/zzKz+WY2f/Paja2oMwAA22hVO7Vl/Yb2VBgAhohSwYa7b3H3KZL2lHS4pANSi9X531nuPtXdpw4fN3rgNQUAoI5WtVPDxo7JWU0AGHIauoO4uz9jZvMkHSFpRzMbHq8a7SlpRYb6AQ1JJYPv+RfFZLzlN5GMBwxGtFNoRjPJ4GWlksFHTVpXKNu0bIeBrwRdgaTxoN+eDTN7uZntGH/fXtKbJC2W9GNJJ8TFTpN0S65KAgBQD+0UAHSvMj0bu0uaa2bDFIKTG9z9O2b2gKTrzOwfJd0r6WsZ6wkAQD20UwDQpfoNNtz9PkmvSZQ/ojAuFgCAjqGdAoDuxR3EAQAAAGTRUII40ItSyeDD7xqfXHbzUWtyV6cph018LFm+YMVeba4JgI6xRFlyni20QjPJ4GWlksHHLktfD14/qbXZxGWTmNEagz0ZPIXdCQAAAEAWBBsAAAAAsiDYAAAAAJAFwQYAAACALAg2AAAAAGTBbFQYkurNOjXmtnGFsg0z1+auTmn1Zp06Yd+FhbIbl0zJXR0AnZCaeYoZqgaderNO7fGTYvnjbyh37bjszFO2JbFcG2blwuBEzwYAAACALAg2AAAAAGRBsAEAAAAgC4INAAAAAFmQIA5USSWD7/zNMYWyp0/d0I7qlJZKBj/ngHmFsisWz8hfGQDtR9L4kJFKBt//31cVyh5634RCWTPJ4CSNY6Do2QAAAACQBcEGAAAAgCwINgAAAABkQbABAAAAIAsSxIF+pJLBJ14+slC24rzn21Gd0kgGB4Y4ksaHjFQy+L5/9/NC2ZLLjiiUkQyO3OjZAAAAAJAFwQYAAACALAg2AAAAAGRBsAEAAAAgCxLEgQHotmTwZhw28bFC2YIVe3WgJgCyI2m859mLxbLUncFTyeBlkQyOVqJnAwAAAEAWBBsAAAAAsiDYAAAAAJAFwQYAAACALEgQBzLauGb7Qtno8c92oCb1pZLBT9h3YaHsxiVT2lEdAO1WNmm83rLIIpUILqWTwZu54/fYZcUXXD+pzsqBAaBnAwAAAEAWBBsAAAAAsiDYAAAAAJAFwQYAAACALEgQBzJKJYNvWrZDoWzUpHXtqE5pqWTwcw6YVyi7YvGM/JUB0H71EsG523jbpBLBpfLJ4GWXSyWD7/GTYtnjb+D6NAaGPQcAAABAFgQbAAAAALIg2AAAAACQBcEGAAAAgCxIEAfaLJUM/uL94wtl2x20ph3VKY1kcACl7zZO0ng2zSSDl5VKBt9/9upC2UNn7jTwlWDIoGcDAAAAQBYEGwAAAACyINgAAAAAkAXBBgAAAIAsSieIm9kwSfMlPe7ux5rZPpKukzRB0q8kneruz+epJjC4pZLBx9w2rlC2YebadlSnKSfsu7BQlrojOdBqLWunahOeSXbuW+L9Sd392oo3pUaLNJMMXlYnk8FT+069O6yj+zTyUZ0raXHV35+RdJm77ydptaQzWlkxAAAaRDsFAF2mVLBhZntK+t+SZse/TdIbJd0YF5kr6fgcFQQAoD+0UwDQncr2bFwu6SOSKh1ZO0t6xt03x7+XS9oj9Y9mdpaZzTez+ZvXbmyqsgAA1NGSdmrL+g35awoAQ0i/wYaZHStppbsvqC5OLJoc1erus9x9qrtPHT5u9ACrCQBAWivbqWFjx2SpIwAMVWUSxI+U9A4ze7ukUZLGKVxB2tHMhserRntKWpGvmsDQk0oGn3D12OSyq05Zn7s6paWSwS89+Jbksh+777jc1cHQ0Np2qjYk4Q7ZDSub0EvS+OAzdln6Ovb6SeU+7NL7Tovvmo58+u3ZcPcL3X1Pd58s6d2S7nD3kyX9WNIJcbHTJKXPJgAAyIh2CgC6VzMTh31U0gfNbInC2NivtaZKAAC0BO0UAHRY6ftsSJK7z5M0L/7+iKTDW18lAAAGhnYKALoLt0QBAAAAkAXBBgAAAIAsGhpGBaCz6s06NfHykYWyFec9n7s6pdWbdeqGw2YXyk5ccGbu6gCNSc08xQxVDWOGqqGh3qxTe/ykWP74G4o7QDMzTzFDVXeiZwMAAABAFgQbAAAAALIg2AAAAACQBcEGAAAAgCxIEAcGgVQy+N4XvVAoe/SSEe2oTmkkg6NnkTTeEiSNDx2pZPD9Z68ulD105k6FMpLBexs9GwAAAACyINgAAAAAkAXBBgAAAIAsCDYAAAAAZEGCODBIpZLBN67ZvlA2evyz7ahOU07Yd2Gh7MYlUzpQE6APZZPG6y0LSSSN97p6n0vqM0wlg4+atK5QtmnZDsXXIxm8Z9CzAQAAACALgg0AAAAAWRBsAAAAAMiCYAMAAABAFiSIA0NIKhk8lXiXStDrpFQy+KUH31Io+9h9x7WjOkB59RLBudt4Q0ga705lPxep/B2/U20Sehs9GwAAAACyINgAAAAAkAXBBgAAAIAsCDYAAAAAZEGCODDEpZLBX7xvfKFsu4PXtKM6paWSwW84bHah7MQFZ7ajOkBjyt5tnKTxuhpKTiZxPItkkn4iEVxKJ4OXTRpPGbusuPL1k/iguxE9GwAAAACyINgAAAAAkAXBBgAAAIAsCDYAAAAAZEGCOICCVDL48LuKSeObj+qupHGSwdHTSBpvWr1EcO423j71ErybSQZPSSWDT7yz+OVYMT31JUI70bMBAAAAIAuCDQAAAABZEGwAAAAAyIJgAwAAAEAWJIgDKCWVDL7zN8cUyp4+dUM7qtOUcw6YVyi7YvGMttcD6FciGZxk58aVvds472M+zSSDl5VKBh81aV2hbNOyHVq+7kbuaD/U8DYAAAAAyIJgAwAAAEAWBBsAAAAAsiDYAAAAAJAFCeIABiyVDD7x8pGFshXnPd+O6pSWSga/4bDZhTLuSI5uRLJza/A+Dg2dTAZv9V3TexU9GwAAAACyINgAAAAAkAXBBgAAAIAsCDYAAAAAZFEqQdzMlkpaJ2mLpM3uPtXMJki6XtJkSUslnejuq/NUE0CvSCWD733RC8llH71kRO7qlJZKBl807ZrksgfefXLu6qBBQ72dItm5NXgfh66xy9LX39dPKn7YzSSDD8Wk8UZ6No529ynuPjX+fYGk2919P0m3x78BAOgU2ikA6DLNDKM6TtLc+PtcScc3Xx0AAFqGdgoAOqxssOGSfmhmC8zsrFi2m7s/IUnxcdfUP5rZWWY238zmb167sfkaAwBQ1JJ2asv64r1jAAADV/amfke6+woz21XSj8zswbIrcPdZkmZJ0vb7TvQB1BEAgP60pJ162aS9aKcAoIVK9Wy4+4r4uFLSzZIOl/Skme0uSfFxZa5KAgDQF9opAOhO/fZsmNkYSdu5+7r4+1skfUrSrZJOk/Tp+HhLzooC6F31Zp3a++ziud+jVyZHunQEs071BtqpNGZWag3ex6EhNeuUJE28s9jZuWK6FcqYeaq+MsOodpN0s5lVlr/W3b9vZvdIusHMzpC0TNI781UTAIC6aKcAoEv1G2y4+yOSDkmUPy3pmByVAgCgLNopAOhe3EEcAAAAQBYEGwAAAACyKDv1LQC0XCoZfNOyHQployata0d1mnLOAfMKZVcsntH2egB9Idm5NXgfe1vZz09KJ4NPn7aoUHbn3QcWX3MIJoOn0LMBAAAAIAuCDQAAAABZEGwAAAAAyIJgAwAAAEAWJIgD6CqpZPAX7xtfKNvu4DXtqE5pqWTwGw6bXSg7ccGZbagNUF4jybIkPNdH0nh3Kv25JO72LaWTvFPJ4Km2KzXhyVBEzwYAAACALAg2AAAAAGRBsAEAAAAgC4INAAAAAFmQIA6g66WSwYf/TzFpfPPruytpPJUMvmjaNdv8ffiYVe2qDlBavSRmEp4bQ9J455VNBq93t++yy5IMXh89GwAAAACyINgAAAAAkAXBBgAAAIAsCDYAAAAAZEGCOICelEoGH3PbuELZhplr21Gd0g68++Rt/l66YVaHagI0joTn5vEedl4qwbuRO4g3Y+yy4oe9ftLg/rDp2QAAAACQBcEGAAAAgCwINgAAAABkQbABAAAAIAsSxAEMGqlk8ImXjyyUrTjv+XZUBxgSSHhuHu9N57U6EbyeVDL49GmLCmV33n1gy9dd9rvaavRsAAAAAMiCYAMAAABAFgQbAAAAALIg2AAAAACQBQniAAa1VDL43he9UCh79JIR7agOMCSQNA6Ul0oGHzVpXaFs07IdSr9m6e9g4s7prU6Wp2cDAAAAQBYEGwAAAACyINgAAAAAkAXBBgAAAIAsSBAHMOSkksH3Pntlcbkrd21HdYAhgaRxoLxkMrgnFrT0/zeTDF5YLrXeBtCzAQAAACALgg0AAAAAWRBsAAAAAMiCYAMAAABAFiSIA4DSyeB7/sWi5LLLbyre7RVA40gaBxqQSAYfuyzdb7B+UvFLUyoZPLVcnST0sujZAAAAAJAFwQYAAACALAg2AAAAAGRBsAEAAAAgi1LBhpntaGY3mtmDZrbYzKaZ2QQz+5GZPRwfd8pdWQAAUminAKA7lZ2N6guSvu/uJ5jZSEmjJf29pNvd/dNmdoGkCyR9NFM9AaDt6s069eL94wtl2x20Jnd10DfaqUGCGaqA8t+D1KxTkvS5Y68ulJ3/nVOKr5mYoarV+u3ZMLNxkqZL+pokufvz7v6MpOMkzY2LzZV0fK5KAgBQD+0UAHSvMsOoXinpKUlfN7N7zWy2mY2RtJu7PyFJ8bE4Sb0kMzvLzOab2fzNaze2rOIAAEQta6e2rN/QvloDwBBQJtgYLulQSV9x99dI2qDQFV2Ku89y96nuPnX4uNEDrCYAAHW1rJ0aNnZMrjoCwJBUJthYLmm5u/8i/n2jwkH9STPbXZLi48o8VQQAoE+0UwDQpfpNEHf3P5jZY2a2v7s/JOkYSQ/En9MkfTo+3pK1pgDQJVLJ4MPvKiaNbz6KpPF2oJ0a/Egax2BWev/ekliuToJ3Khl8+rRFhbI7705PhNJKZWejOkfSNXGGj0ckvVehV+QGMztD0jJJ78xTRQAA+kU7BQBdqFSw4e4LJU1NPHVMa6sDAEDjaKcAoDtxB3EAAAAAWRBsAAAAAMiibM4GAKAPqWTwMbeNK5RtmLm2HdUBBr2ySbX1lgW6RTPJ4Knl6i2bSgZ/2V7rC2XPPTY2/aIDRM8GAAAAgCwINgAAAABkQbABAAAAIAuCDQAAAABZkCAOAJmkksEnXL1t4t1jT9e5/SuAhtVLBOdu4+g1ZZPB691BvKxWJ4On0LMBAAAAIAuCDQAAAABZEGwAAAAAyIJgAwAAAEAW5u7tW5nZU5IelbSLpD+2bcV5sS3diW3pTmxL0d7u/vIWvA5agHaq67Et3Ylt6U5d0U61Ndh4aaVm8919attXnAHb0p3Ylu7EtqBXDKbPl23pTmxLd2JbWo9hVAAAAACyINgAAAAAkEWngo1ZHVpvDmxLd2JbuhPbgl4xmD5ftqU7sS3diW1psY7kbAAAAAAY/BhGBQAAACCLtgcbZvZWM3vIzJaY2QXtXn8zzOwqM1tpZr+pKptgZj8ys4fj406drGNZZraXmf3YzBab2SIzOzeW99z2mNkoM/ulmf06bssnY/k+ZvaLuC3Xm9nITte1DDMbZmb3mtl34t89uR2SZGZLzex+M1toZvNjWc/tY5JkZjua2Y1m9mD83kzr1W1B32inugPtVHcbLG0V7VR+bQ02zGyYpC9LepukV0s6ycxe3c46NGmOpLfWlF0g6XZ330/S7fHvXrBZ0vnufoCkIyS9P34Wvbg9z0l6o7sfImmKpLea2RGSPiPpsrgtqyWd0cE6NuJcSYur/u7V7ag42t2nVE2/14v7mCR9QdL33f1Vkg5R+Ix6dVtQB+1UV6Gd6m6Dqa2incrJ3dv2I2mapB9U/X2hpAvbWYcWbMNkSb+p+vshSbvH33eX9FCn6zjA7bpF0pt7fXskjZb0K0mvU7iRzfBYvs2+160/kvZUOBi8UdJ3JFkvbkfV9iyVtEtNWc/tY5LGSfq9Yp5bL28LP/1+1rRTXfpDO9U9P4OpraKdyv/T7mFUe0h6rOrv5bGsl+3m7k9IUnzctcP1aZiZTZb0Gkm/UI9uT+zOXShppaQfSfqdpGfcfXNcpFf2tcslfUTSi/HvndWb21Hhkn5oZgvM7KxY1ov72CslPSXp63HYwGwzG6Pe3Bb0jXaqC9FOdZ3B1FbRTmXW7mDDEmVMh9VBZjZW0k2SznP3tZ2uz0C5+xZ3n6JwteVwSQekFmtvrRpjZsdKWunuC6qLE4t29XbUONLdD1UYkvJ+M5ve6QoN0HBJh0r6iru/RtIG9U63OhrT69+5QYd2qrsMwraKdiqzdgcbyyXtVfX3npJWtLkOrfakme0uSfFxZYfrU5qZjVA4gF/j7t+KxT27PZLk7s9ImqcwvndHMxsen+qFfe1ISe8ws6WSrlPonr5cvbcdL3H3FfFxpaSbFRrYXtzHlkta7u6/iH/fqHBQ78VtQd9op7oI7VRXGlRtFe1Ufu0ONu6RtF+csWCkpHdLurXNdWi1WyWdFn8/TWFMadczM5P0NUmL3f3zVU/13PaY2cvNbMf4+/aS3qSQFPVjSSfExbp+W9z9Qnff090nK3w37nD3k9Vj21FhZmPMbIfK75LeIuk36sF9zN3/IOkxM9s/Fh0j6QH14LagX7RTXYJ2qjsNpraKdqo92n5TPzN7u0IEPEzSVe5+aVsr0AQz+w9JMyTtIulJSZ+Q9G1JN0iaJGmZpHe6+6pO1bEsMztK0v9Iul9bx1z+vcJ42J7aHjM7WNJchX1qO0k3uPunzOyVClddJki6V9Ip7v5c52panpnNkPQhdz+2V7cj1vvm+OdwSde6+6VmtrN6bB+TJDObImm2pJGSHpH0XsX9TT22Legb7VR3oJ3qfr3eVtFOtale7Q42AAAAAAwN3EEcAAAAQBYEGwAAAACyINgAAAAAkAXBBgAAAIAsCDYAAAAAZEGwAQAAACALgg0AAAAAWRBsAAAAAMji/wOqEj71zOmYrAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "L = liouvillian(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "\n", + "# represent the Liouvillian\n", + "plt.figure(figsize=(14,6))\n", + "plt.subplot(121)\n", + "plt.imshow(np.real(L.full()))\n", + "plt.title(\"Real values of the Liouvillian\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.imshow(np.imag(L.full()))\n", + "plt.title(\"Imaginary values of the Liouvillian\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Liouvillian Spectrum, $\\texttt{eigenstates}$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "L = liouvillian(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", + "\n", + "# Plot the Liouvillian spectrum in the complex plane\n", + "eigenvalues_L, eigenvectors_L = L.eigenstates()\n", + "\n", + "\n", + "real_eigenvalues = np.real(eigenvalues_L)\n", + "imag_eigenvalues = np.imag(eigenvalues_L)\n", + "\n", + "plt.figure(figsize=(10,10))\n", + "plt.plot(real_eigenvalues, imag_eigenvalues,\"o\")\n", + "plt.title(\"Real values of the Liouvillian\",fontsize=fs)\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us decipher the spectrum of the Liouvillian:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10,10))\n", + "plt.plot(real_eigenvalues, imag_eigenvalues,\"o\")\n", + "plt.title(\"Real values of the Liouvillian\")\n", + "plt.axvline(x=0,color=\"red\")\n", + "plt.axhline(y=0,color=\"black\",linestyle=\"dashed\")\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We find symmetries in the Liouvillian spectrum with respect to the real and imaginary axis." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(6,6))\n", + "plt.plot(real_eigenvalues[-1],imag_eigenvalues[-1],\"o\",markersize=20,label=\"$\\lambda_0$\")\n", + "plt.plot(real_eigenvalues[-2],imag_eigenvalues[-2],\"*\",markersize=20,label=\"$\\lambda_1$\")\n", + "plt.plot(real_eigenvalues[-3],imag_eigenvalues[-3],\"s\",markersize=20,label=\"$\\lambda_2$\")\n", + "plt.xlim([-2,2])\n", + "plt.ylim([-2,2])\n", + "plt.legend(fontsize=20)\n", + "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", + "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Photon counting statistics: $\\texttt{mcsolve}$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10.0%. Run time: 4.65s. Est. time left: 00:00:00:41\n", + "20.0%. Run time: 9.36s. Est. time left: 00:00:00:37\n", + "30.0%. Run time: 14.29s. Est. time left: 00:00:00:33\n", + "40.0%. Run time: 19.73s. Est. time left: 00:00:00:29\n", + "50.0%. Run time: 27.13s. Est. time left: 00:00:00:27\n", + "60.0%. Run time: 32.55s. Est. time left: 00:00:00:21\n", + "70.0%. Run time: 37.79s. Est. time left: 00:00:00:16\n", + "80.0%. Run time: 42.91s. Est. time left: 00:00:00:10\n", + "90.0%. Run time: 48.88s. Est. time left: 00:00:00:05\n", + "100.0%. Run time: 54.61s. Est. time left: 00:00:00:00\n", + "Total run time: 54.67s\n" + ] + } + ], + "source": [ + "# set dynamics options\n", + "my_options = Options(average_states = False, store_states = True)\n", + "# solve dynamics\n", + "results_mc = mcsolve(H, psi0, tlist, \n", + " c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], \n", + " options=my_options, progress_bar=True)\n", + "\n", + "# store time evoluted variables\n", + "nph_mc_t = results_mc.expect[0]\n", + "sz_mc_t = results_mc.expect[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The default options for $\\texttt{mcsolve}$ imply solving the dynamics for 500 trajectories. \n", + "\n", + "This option can be controlled by setting a different number in $\\texttt{Options(ntraj=500})$." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "500" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rho_mc_t = results_mc.states\n", + "len(rho_mc_t)\n", + "#help(expect)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "sz_stoch_t = []\n", + "nph_stoch_t = []\n", + "for i in range(len(rho_mc_t)):\n", + " sz_stoch_t.append(expect(sz,rho_mc_t[i]))\n", + " nph_stoch_t.append(expect(a.dag()*a,rho_mc_t[i]))" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(14,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t, label=\"me solve\")\n", + "plt.plot(tlist, sz_mc_t, label=\"mc solve (500 trajectories)\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5, label=\"me solve\")\n", + "plt.plot(tlist, nph_mc_t/nph/0.5, label=\"mc solve (500 trajectories)\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.show()\n", + "plt.close()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Lindblad master equation as the limit of the stochastic evolution: $\\texttt{mesolve}$ and $\\texttt{mcsolve}$" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10.0%. Run time: 0.36s. Est. time left: 00:00:00:03\n", + "20.0%. Run time: 0.53s. Est. time left: 00:00:00:02\n", + "30.0%. Run time: 0.74s. Est. time left: 00:00:00:01\n", + "40.0%. Run time: 0.90s. Est. time left: 00:00:00:01\n", + "50.0%. Run time: 1.09s. Est. time left: 00:00:00:01\n", + "60.0%. Run time: 1.26s. Est. time left: 00:00:00:00\n", + "70.0%. Run time: 1.45s. Est. time left: 00:00:00:00\n", + "80.0%. Run time: 1.63s. Est. time left: 00:00:00:00\n", + "90.0%. Run time: 1.82s. Est. time left: 00:00:00:00\n", + "100.0%. Run time: 2.00s. Est. time left: 00:00:00:00\n", + "Total run time: 2.12s\n", + "10.0%. Run time: 0.40s. Est. time left: 00:00:00:03\n", + "20.0%. Run time: 0.76s. Est. time left: 00:00:00:03\n", + "30.0%. Run time: 1.14s. Est. time left: 00:00:00:02\n", + "40.0%. Run time: 1.52s. Est. time left: 00:00:00:02\n", + "50.0%. Run time: 1.96s. Est. time left: 00:00:00:01\n", + "60.0%. Run time: 2.33s. Est. time left: 00:00:00:01\n", + "70.0%. Run time: 2.72s. Est. time left: 00:00:00:01\n", + "80.0%. Run time: 3.11s. Est. time left: 00:00:00:00\n", + "90.0%. Run time: 3.49s. Est. time left: 00:00:00:00\n", + "100.0%. Run time: 3.99s. Est. time left: 00:00:00:00\n", + "Total run time: 4.05s\n", + "10.0%. Run time: 1.32s. Est. time left: 00:00:00:11\n", + "20.0%. Run time: 2.80s. Est. time left: 00:00:00:11\n", + "30.0%. Run time: 3.91s. Est. time left: 00:00:00:09\n", + "40.0%. Run time: 4.96s. Est. time left: 00:00:00:07\n", + "50.0%. Run time: 5.83s. Est. time left: 00:00:00:05\n", + "60.0%. Run time: 6.61s. Est. time left: 00:00:00:04\n", + "70.0%. Run time: 7.64s. Est. time left: 00:00:00:03\n", + "80.0%. Run time: 8.43s. Est. time left: 00:00:00:02\n", + "90.0%. Run time: 9.18s. Est. time left: 00:00:00:01\n", + "100.0%. Run time: 9.92s. Est. time left: 00:00:00:00\n", + "Total run time: 10.04s\n" + ] + } + ], + "source": [ + "# 50 trajectories\n", + "my_options50 = Options(ntraj=50)\n", + "results_mc50 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options50, progress_bar=True)\n", + "nph_mc_t50 = results_mc50.expect[0]\n", + "sz_mc_t50 = results_mc50.expect[1]\n", + "# 100 trajectories\n", + "my_options100 = Options(ntraj=100)\n", + "results_mc100 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options100, progress_bar=True)\n", + "nph_mc_t100 = results_mc100.expect[0]\n", + "sz_mc_t100 = results_mc100.expect[1]\n", + "# 200 trajectories\n", + "my_options200 = Options(ntraj=200)\n", + "results_mc200 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", + " e_ops=[a.dag()*a,sz], options=my_options200, progress_bar=True)\n", + "nph_mc_t200 = results_mc200.expect[0]\n", + "sz_mc_t200 = results_mc200.expect[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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4GMOHD5db3qpVKwCV5zkz89Vvy2zZsqXMZClVajqXdbnSbmBgAC8vL3z00Udyy0QiEQBAXV0dS5cuxdKlS3Hr1i18//33mDlzJmxsbDB06FBp/fz8/Fo/T6T50dBmePIE4HIfKTsUoiSUm2tHuZlyM+VmWfTLbz344iNf5IrOo1CnPU589TsqarlaRkhjVzXs6qeffnqt9Y2MjODv748BAwbgxo0bAIDevXsjOzsbcXFx0nrFxcWIjo6WXilWxNvbG7GxsYiKikJaWhq8vb2ly2xsbGBqaor09HQ4ODjIvWqaMOPFde/cufPS/Xn06BHOnTuHHj16SMuGDRuGCxcuyCS7Q4cOoaysTOYLv7rqV/JfpqSkBHw+XyZRVU12oYimpib69OmDmzdv1nhMqhLsoEGDcPz4cTx6VHOnQVGsvXv3xqVLl2SO3YMHD3D+/PmXnsuaDBo0CNevX0ePHj3kYq2acfNF7du3R2hoKAQCgfTzVSU9PR3W1tavHANputR1K6/hF91/K5NLE6I0lJtlUW6m3Py66JffesBX4eHjeQvwc9BaZLVwwR8ffwm3X9eDV4dhG4Q0NjY2NvDz88Ps2bORnZ2NgQMHIj8/H5GRkfj9999rXCcoKAh5eXnSYVWXL19GbGwsVq1aBQBwc3ODo6Mjxo8fj1WrVsHQ0BChoaEoKSnB3Llza43H3d0dQqEQ/v7+sLS0RK9evaTLeDwe1q5di8mTJ6OwsBDDhg2Dmpoa0tLScODAAURGRkIorPkZoI6Ojti/fz8kEgl4vMrrgFevXsWCBQswduxYmJubIyMjAytXrgSPx8PMmTOl644ZMwYrVqzAqFGjsGzZMhQUFGDWrFn44IMPan2OoI2NDQDghx9+gLe3N4RCofQxAzUZMmQI1q1bh5kzZ+L999/H+fPn8fPPP9d6vABgzZo1GDRoEHg8HsaMGQNtbW1kZGQgOjoaK1asgLW1NWbNmoWffvoJAwYMwMKFC9G6dWskJSWhqKgIgYGBaNOmDTQ0NLBz507o6uqCz+fDwcEBvr6+WL16NYYNG4alS5dCRUUFwcHBEIlE8Pf3f2ls1QUHB6NXr15wd3fHtGnTIBKJ8ODBA/zxxx/w9fWFs7MzvLy80KNHD3Tr1g0aGhrSmVBfvK+qqKgIycnJWLZs2SvHQJouLZEGkA6wosfKDoWQBkW5mXIz5eZ6UpdZsZryq6Fme67J7XsP2br//ci2fHSEnZn2PyaRSN7atkn9ai4zSlb//FfNXPj06VNp2Z07dxgAFhUVJS2rqKhgK1asYJaWlozP5zNTU1O5WRtfFBUVxVxdXZlIJGICgYBZW1uzlStXyvwfyM7OZpMnT2Z6enpMXV2dDRw4kCUkJMi0U31mxCoTJ05kANj8+fNr3P6RI0dY//79mVAoZNra2qxLly5s4cKFrLy8XGHMWVlZTFVVlcXFxUnL7t+/z4YNG8ZMTEwYn89nBgYGbNSoUSwpKUlu/Xv37rGRI0cyTU1NZmBgwKZPn86KiooUbq9KaGgoa9OmDVNRUWHm5uaMsZrPS5XVq1czMzMzJhQK2aBBg1hKSgoDwDZs2CCtY25uzubMmSOz3l9//cXc3NyYtrY2EwqFzM7Ojs2aNYvl5+dL66Snp7Nx48YxPT09pqGhwTp37sx+++036fKff/6ZtW/fnvH5fFaZLirdvn2bjRw5kmlpaTFNTU3m7u7OUlJSZLZfPcYq1WeUZKxyFtPRo0czfX19pq6uzqysrJifnx+7d+8eY4yxNWvWsB49ejAdHR2mpaXFevXqxQ4cOCDTxr59+5iWlhZ79uxZjcf9VdFsz00jN2ecCGcb/WPYyo9r/m4gzQvlZsrNlJspNytS19zMVdZtvhwcHFhtD+uub//8FYM/dzyFZkkJOrRNRu/gJS9fiTQ6SUlJsLOzU3YYpIGNHDkSZmZm2LRpk7JDeSOGhoaYM2fOS5+f2JxNmDABmpqa0tlG31Rt3wEcx11ijDnUy4beUfWVmyVp57BldQmel8di5ralbzSjK2n8KDe/Gyg3Nx+NMTfTPb/1rEufQejokoNiDRHSr+ni1m/hyg6JEKLAV199hV27duHJkyfKDuW1pKen47vvvkNeXh4cHN7dvti9e/dw8OBBzJ8/X9mhkLeMpy0Cv/wp1CQaKKuQKDscQkg9oNzcPDTW3Eyd3wbg7P0xjMwvIdeoK1LC/0bKH4eUHRIhpAY9e/bEmjVrkJGRoexQXsv69euxfPlyzJ49G0OGDFF2OEpz//59fP/999LnYpJ3iLouVMTPoMqEKCwpV3Y0hJB6QLm5eWisuZmGPTcQVlGOX+ZvQcHTDrC7sRFGqz9Fp36D33oc5PXQ0CpC3m007Llh1VtuLi/FjmnbUcETwPiLYfDo0urN2ySNFuVmQt5tNOy5EeNU+Rj31UQI+Y+QYj0Vj2cHIemf/1N2WIQQQkjzwVcHjysE42lh259pyo6GEEJII0ed3wakpmcIr5l9ATVVpFt9hIf/88f9uzdeviIhhBBC6oTjPYNYRQuS5j2QjRBCSD2gzm8D02vXFu+Na4EiLXPktRiDm5O8kXHrb2WHRQghhDQLPNUiSFQ1wEqfKzsUQgghjRx1ft+Cti490dUqBdkm/VCm3hvpU6YgM+2assMihBBCmjwVQQkAQPNZgZIjIYQQ0thR5/ct6ffhMLQRXMIdq7GQ8Nrg1jRfZObeUXZYhBBCSJOmKiwDAGgVU+eXEEJI7ajz+5ZwBuYY4qEOHZUcXO/kB608VZz/aCyKSgqVHRohhBDSZAm0K5/vq1VSrORICCGENHbU+X2L1AfNwPDhReBzfCT0DoDtzVLsnuKEPckRKJfQ8wkJIYSQV6WupwIA0HxO9/wSQgipHXV+3zJDdz+4OtyCWMUc5/r4oM+1UjxcsgRDItyRkJmg7PAIUSoLCwvMmTPnrW2vuLgYJiYmiI2NlZZFRERg1KhRaNmyJTiOQ3h4eI3rPnjwAF5eXtDS0oJIJMKnn36K4mL5X55+/PFHtG/fHurq6ujRowdiYmJeGldYWBgOHDjw2vtVk/DwcHAch2fPntVru7t371Z4jF7XmTNnwHEcrl+/Xm9tMsbQqVMn7Nq1q97aJI1DSxNdAIBQTJ1fQhoC5eZKlJubR26mzq8StJ/2Obq1TEC5oAdievjgvcsMdv9XiA9PfAj/Y1/gZt5NZYdIyDthw4YNsLS0hJOTk7QsMjIS6enpGDFihML1Kioq4Obmhrt37yIiIgLr16/Hnj174OfnJ1Pv999/R0BAAKZMmYKjR4/C3t4eI0aMeGniaIgE6+7ujvj4eAiFwnpttyESbPfu3REfHw8rK6t6a5PjOAQGBmLJkiWoqKiot3aJ8pmamIInLoOmmFN2KISQekC5+c1RblaMOr/KwHHoM3UQzNT+gapONxTqtUX/VCs8z+uHcw//xLioD5CW90jZURLSrEkkEmzatAnTpk2TKY+IiMDff/+Nb7/9VuG6e/bsQVJSEvbu3Qt3d3dMnDgRGzZswK+//opbt25J6wUFBcHHxweLFi2Ci4sLwsPD0a5dO6xatape9qGkpKTOdY2MjNCnTx/weI33a58xhtLSUujo6KBPnz7Q0NCo1/bHjh2LR48e4ejRo/XaLlEuDS0jqJYXQiBRA2P0sF9CmjLKzY1Pc8vNjfdIN3O8Nj3hNtkcQt4TXO84DR3vpiCyqB1UcsdBguf4KuosbmY9pUROXpuvry8cHBwQHR2NDh06QCgUwt3dHXl5eUhNTYWLiws0NTXh4OCAq1evyqwrFouxcuVKWFtbQyAQwMzMDL6+vrVub9u2bbC3t4eGhgZEIhGcnJyQmJgoXZ6bmwsfHx8YGhpCKBTC2dkZFy9eVNjejh07IBAIkJ+fL1OemJgIjuNkhigdPHgQDg4OUFdXh4mJCQIDA1FeXvt99KdOncKDBw8watQomfK6JKCjR4+iZ8+esLS0lJZ5enpCTU0Nx44dAwCkpaUhJSUF48aNk2l77NixtX7BOzs749KlS9i5cyc4jpMZ3mVhYYHZs2dj2bJlMDMzg46ODgAgPj4eHh4eaNWqFTQ1NdG1a1f88ssvMu3WNLSqtLQUgYGBaN26NQQCAbp06YIjR47IxfTjjz+iU6dOUFdXh7GxMcaMGYOCggL4+vpi7969iI2NlcYaHBwsXW/jxo1o3749BAIB2rVrJ/dHS3BwMEQiEc6ePYuePXtCXV0de/bsqXFolUQiwapVq9CuXTsIBAJYW1tj586dMu2dPXsWAwYMgI6ODnR0dNC1a1fs2bNHulxdXR3Dhw/HTz/9pPD4k6ZHoGEITvIUKpw6KiSUM0njRrmZcvOLKDe//dxMnV8lUu85CsN82qBcVRPJPaaB90s4frp5GaoVDP+X/hBu6+Lguekc7uXRDJbk9WRkZGDx4sVYvnw5wsLCcP78efj5+cHb2xve3t6IjIxERUUFvL29ZS60+Pv7IygoCOPGjcPhw4exdu1aFBUVKdxOXFwcAgICMGnSJBw9ehTbt29Hv379UFDw36NHPD09cfz4cYSGhiIiIgISiQQuLi5ITU2tsc2qxLd//36Z8oiICLRo0QLOzs4AKof2jBo1Cr169cKhQ4cQFBSEsLAwLFiwoNZjExMTA2traxgaGtZarybJycmwtbWVKVNTU4OVlRWSk5OldQDI1bOzs0NeXh5ycnJqbHvz5s2wtbXF8OHDER8fj/j4eLi7u0uX//rrr4iNjcXmzZsREREBALh79y4cHR2xdetWREVFYfTo0Zg6dSp+++23WvdjzJgxCA8Px5dffomoqCj07NkTHh4euHLlirTO8uXL4e/vDycnJxw4cABbtmyBrq4unj17Jr1q3q1bN2msH330EYDKpDxjxgx4eHggKioKY8eOxezZs+WurBcXF8PHxwcfffQRjh07hl69etUY64wZM7B8+XL4+fkhOjoaXl5emDZtGg4fPgwAKCwsxIgRI9C2bVvs3bsXkZGRmDx5stwfaP369UNMTAxdWGxGeDqtwPAMPE6IcrFE2eEQ8lKUmxWj3Ey5uaGpNvgWSK2MevWDS86fOBllg8w+7jA9F4WQJCDpf/dQ1uI9bDydiolb/w9xgS7KDpUcnQ9kXVPOtk06AcNefThOXl6ezP0ZV69eRUhICHbu3IkpU6YAqBzO4u7ujuTkZNjZ2SE5ORnbtm3D+vXr8dlnn0nbGj9+vMLtJCQkoHPnzjJJzcPDQ/rvY8eO4dy5czhz5oz0Hh5XV1dYWFggJCQEP/zwg1yburq6GDp0KCIiIjB16lRpeUREBMaOHQsVFRUwxjB37lxMmTIFmzdvltYRCAT45JNPsGDBAoUJ9NKlS+jYsWOtx0+RJ0+eQE9PT65cX18fT548kdYBIFdPX19futzIyEiujQ4dOkBTU1M6FKomhw8fhrq6uvS9t7e39N+MMQwcOBD379/Hjz/+iAkTJtTYRkxMDKKjo2XOyXvvvYeUlBSsWLECe/bsQX5+Pr7++mvMnDkT33zzjXTdF6/IGxgYQCKRyMQqkUgQHBwMX19frF27Vtp2QUEBVq5ciZkzZ0rjLykpwTfffIORI0dK18/MzJSJNTU1FVu2bMGOHTvg4+MDABg8eDAyMzOxZMkSjBgxAikpKSgoKMDGjRuhra0t3WZ1Xbp0wZMnT5Camor27dvXeGxIE6NnDjH3FJyKOZ5XSCBUU3ZA5K2i3KxwO5SbK1FurkS5uRL98tsI2LgPQGdHPdwUDEXBJF8Y5wOdNkWhQ/vb8Hdqi4y8Yqw+loyH+XW/h4AQoHIozosTE7Rr1w5AZXKrXvbgwQMAwOnTpwHgpUOpXtS1a1dcvnwZs2bNQlxcHJ5Xe+RIQkICjIyMZCav0NTUxIgRI3D27FmF7Y4fPx4xMTHIzc0FAFy5cgUpKSnSZJ+SkoKMjAyMGzcOFRUV0perqytKS0trnbwiKysLIpGozvtYHcfJT67DGJMrr/6+6qpmTevXxaBBg2SSK1CZrD/77DOYm5uDz+eDz+cjLCwMKSkpCts5efIkTExM4OjoKHPsBg0aJB3yFh8fj5KSEpk/cOri/v37ePjwIcaOHStTPn78eBQWFuLatf/+UOU4DsOGDau1vZiYGPB4PHjNzLBlAAAgAElEQVR5ecnFeuXKFYjFYlhZWUFLSwsffPABDh48KHdVuUrVOc/KynqlfSKNmNAAYl4hKlS1UFYuVnY0hLwU5WbKzYpQbm743Ey//DYS/SZ0QW7CJlzJ7IH+E9Rh/Mv3+PDUQkzq/gk6tTHFljO3seXMbSz37IhJfcxxM+sp0nKeoZelAQy1BMoO/93wGld3la36lU01NTW58qqy0tJSAMDjx4+hqakpvWelLgYPHowdO3bgu+++w/r166GlpYVJkyYhJCQEmpqayMzMhLGxsdx6xsbGyMvLU9iuh4cH+Hw+9u3bBz8/P0RERMDU1BT9+/cHAGniHT58eI3r37t3T2HbpaWlEAhe7/+Ovr5+jV/g+fn50mNbdRU5Pz8furq6MnUA+XNTVzUdR19fX/z1119YtGgROnToAB0dHWzZsgUHDx5U2E5ubi6ysrLA5/PllqmoVD439fHjxwCAli1bvlKMVVeHq8da9f7Fc66vry/9DNYWq1gsljmO1bdnZmaGEydOYMmSJRg3bhwkEgnee+89bNiwAW3btpXWrTrnVZ930gxwHMr5T8HnVJB17wmMdet3MhbSyFFuVohycyXKzZUoN1eizm8joaKqgqGG67G7cAMuPumEbnwtvP/EFFuurYeugS5ixkQj4Ocr+PpIEjafTsXDgv8+HF1a62GIXQs4thPB2lgbmgI6reT1GRoaoqioCIWFha+UZH18fODj44OcnBzs27cPs2bNgo6ODlatWoWWLVsiOztbbp1Hjx7BwMBAYZtaWlpwd3dHREQE/Pz8sHv3bowbN056ZbZq3bCwMHTr1k1u/RcnvajOwMBA4RXIl7G1tZXeN1Tl+fPnSEtLQ0BAgLQOUHl/kbm5ubRecnIyDAwMahxWVRfVr0qXlpYiOjoaGzdulG4bqBzeVBsDAwOYmprW+tiGqmFpmZmZr3QlviohVz/njx49km67Sl2ushsYGEBVVRXnzp2rcdKTFi1aAAD69u2LY8eOoaSkBCdPnsQXX3yBDz74AH/99Ze0btU5r+1zR5qe52qF4FcAaUkP0KVjK2WHQ0i9o9z8cpSba0e5uRINe25ENNTKMLzXPygr53Ct48cYGwd8KfBCQWk+RLrAMs+OGNG5JSyNNNG1tR6WjrTHF0OsAcYQeiIFXpvPwz7oOAauOY3Pf7+MiAsZuPGwEBKa/ZK8gqphV687656RkRH8/f0xYMAA3LhxAwDQu3dvZGdnIy4uTlqvuLgY0dHR0ivFinh7eyM2NhZRUVFIS0uTuYfGxsYGpqamSE9Ph4ODg9yrtgkzbGxscOfOndfax2HDhuHChQu4e/eutOzQoUMoKyvD0KFDAQBt27aFtbW1zIyGEokEe/bseelQIjU1tTpf/SwrK4NYLJa5Uv706VMcOnSo1vUGDRqErKwsaGlp1XjsgMqEpaGhITdz48tiNTMzQ6tWrWT2HaicAEVHRwedOnWq075VcXV1hVgsRkFBQY2xVr86raGhgffffx/Tpk2TfgarpKeng8fjSYcUkuahXOMpAKA0+/X+aCaksaPc/HKUm2uPlXJzJfqJsDFRVYORdi5cptjhj20MN8R90TU4HKMG8lA8phh92rZEn7byXxifDWqP7MJSXLmXj5tZT5GUVYhzqY9x8MpDAEBnM10c+rT2LzFCqtjY2MDPzw+zZ89GdnY2Bg4ciPz8fERGRuL333+vcZ2goCDk5eXB2dkZIpEIly9fRmxsrHT2QDc3Nzg6OmL8+PFYtWoVDA0NERoaipKSEsydO7fWeNzd3SEUCuHv7w9LS0uZGQd5PB7Wrl2LyZMno7CwEMOGDYOamhrS0tJw4MABREZGKnxwvKOjI/bv3w+JRCJzxfLGjRu4ceOGNGlcvHgRWlpaMvdFjRkzBitWrMCoUaOwbNkyFBQUYNasWfjggw9kJmoIDg7GpEmTYGFhAUdHR+zcuRO3bt3Cr7/+Wus+29ra4vjx4zh+/DgMDQ1haWmp8I8FXV1d9OzZE0uXLoWOjg54PB5WrVoFXV1dFBYWKtzGkCFD4ObmhiFDhmDevHmwt7dHYWEhrly5gtLSUqxcuRJ6enpYtGgRFi5ciOfPn2P48OEoKytDdHQ0goKCYGpqCltbWxw8eBAHDhyQJtZWrVohODgY/v7+MDQ0xJAhQxAbG4stW7bg66+/lrsv6mVsbGwQEBAAb29vBAYGwsHBAaWlpUhMTERKSgq2bt2K6OhobN++HZ6enmjTpg0ePHiAH374QeYeOqDyfNrb2yscpkWapgqtYuApcDtV/lcsQpoDys2Umyk31xPGWLN+9ejRgzUZoTaMHfyUMcbYuchbbKN/DDs25gt2op8tu/ron1dqSiKRsFuPCpn5vMPMfN5hZrUgmnVZcpydSMxqiMibnRs3big7hDfm4+PDqn/+d+zYwQCwp0+fSsvu3LnDALCoqChpWUVFBVuxYgWztLRkfD6fmZqaMl9fX4XbioqKYq6urkwkEjGBQMCsra3ZypUrmUQikdbJzs5mkydPZnp6ekxdXZ0NHDiQJSQkyLRjbm7OZs+eLdf+xIkTGQA2f/78Grd/5MgR1r9/fyYUCpm2tjbr0qULW7hwISsvL1cYc1ZWFlNVVWVxcXEy5UFBQQyA3MvJyUmm3r1799jIkSOZpqYmMzAwYNOnT2dFRUVy2wkLC2NWVlZMTU2NdevWjZ08eVJhTFVu377NBg0axHR0dBgAtmPHDsaY4uNz69Yt5uLiwoRCIWvdujVbvXo1CwoKYoaGhtI6Vef+2bNn0rLS0lK2ePFiZmVlxfh8PjM2NmZubm7s8OHDMu1///33zM7OjqmpqTFjY2M2duxYVlBQwBhjLCcnh3l6ejJ9fX0GgAUFBUnX27Bhg7RtS0tL9s0338gd6xdjrHL69GkGgF27dk1aJpFI2Lfffss6dOjA1NTUmEgkYgMHDmQ7d+5kjDGWnJzMRo8ezczMzJiamhozNTVl/v7+7PHjxzJtd+7cmQUHB9d2+BljtX8HALjIGkF+a8qv+s7NG1f1Yhv9Y1jQRzvqtV3SuFBuptxMufk/lJtl1TU3c5V1my8HBwdW28O6G5V1nQBzR8Dre0gkDNEb/8G9G7no/vc32DnoPrp4T0dAl4CXt/OCs7dyEX7+Dsz0hQg/n47ZQ6wxYxA93uNlkpKSYGdnp+wwSAMbOXIkzMzMsGnTJmWH0uA2bNiAuXPnvtMTPd28eRP29vZITU2FhYVFrXVr+w7gOO4SY8yhAUJ8Z9R3bg7/1RulpyYjX5KN+dtfbQZU0nRQbn43UG5+t7zt3Nyo7vnlOG4ox3E3OY5L5Thufg3LzTmOi+E47irHcWc4jjNTRpwNRkUNSD0JSMTg8TgM+dAe2iIhrnb0w+Asa2y+vBEzT89EVlHdpwHv316ErT49EfR+BwBABd3/S4jUV199hV27dkmf+9ccicVinD59Grt27UKPHj2UHY5Sffvtt9KhbqR5EWrrQPC8AAL2eo8pIYQ0HpSb3y1vOzc3ms4vx3EqADYBGAagA4AJHMd1qFYtFMBPjLHOAJYCWPl2o2xgJp2AohwgvvJKl7omHyM+7QIINFBYMQo//GaCuxdjEfBHAHKKc16paY7jwOMASTP/pZ+QV9GzZ0+sWbMGGRkZyg6lwTx9+hRubm4Qi8XYuHGjssNRGsYYLC0tsXTpUmWHQhqAtrouVMsLocrJPx6EENK0UG5+dygjNzemCa96AUhljKUBAMdxvwMYCeDF6cA6AJj1779PA1A8D3hTNHo7UPYM+GMRIKkAHKZC30Qfw2f2RNS6y0iTeOOrW7H40PgaxkSNwVCLoZjRbQa01LTq1Lwqj0e//BJSzYuPIGiO9PT08Pz5c2WHoXQcx2HevHnKDoM0EG2BLh6LC6HCGUEsYVDh0S/AhDRllJvfDcrIzY3ml18ApgBefOr1/X/LXvQPgNH//tsLgDbHcYrnS29qeDzAYwNgMQCIWQKEuQDFeTCzMYCrrz3ytdviTo49tud6ooOwLX5N/hUJWQmv1Dw99ogQQkhzo63dCpAUgKkI8bioTNnhEEIIaaQaU+e3psu01XtqcwA4cRx3GYATgAcAKuQa4jg/juMuchx3MSfn1YYHK51OS8D3MDAhAnhyB/i/7wEANr1N0KOvFh4Z98LDP4rw2ZJr8DkpxvP09Do3Tb/8EkIIaY4sWnSGmCsEeAIk3qVn/RJCCKlZY+r83gfQ+oX3ZgAevliBMfaQMTaKMdYNwMJ/ywqqN8QYC2OMOTDGHIyMjBoy5oZjMxRQ1wVK/kvivaf0hF2/lrhrPgwP+0yC2yWGNv4hKDh4sE5N8jhATJ1fQgghzYyulgmAymdnFuTRL7+EEEJq1pg6vxcAtOc4zpLjODUA3gAOvViB4zgRx3FVMS8AsP0tx/h2qQgA8X/3A3AcB+eJNmjb1QjJFZ0RMqEfyvgcksK+wfPS4pc2p6rCo84vIYSQ5kdNExWqldfCd52+reRgCCGENFaNpvPLGKsA8CmA4wCSAOxmjCVyHLeU4ziPf6s5A7jJcVwKAGMAK5QS7NuioibT+QUAngoP731oj9Z2+uj98APctO8H3dvZuNWtB5K++ATPnxYqbo7H0bBnQgghzY+aNp4YVHZ+1bJyUCGWKDkgQgghjVGj6fwCAGPsCGPMmjFmxRhb8W/ZYsbYoX//HckYa/9vnY8YY817bJOqfOcXAFT4PAwL6AwTSz08MZiIk97D8bcVBxw5hXnLnLAnZU+NzalwHE14RQghpPlRUUWBqLLz26qsGE9L5aYDIYQQQhpX55dUo6IGVNTcv+cLVDDi087Qb6kJtbz3YRsUAcbj4HeoFNn7FHR+6Zdf0shZWFhgzpw5b217xcXFMDExQWxsLACgsLAQQUFB6NWrF3R1dWFiYgIvLy+kpKTIrVtQUICpU6dCX18furq6mDhxIh4/fixX7+DBg+jUqRPU1dXRoUMHREREvDSu3bt3Izw8/I3370VnzpwBx3G4fv16vbZ74sQJrFu3rl7bTE9PB8dxOHz4cL226+7ujmXLltVrm6TxEOuVgJNUQK9CjK1n05QdDiHNBuXmSpSbm0dups5vY6bCB8TlChcLhHx4fNYV2oYa+HvXY8B/EQCg54GbNTfH4yBh1PklpMqGDRtgaWkJJycnAEBGRgZ+/PFHuLm5ITIyEj/88AMyMzPRu3dv3Lt3T2bd8ePH48yZM9i6dSvCw8Nx4cIFeHp6ytQ5e/YsRo8eDRcXFxw9ehTu7u6YMGECTpw4UWtcDZFgu3fvjvj4eFhZWdVruw2RYFu2bIn4+Hj079+/XtudP38+vvnmG+Tn02zAzZFIQwX88kJoMYYLd54oOxxCyGui3PzmKDcrpvpWtkJej4oAKM6ttYpQRw2es7rhwLeX8WdqS3BDB2DAsT+Rf+I49N5zk6mryuNw/UEBNp1OhY4GH2b6GnC0EkFNVf4aCGMM+cXlSH9chNM3c8Dncbj2oACLRnRAawNhve4mIcogkUiwadMmLFq0SFpmaWmJ27dvQ0NDQ1o2YMAAtGnTBtu3b0dQUBAAID4+HsePH0dsbCwGDhwIADA1NUXv3r1x8uRJDB48GACwbNkyDBw4EN999x0AwMXFBYmJiVi6dCnee++9N96H8vJy8Hg8qKiovLSujo4O+vTp88bbbGilpaVQV1dvkFgHDBgAQ0ND7Nq1CzNmzKj39olytYcqHokLoa2igsJSxReOCSGNF+Xmxqk55Wb65bcxa90LuH8BSI2ptVpVB1jHSAPPy8fikcgaJ9bOwo7rO5BVlCWt191cHxl5xQg5fhOLDlzH1B0XMPaHeJSLJbh2vwDfx97GyqNJ8Np8Dp2CT6Dbsj/gtfk8vou5hbV/pODEjUe4eDevofea1BNfX184ODggOjoaHTp0gFAohLu7O/Ly8pCamgoXFxdoamrCwcEBV69elVlXLBZj5cqVsLa2hkAggJmZGXx9fWvd3rZt22Bvbw8NDQ2IRCI4OTkhMTFRujw3Nxc+Pj4wNDSEUCiEs7MzLl68qLC9HTt2QCAQyF0JTExMBMdxiIn57//FwYMH4eDgAHV1dZiYmCAwMBDl5bX/8Xvq1Ck8ePAAo0aNkpZpamrKJFcAMDAwgLm5ObKzs6VlR48ehbGxsTS5AkCvXr1gaWmJo0ePAgDKyspw+vRpjBs3TqY9b29vxMfHo6BA7iltACrP2969exEbGwuO48BxHIKDgwEAzs7OGDNmDMLCwmBlZQV1dXU8fPgQycnJ8Pb2RuvWrSEUCmFvb49169ZBIvlv0p+ahlZJJBKsWrUK7dq1g0AggLW1NXbu3CkX0/79+9GrVy9oaGjA0NAQw4cPx927dxEcHIy1a9fi7t270lhf/Jzs3r0bnTp1gkAgQOvWrbFw4UJUVPx3L2Z4eDg4jkNCQgKcnZ2hoaGBkJAQhUOrtm7dCnt7ewgEApibm2PNmjUyyxMTEzF06FAYGBhAU1MTdnZ22LRpk0yd0aNH46effqrx2JOmrYOoS+WzfiGge35Jo0W5mXIz5Wbl5mb65bcxG7QYuLgDiJoJ/O9s5XN/FajqAO//9m8k2U9H53+24JfwUHzT6Rt8YPsBFvRegNCxXRA6tgtKy8UoLCnHxK3/h3/u5aP9wqMybRloqsGrmyksRJow1av8shGo8jA1/AJoAs2mJSMjA4sXL8by5ctRXFyMGTNmwM/PD+np6fj4448RGBiIBQsWwNvbW5q4AMDf3x8//fQTAgMD4eTkhLy8PERGRircTlxcHAICArB06VL07dsXhYWFcknE09MTqampCA0NhUgkQkhICFxcXHD58mW0a9dOrs1Ro0YhICAA+/fvx9SpU6XlERERaNGiBZydnQFUfolPmDAB/v7++Prrr3H79m0sWLAAEokEoaGhCmOOiYmBtbU1DA0Naz2GOTk5SE1NxfTp06VlycnJsLW1latrZ2eH5ORkAMDt27dRXl4uV8/Ozg4SiQQpKSno2bOnXBuLFi1CRkYG8vPzsXnzZgCAmZmZdPm5c+dw+/ZtrF69GkKhELq6ukhJSYGNjQ0mTpwIbW1tXLlyBUFBQSgpKcGCBQsU7tuMGTOwc+dOLF68GN27d8cff/yBadOmwdDQECNGjAAA7Nq1C1OmTIG3tzcWLVoExhhOnTqFnJwcfPTRR7h16xZOnTqF/fv3AwCqnq1+4sQJjB8/HlOmTEFISAiuXr2KRYsW4fHjx/j+++9l4pgwYQL+97//ISgoCHp6ejXGGhISgi+//BKBgYFwdnbGpUuXsGjRIgiFQnz66acAAA8PD9ja2uLnn3+GQCDAzZs3UVgoOwN+v379EBISgidPnkBfX1/hsSFNj5WlK05y6RCrWKKwhH75JY0X5WbKzZSblZibGWPN+tWjRw/WpF3YxliQDmM7PRjLSHhp9eLCMvZr0Hm2+eNjLG7UJ+yLnyawjjvsWURyBHv2/JlM3bJyMfPZ/n/sfz9fZD/EprLM/BImFkuYWCyRa/f+k2JmPu8w+z3hbr3tWmN248YNZYfwxnx8fJiKigpLTU2Vls2dO5cBYDt37pSWRUdHMwDSfU5KSmIA2Pr16+u8rZCQENa9e3eFy48ePcoAsDNnzkjLnj17xkQiEfPz85OWmZubs9mzZ0vfe3h4MDc3N5m2rK2t2SeffMIYY0wikbA2bdowX19fmTrbtm1j6urqLDc3V2FMQ4YMYWPGjHnpvk2ePJkZGBjItDV48GA2cuRIuboTJ05kffv2ZYwxdvbsWQaAXb58WabOrVu3GAB2/PhxhdscPXo0c3Jykit3cnJi6urqLDMzU+G6EomElZeXsxUrVjBLS0tp+enTpxkAdu3aNWkcHMex8PBwuf11cHBgjDEmFotZq1atmJeXl8LtzZ49m5mbm8uV9+7dmzk7O8uUrV69mvF4PHbv3j3GGGM7duxgANi6detk6t25c4cBYFFRUYwxxgoKCpimpiYLDg6Wqbdo0SJmbGzMKioqWE5ODgPArl69qjDWF9s+ceJErfVq+w4AcJE1gvzWlF8Nkptvn2Fbps1iG/3+YFZzD7GKGnIZadooN1NurkK5mXJzdXXNzfTLb2PnMA3ITQX+2gSknQE6jgYs+gN2IwFN+atiGtpq8JrrgL1fHMA10Ui4b/0ZQwR8XDkTjJlWIejrGYBpnT4EAKip8hA+tVedwlD596rju/zL7+qE1UjOS1bKtm0NbDGv17xXXs/CwkJmEoWqq7iurq5yZQ8ePICdnR1Onz4NAC8dSvWirl27IjAwELNmzYKXlxf69OkDNTU16fKEhAQYGRlJJ68AKocxjRgxAmfPnlXY7vjx4+Hj44Pc3FyIRCJcuXIFKSkp2Lp1KwAgJSUFGRkZGDdunMyQHVdXV5SWluL69esy23xRVlbWSyeY2LJlC37++Wfs3btX7ip01ZX4FzHG5Mqrv6/8fq55/bro0aMHTExMZMpKS0uxcuVK/PLLL8jIyJAZVlZRUQFVVfmv+piYGPB4PHh5eckcu0GDBuG3336DWCxGSkoKHj58KHN1vy7EYjH+/vtvuck2xo8fj3nz5iE+Ph5jx46Vlru7u9faXnx8PIqKijB27Fi587xs2TLcv38frVu3RuvWrREQEIDPPvsMLi4uaNGihVxbIpEIQOX5J82MeT9wqjsBjgfjsmI8K62ArpCv7KhIA6PcrBjl5kqUmytRbq5E9/w2BUO/Bj69CLSwB67vBQ7PAkLaAlscgZ9HA4n7Zaqra/Ix9puRaGmhiSQ7H6gZvg+PBA5f/PIMtr6huLdoIdhL7rmoToVX1fl9h3u/TVD1YSpVSe/F8qqy0tJSAMDjx4+hqakJHR2dOm9n8ODB2LFjB+Li4uDs7AyRSITp06ejqKgIAJCZmQljY2O59YyNjZGXp/g+cg8PD/D5fOzbtw9A5bAqU1NT6UyDubmVE8INHz4cfD5f+rK0tAQAuVkgX1RaWgqBQKBw+aFDhzBjxgysXr0aXl5eMsv09fVrnJUwPz9femyrhu1Ur1f1XtEQopep6TjOmzcPoaGh8PPzw5EjR3DhwgV89dVXAP47r9Xl5uZCLBZDV1dX5tj5+vqioqICmZmZ0sdDtGzZ8pVizM3NRXl5uVysVe+rn/Oa9ql6ewBgb28vE6uLiwuAyvPM4/Fw4sQJmJiYYNq0aTAxMcGAAQNw+fJlmbaqzrmi40KaMBU+VAWVwzlNykpp0ivSaFFuptxMuVl5uZl++W0qRO2B6ecrH32U/ieQFAU8zQJuHgVSTwKMAR3/mxxATVMNHnP64MT2RCRddobmsg/wNOcX5BzcC/09+/DMZRC0X7jC+DKq/3Z+3+XnBL/O1d2myNDQEEVFRSgsLHylJOvj4wMfHx/k5ORg3759mDVrFnR0dLBq1Sq0bNlSZlKKKo8ePYKBgYHCNrW0tODu7o6IiAj4+flh9+7dGDdunPTKbNW6YWFh6Natm9z6VYm2JgYGBgqn1T9//jy8vb0REBCAuXPnyi23tbXFn3/+KVeenJwsfaSClZUV+Hw+kpOTZa5wJycng8fjwdraWmFstanpqvSePXswY8YMBAYGSsuio6NrbcfAwACqqqo4d+4ceDz566AtWrTA06dPAVT+gfQqRCIR+Hy+3Dl/9OiRdNsvetmV9qr6hw8frjEZ29jYAKg8L3v37kV5eTn+/PNPzJs3D+7u7rh//750H6vOeW2fO9J0qasVovQ5oF9RhoKScrRWdkCkwVFurh3lZsrNVSg3V6JffpsaFT5g5QqM+BaY8Bvw+ZXK8sipQEg7YLUlED4C+NEVKj/0gVvr32FrlY+LfzzEI64/tg+pnHb9/uJFtWxEHk/6y++72/l9V1QNu3rdWfeMjIzg7++PAQMG4MaNGwCA3r17Izs7G3FxcdJ6xcXFiI6Ofunz4ry9vREbG4uoqCikpaXB29tbuszGxgampqZIT0+Hg4OD3Ku2CTNsbGxw584dufLExESMGDECQ4cOlT4Gobphw4YhKytLZljYxYsXkZaWhmHDhgGovIrp4uKCPXv2yKwbERGBvn37QldX8QR2ampqr3T1s6SkROZKuVgsxu+//17rOq6urhCLxSgoKKjx2KmpqUmPb02zTNYWq4qKCnr06CG377t37waPx0Pfvn3rvG8A0LdvX2hoaODhw4c1xqqtrS1Tn8/nw9XVFV988QUyMzNl/pBKT08HgNf+A4c0btomlZ0CfUkZ/kp7rORoCKk/lJspN1Nurh/0y29Tp28B+B4Bjn8JCA0q7wt+kg6oqAF5t8HLvQlXxkFdOAVXLnuil2g6Yu2/h1NiHiqePIFqHWdUU6XO7zvDxsYGfn5+mD17NrKzszFw4EDk5+cjMjJS4Zd2UFAQ8vLypMOqLl++jNjYWKxatQoA4ObmBkdHR4wfPx6rVq2CoaEhQkNDUVJSUuPV2xe5u7tDKBTC398flpaW6NXrv/vUeTwe1q5di8mTJ6OwsBDDhg2Dmpoa0tLScODAAURGRkIorPm51I6Ojti/fz8kEon0ymN2djaGDh0KLS0tfPbZZ0hISJDW19HRQYcOHQBUfuG7ublhypQpCA0NBY/Hw7x589C/f3/pcwSBytkhnZ2dMXPmTHh6euLIkSM4cuQIjh07Vus+29ra4uDBgzhw4ADMzMzQqlUrtGrVSmH9IUOGYNOmTWjXrh0MDAywadMmlJWV1boNGxsbBAQEwNvbG4GBgXBwcEBpaSkSExOl927xeDysWbMGEydOxMSJEzFhwgRwHIdTp05hwoQJcHBwgK2tLR49eoTw8HB07NgRIpEIFhYWWLJkCdzc3DB16lR4e3vj2rVrWLRoET7++GOZGTLrQk9PD8HBwfj8889x9+5dDBw4UDor5+nTp7F//35cvXoVc+bMwfjx49G2bVs8efIEq1evRpcuXWSuJF+8eBG6urqwt7d/pRhI09CmbVvcuyWBHp6jtHQA8D4AACAASURBVFys7HAIqTeUmyk3U26uJ3WZFaspv5r8bM9v4mk2Y4kHGTu7jrEgHfZP+G62KSCGbfo8gl3p2JMVREfXuamS5xXMfN5htun0rXoLL6c4hx1KPcTuFjS+GaSby4yS1T//VTP4PX36VFpWffY+xhirqKiQzkjI5/OZqamp3KyNL4qKimKurq5MJBIxgUDArK2t2cqVK5lE8t9sq9nZ2Wzy5MlMT0+Pqaurs4EDB7KEBNkZzKvPKFll4sSJDACbP39+jds/cuQI69+/PxMKhUxbW5t16dKFLVy4kJWXlyuMOSsri6mqqrK4uDhpWdWsizW9qs/w+OTJE+br68t0dXWZtrY2mzBhAsvJyZHbzv79+5m9vT1TU1NjNjY27LffflMYU5WcnBzm6enJ9PX1GQAWFBTEGKucUXL06NE17ounpyfT1tZmLVq0YHPnzmVhYWEy57pq365fvy5dTyKRsG+//ZZ16NCBqampMZFIxAYOHCgz4yhjjO3du5d1796dCQQCZmBgwIYPH87S09MZY4yVlJQwX19fZmRkxAAwHx8f6Xq///4769ixo/Qz9OWXX8qck5o+j4zV/JlkjLFdu3ax7t27M3V1daanp8d69erF1q5dyxhj7NGjR2zSpEnM0tKSCQQCZmxszLy9vdndu7LfLx4eHrV+lqvQbM9NMzc/vhTOwnz3sW+nfsvWHEtqkG0Q5aHcTLmZcvN/KDfLqmtu5irrNl8ODg6stod1vxOK84A1lsDQ1bijMRpHwv6BoCgPDpmR6HIsok4z25WLJWi/8ChmD7HGjEHt3yicK9lXEHY1DOcenoOESdCnZR/8+N6P1bZXjgpWAQ1VDQWtNKykpCTY2dkpZdvk7Rk5ciTMzMzkHrbeHEVFRcHDwwMPHz585UkymouCggIYGxvj5MmTLx3SV9t3AMdxlxhjDv/P3p3HRVXvjx9/ndkXGHZQQQRF3Hdc0tw1cy0tlboatlz023Yzr1b3VlrXyluZt/2XLerttqBmbmSbqeSWS5qJGiJuIMq+wwAzn98fA5MIKCqb8nk+HqPMmc/5nPcZBt58zvksdRFjY6Qoyu3Am4Aa+EgIseiS1wOBFYB7WZmnhRDfXK7OusrN9oRtrHg+gUJtMWmTBvL8+I61fgyp4cjc3DTI3Ny01HdulmN+mwJ12bT2NivB3XzQT7pAoV7HLwHT2ffNNnYm7eRKF0HKlzq6ngmvCksLefjHh5m+aTqx6bE82PlBvAxeJOUlkV6YztsH3uZvP/2NsWvGEvZZGCNXj6TELmfrlOrOs88+y6effkpmZmZDh1Kndu7cyQcffEBAQMAVZ2+8mb3//vv069fvislV+pOiKGrgXWA00BG4R1GUS1uUzwIrhRA9gHDgvfqN8k8qF1/UtixUKheKSmW3Z0m6Ecnc3LTUd26Wjd+mQFM22L60GIAxfYdyqkMUuuJc9qwv4T+fLWfc1+P4Ku6rahvBKpWCSoGiUhsbD53j6a9+Y0/S7yRkJ9QohPjMeKZ9M42fk37mr13+yqZJm3i85+MMaTmE8/nnGbFqBEsPLeVkzknaebajT7M+ZFuzySvOq413QJKq1Lt3b1599VXOnDnT0KHUqQkTJnDixAmWLVtW5eyRTYWbm1u1E6VI1eoDxAshEoQQxcCXwB2XlBFA+fSzbsC5eoyvIpM3ishCqCwUFcvGryTdiGRublrqOzfLCa+aAlXZt9nmaPy2cGnBvx75mJ2PPkBq5gAGJ4STfn4n/8p8gf8e+S8mjQmbsOFj8mFwwGCS85NJzk9G65PLJ795ohzJRmv5jegfM3DVubLznp3VHvp8/nme3f4sv5z/Bb1az/O3PM/k0D8X0O7l14v9F/bT0asjd4feTe9mvQFYG7+W3cm7yS/Jx1XnyomsEyTnJzPQfyBqlbru3iupyZk1a1ZDh1Dnytfia+r+7//+r6FDuBH5AxcvypkI9L2kzALge0VRHgPMwAgaiskThSzsajNWa2mDhSFJ0vWRubnpqO/cLBu/TUH5mN6YV0HYof+jmIwe9J85j8QnnuSPvHMQOJLH9wayd+wehKGU9MJ0YhJjiEmMQaNoKBWl6MpmpldQYSu2YFK7klucS4mtBK1a6zyc1WZlRewKfkn+hT3nHTPyPdL9Ee4OvRtvo3eF0Ma3Gc/4NuMrheyidQFgwtoJqBU1RTbHdO0f3vYh/Zr3q+13SJIkSapaVZNCXNpF6B5guRBisaIotwCfKorSWQhhr1CRokQCkQCBgYF1EiwqNWp1NgC2fNn4lSRJkiqSjd+motWtcHo7/Pw6uLeEXjMw9exJaMxW2uTksP2epznifwd9fxhPf/9TBM+4kzhNGh56D/xMfuQU55CYm4if2Y+0bB1j3tzBHSPPsCHxPfJK8tDatMRnxXMi6wQ/nP6BHed24O/iz/SO07mt1W109+1+VeG29WiLWWumhUsL+jbri4/JhyX7l5BRmAFAQnYCsWmx3NLilkoNakmSJKnWJAItL3oeQOVuzQ8CtwMIIXYpimIAvIGUiwsJIZYCS8Ex4VVdBazV5wNgz5dzRkiSJEkVycZvU3F/NJw7CEsHQ0lhhZfUFgtdpw/CsPgNDnWeyeb4QHov/Zaw5yKcZTwMHngYHGsC5+Q5xuHqFMcabYOiBlU6XFefriy/fTlalbbSazXRytKKnffsRKU4xkCkFqSyZP8S1p1Yx8q4ley/sB+Av3b5K4/3fPyajiFJkiRd0V6graIowUASjgmt7r2kzBlgOLBcUZQOgAFIrdcoL6I3F0MJeOXc3OMFJUmSpKsnG79NiXfZEkVlY38v5hEeTti48XTMLWb9U2v5JakVuR8fZNB9XVFrKw7CV6scveBCLX0Z23osdmGnrXtbQtxDCHILwqKz4GX0uu5wyxu+AG56N0waE7uTdxPiHsL9ne5nddxqcopzrvs4kiRJUtWEEKWKojwKfIdjGaNPhBCxiqK8iGNNxfXAHOBDRVFm4+gSPUM04DqKvi0DOJMA7oUNN++WJEmS1DjJxm9TUr7kUWnlxi+A2sWMq4uZUSN07PryR44wgrSU/YyK7IzF68/1dsuXPdIpLiwauKjKumqbTq0jelI0Ro0Rs9YMwPenv+d45nHSCtNk12dJkqQ6UrZm7zeXbHv+oq+PAAPqO67qeHccgDquEL21oSORJEmSGpumO692U6TSAEqVd34v5vWXcDoU76XL4aVkJmYTNX8HB/7xNvm7dzuqKfvU2Oz2y9RS+7yN3s6GL4BWpeXXlF95cuuT9RqHJEmS1HhZmgWht2ajKdU3dCiSJElSIyMbv02Jojju/touuhxuK4XMUxXuBitqNZ4REfik/UavnS+iyzrHzoxOxLz2LXabHU1Z69dWv23fSp7q8xQAZ+S4LkmSJKmMq68/+uIstHZTQ4ciSZIkNTKy8dvUaPRweid8PQv+30B4uQW82Q0W+sAHg+HVNvB6KJ7FnxI6rZQuww8zuecq/HMOkeAziK8WbCPvt6MA2BpuSBcAt/rfypTQKdhFA7fCpVoTFBTE3//+93o7XkFBAc2aNWPbtm3ObUOGDEFRlEqPoqKiCvsmJSUxceJEXFxc8Pb25tFHH6WgoKDSMT788EPatm2LwWCgV69ebN68+YpxLV26lLVr117/CV5k+fLlKIpCXtmEdbVl5cqVLF++vFbr3Lp1K4qicPjw4VqrUwhBly5d+PTTT2utTqlx0np6o7dmYRfuYJMzPkvS9ZK52UHm5psjN8vGb1Pj4guJe+HEFjD7QN+Z0Lw7+HYEs7fjda0RVBrUnUeic7Fh0ibTr1MBHY8uJz25kM3/TSIsrwBhbfgBVWatmUxrJhfyLzR0KNIN6O233yY4OJjBgwdX2D506FB27dpV4aHX/9mFsrS0lFGjRnH69GmioqJ48803WbVqFZGRkRXq+fLLL5k1axb33XcfmzZtolOnTowbN+6KiaMuEuzYsWPZtWsXJlPt3g2riwTbs2dPdu3aRZs2bWqtTkVRmDdvHi+88AKlpXL915uZymxCW5yFHTdKiir/0StJUuMmc/P1k7m5enLCq6bmoR/BbnM0dGuiKBsyEvCc9hc6e0TT7NBP7M3pyFBNEJrPfqbkljZo1FBy9iy2vHwMHdqjqNXO3c9lFXLwbBbtm7nS2sel1k8nwDUAgO1J2xkYMJDF+xZzOO0wrjpXvhz3Za0fT7p52O123n33XZ577rlKr3l6etKvX79q9121ahVHjx4lPj6e4OBgALRaLeHh4cyfP5+2bR0zq8+fP5+IiAjnMQYPHsyBAwdYtGgR//vf/677HAoLCzEajVcuCPj4+ODj43Pdx6xLQgisVisWi+Wy7/+1mjx5Mg8//DCbNm1i/PjxtV6/1DgoioIgGxQ1pxOTCGnn1tAhSZJUQzI3Nz43W26Wd36bGqNHzRu+4OgmXWpF16oVPg8/TNtX/sng0HN4Jm8nUxXM5w9/zb6B4zlx+2hO3X03KZ/+jwNnMtn6Rwpv/nicAf/+iYc/+5X562Pr5HRuD74dgILSArYlbuObk99gEzZi02MpaeLd3WbMmEFYWBjR0dF07NgRk8nE2LFjycjIID4+nqFDh2I2mwkLC+PQoUMV9rXZbLzyyiuEhoai1+sJCAhgxowZlz3exx9/TKdOnTAajXh7ezN48GBiY//8vqelpREREYGXlxcmk4khQ4awb9++autbtmwZer2erKysCttjY2NRFKVCF6V169YRFhaGwWCgWbNmzJs3j5KSy3//f/rpJ5KSkpg0adJly1Vl06ZN9O7d25lcAe688050Oh3ffvstAAkJCcTFxTFlyhRnGZVKxeTJk9m0aVO1dQ8ZMoT9+/ezYsUKZ7eu8qu3QUFBzJkzh3/9618EBARgsVgA2LVrFxMmTKBFixaYzWa6d+/OZ599VqHeqrpWFRUVMW/ePFq2bIler6dbt258802FSX0BR/ewLl26YDAY8PPz4+677yY7O5sZM2bw1VdfsW3bNmesCxYscO73zjvv0LZtW/R6PSEhISxZsqRCvQsWLMDb25vt27fTu3dvDAYDq1atqrJrld1uZ9GiRYSEhKDX6wkNDWXFihUV6tu+fTsDBw7EYrFgsVjo3r07q1atcr5uMBgYM2YM//3vf6t9/6Wbg17r+Pnfe7L2uudJUm2QuVnm5ovJ3Fz/uVk2fqXL0xgqzA6t8fDA5x9P86s6m07Hl1GiNrCv65OkPvhvBAoZixbxt0VrmLFsL0t+jKOrv+OKe2GxrU7CM2kc3UTO5p7lUKojSYS3CwcgvyQfgBJ7CcVXmOH6ZnXmzBmef/55Fi5cyNKlS9m5cyeRkZGEh4cTHh7O6tWrKS0tJTw8nIuX5Zw5cybz589nypQpbNy4kcWLF5Ofn1/tcWJiYpg1axbTpk1j06ZNfPLJJ/Tv35/s7GxnmTvvvJPvvvuO119/naioKOx2O0OHDiU+Pr7KOssT39dff11he1RUFL6+vgwZMgRwdO2ZNGkSffr0Yf369cyfP5+lS5fyzDPPXPa92bx5M6GhoXh5VV6T+vvvv8dkMmEymRg1alSlP0COHTtG+/btK2zT6XS0adOGY8eOOcsAlcp16NCBjIwMUlNTq4zrvffeo3379owZM8bZrWvs2LHO1z///HO2bdvGe++9R1RUFACnT59mwIABfPTRR2zYsIG77rqL+++/ny+++OKy78Hdd9/N8uXL+cc//sGGDRvo3bs3EyZM4ODBg84yCxcuZObMmQwePJi1a9fy/vvv4+bmRl5eHs899xxDhw6lR48ezlgfeughwJGUH3vsMSZMmMCGDRuYPHkyc+bMYdGiisujFRQUEBERwUMPPcS3335Lnz59qoz1scceY+HChURGRhIdHc3EiRN54IEH2LhxIwA5OTmMGzeO1q1b89VXX7F69WqmT59e6Q+0/v37s3nzZhpwGVqpHri6OnogJaWkNXAkklSZzM3Vk7lZ5ua6Jrs9S5en1kFJAdjtzjWOVIrCqtBhFHZtztQuLTi+8TS/n1BRdMt8hv36H95IWMepcffS554JBHqZmPbRLxQU100/fo1Kg1Fj5Itjjl8kQZYg3A3uAMyLmUdyfjKnck7hofdg8+TNaNXaaz7W+Zdfxnr0WK3EfbX0HdrT7B//uOr9MjIyKozPOHToEK+99horVqzgvvvuAxzdWcaOHcuxY8fo0KEDx44d4+OPP+bNN9/k8ccfd9Y1derUao+zZ88eunbtWiGpTZgwwfn1t99+y44dO9i6datzDM+wYcMICgritdde44MPPqhUp5ubG7fffjtRUVHcf//9zu1RUVFMnjwZtVqNEIK5c+dy33338d577znL6PV6HnnkEZ555pkqEyjA/v376dy5c6XtgwcPJiIigpCQEE6fPs1LL73EwIED+e233wgKCgIgMzMTd3f3Svt6eHiQmZnpLANUKufh4eF8vaquTh07dsRsNuPj41Nt96KNGzdiMBicz8PDw51fCyEYNGgQiYmJfPjhh9xzzz1V1rF582aio6MrfE9uu+024uLieOmll1i1ahVZWVm8/PLLPPHEE7zxxhvOfS++Iu/p6Yndbq8Qq91uZ8GCBcyYMYPFixc7687OzuaVV17hiSeecMZfWFjIG2+8wR133OHcPzk5uUKs8fHxvP/++yxbtoyIiAgARowYQXJyMi+88ALjxo0jLi6O7Oxs3nnnHVxdXZ3HvFS3bt3IzMwkPj7e2QVOuvmYLWqwQ0FqSkOHItUxmZtlbpa52UHm5pppVHd+FUW5XVGUPxRFiVcU5ekqXg9UFGWLoigHFEU5pCjKmIaIs0lR66AgHZbd7tykUSkAbDyUzPTP9vNiVhrfG4tR673Zc8t8cou96fFjFIFejruyapWCzV53V3Je7P8iz/Z9li/GfsFXE74ixD0EF60L5wvOE+IegkVnIdOaSU5xTp3F0FgFBQVVmJggJCQEcCS3S7clJSUBsGXLFoArdqW6WPfu3Tlw4ACzZ88mJiaG4uKKd9r37NmDj49PhckrzGYz48aNY/v27dXWO3XqVDZv3kxamuPuzcGDB4mLi3Mm+7i4OM6cOcOUKVMoLS11PoYNG0ZRUdFlJ684f/483t6VhwC88MIL3H///QwcOJBp06axZcsWFEXhP//5T4VyiqJU2lcIUWn7pc/Lr2pWtX9NDB8+vEJyBUeyfvzxx2nVqhVarRatVsvSpUuJi4urtp4ff/yRZs2aMWDAgArv3fDhw51d3nbt2kVhYWGFP3BqIjExkXPnzjF58uQK26dOnUpOTg6///67c5uiKIwePfqy9W3evBmVSsXEiRMrxXrw4EFsNhtt2rTBxcWFe++9l3Xr1lW6qlyu/Ht+/vz5qzon6cZi8PdHsdsozZF3+KXGR+ZmmZurI3Nz3efmRnPnV1EUNfAuMBJIBPYqirJeCHHkomLPAiuFEO8ritIR+AYIqvdgm5IO42HPB5C037lJo1bxn6ndybWW4m7UEuxtxqzXoMkvZU9UPEeYRmrqAYqGj8H3rnGoTb3rdFmk8nG/5Tp7d2bXvbucz9fFr+PZHc9SUFKAl7HqK401cS1XdxvapVc2dTpdpe3l28qXC0hPT8dsNjvHrNTEiBEjWLZsGW+99RZvvvkmLi4uTJs2jddeew2z2UxycjJ+fn6V9vPz8yMjI6PaeidMmIBWq2XNmjVERkYSFRWFv78/t956K4Az8Y4ZU/V1sLNnz1Zbd1FRUYVZIqtTnoR+/fVX5zYPD48qf4FnZWU539vyq8hZWVm4ublVKAOVvzc1VdX7OGPGDHbv3s1zzz1Hx44dsVgsvP/++6xbt67aetLS0jh//jxabeXeEOqySevS09MBaN68+VXFWH51+NJYy59f/D338PBwfgYvF6vNZqvwPl56vICAAL7//nteeOEFpkyZgt1u57bbbuPtt9+mdevWzrLl3/NLl8eQbi76VqHojmejKpRr/d7sZG6unszNDjI3O8jc7NBoGr9AHyBeCJEAoCjKl8AdwMWNXwGU/9S7AefqNcKmKHgg9H4IYiuO7bizh3/lst7g//ee7Is6yL5t3djp0ZYuW39CPa4PtgZcitesNQPw8eGPmX/L/Gu+qtdUeHl5kZ+fT05OzlUl2YiICCIiIkhNTWXNmjXMnj0bi8XCokWLaN68OSkplbsfXrhwAU9Pz2rrdHFxYezYsURFRREZGcnKlSuZMmWK83tYvu/SpUvp0aNHpf0vnvTiUp6entVegazKxZ+b9u3bO8cNlSsuLiYhIYFZs2Y5y4BjfFGrVq2c5Y4dO4anp+c1z+546ee3qKiI6Oho3nnnHeexwdG96XI8PT3x9/e/7LIN5d3SkpOTq7wSX53yhHzp9/zChQvOY5eryc+jp6cnGo2GHTt2oFJV7rDk6+sLwC233MK3335LYWEhP/74I08++ST33nsvu3fvdpYt/55f7nMn3fjMzX3RW0+gtVqqvOsjSTcamZurJnOzzM1XqzF1e/YHLr4UlFi27WILgGmKoiTiuOv7WP2E1sSpdVDDmZNVKoU+9/RgyrP9MBoV9ntOIDC+EKWkbia8qomWri0B+Or4V5zMOdlgcdwoyrtdXeusez4+PsycOZOBAwdy5Ijj2lXfvn1JSUkhJibGWa6goIDo6GjnleLqhIeHs23bNjZs2EBCQkKFMTTt2rXD39+fU6dOERYWVulR3Zii8n1Pnrzy5+HChQvs2LGDXr16ObeNHj2avXv3cvr0aee29evXY7Vauf12R0+E1q1bExoaWmFGQ7vdzqpVq67YlUin09X46qfVasVms1W4Up6bm8v69esvu9/w4cM5f/48Li4uVb534EhYRqOx0syNV4o1ICCAFi1aVDh3cEyAYrFY6NKlS43OrdywYcOw2WxkZ2dXGeulV6eNRiPjx4/ngQcecH4Gy506dQqVSuXsUijdnFz8fDFYMzGUeJBelN7Q4UjSdZO5uSKZm2VuvlaN6c5vVZcYLu0rew+wXAixWFGUW4BPFUXpLISocBlFUZRIIBIgMDCwToJtUtRaKLVW3p6d6Fg6SWeu9JJ3gAuj+ubyy2fbEdzG0AyF04fTadX52rsdX6t2nu1YMmQJs7fOJsfa9Mb9Xq127doRGRnJnDlzSElJYdCgQWRlZbF69Wq+/LLqtZPnz59PRkYGQ4YMwdvbmwMHDrBt2zbn7IGjRo1iwIABTJ06lUWLFuHl5cXrr79OYWEhc+fOvWw8Y8eOxWQyMXPmTIKDgyvMOKhSqVi8eDHTp08nJyeH0aNHo9PpSEhIYO3ataxevbraheMHDBjA119/jd1ud16xPHToEM888wyTJ0+mVatWnDlzhldeeQWVSsUTTzzh3Pfuu+/mpZdeYtKkSfzrX/8iOzub2bNnc++991aYqGHBggVMmzaNoKAgBgwYwIoVKzh+/Diff/75Zc+5ffv2fPfdd3z33Xd4eXkRHBxc7R8Lbm5u9O7dmxdffBGLxYJKpWLRokW4ubmRk1P9533kyJGMGjWKkSNH8tRTT9GpUydycnI4ePAgRUVFvPLKK7i7u/Pcc8/xz3/+k+LiYsaMGYPVaiU6Opr58+fj7+9P+/btWbduHWvXrnUm1hYtWrBgwQJmzpyJl5cXI0eOZNu2bbz//vu8/PLLlcZFXUm7du2YNWsW4eHhzJs3j7CwMIqKioiNjSUuLo6PPvqI6OhoPvnkE+68804CAwNJSkrigw8+qDCGDmDfvn106tSp2m5a0s1B6+ODoSgTnb0riTmJeBuvYok/SWqEZG6WuVnm5loihGgUD+AW4LuLnj8DPHNJmVig5UXPEwDfy9Xbq1cvIV2nzQuFmO8mhN0uROxaIXa+K8T/Jgsx3+J4bJhd5W55u3aJI+3ai11ht4vFM6PFOzM3i29e2SzOf/m1sJeU1OspHLhwQHRe3lks+mWR+Pj3j8XivYvFs9ufFY9uflRMi54mxq0ZJ8I3hAtrqVUIIcSRI0fqNb66EBERIS79/C9btkwAIjc317nt5MmTAhAbNmxwbistLRUvvfSSCA4OFlqtVvj7+4sZM2ZUe6wNGzaIYcOGCW9vb6HX60VoaKh45ZVXhN1ud5ZJSUkR06dPF+7u7sJgMIhBgwaJPXv2VKinVatWYs6cOZXq/8tf/iIA8fTTT1d5/G+++UbceuutwmQyCVdXV9GtWzfxz3/+U5Rc5nN2/vx5odFoRExMjHNbYmKiGD16tGjWrJnQarXC09NTTJo0SRw9erTS/mfPnhV33HGHMJvNwtPTUzz88MMiPz+/UrmlS5eKNm3aCJ1OJ3r06CF+/PHHamMqd+LECTF8+HBhsVgEIJYtWyaEqP79OX78uBg6dKgwmUyiZcuW4t///reYP3++8PLycpYp/97n5eU5txUVFYnnn39etGnTRmi1WuHn5ydGjRolNm7cWKH+//f//p/o0KGD0Ol0ws/PT0yePFlkZ2cLIYRITU0Vd955p/Dw8BCAmD9/vnO/t99+21l3cHCweOONNyrUe2mM5bZs2SIA8fvvvzu32e12sWTJEtGxY0eh0+mEt7e3GDRokFixYoUQQohjx46Ju+66SwQEBAidTif8/f3FzJkzRXp6eoW6u3btKhYsWHC5t18IcfnfAcA+0Qjy5o38qOvcbC8uFt8Nm+nIO7Hf1+mxpPojc7PMzTI3/0nm5opqmpsVR9mGpyiKBogDhgNJwF7gXiFE7EVlNgFRQojliqJ0ADYD/uIyJxEWFiYut1i3VAPbXoMtC6HHNDjwP8c2kzcUlK2fqDHAsxcq7SZKS8n8/AsuvPwydkXD2e73kGDpjbYkn/4jPOh07+BK+9SV5Lxkbvvqz6nVdSod7gZ3PPQeuOvdyS3J5Uj6Eb676ztauLTg6NGjdOjQod7ikxrGHXfcQUBAAO+++25Dh1Ln3n77bebOndukJ3r6448/6NSpE/Hx8c6lMapzud8BiqLsbNC0DAAAIABJREFUF0KE1UGITUZ95OYtQ8I50j4Sr7/kEj7wjivvIDV6Mjc3DTI3Ny31nZsbTbdnIUSpoiiPAt8BauATIUSsoigv4mjJrwfmAB8qijIbR5foGZdr+Eq1pHxt3AP/A/dAGDQXukwGrRG+mQeHqu5uo2g0eN43nR0bt9Hi6H5an44maIyFX466sjXGQmL+YQZODcVkufxscrWhuUtzvr/rewQCd707Ro2xwmD+b099y9xtcykoKajzWKTG49lnn2X48OEsXLjQOQPkzcZmsxETE8Onn35aYWxUU7RkyRJnVzfp5qeQD0B+mvy9Lkk3Epmbm5b6zs2NpvELIIT4BsdEVhdve/6ir48AA+o7riYvsB8E9IHQ22DAE382hgE0Oigtrn5fYPuUx9kal8Iv/xgBgAjrwynP/iSoxpN4LJOB4W1pG+bnbIxmFRSTkmvFz9WAm6nyVO/XqrlL9VPCmzSOsScZRdVP7S/dfHr37s2rr77KmTNnbtoEm5uby6hRo+jSpQsffPBBQ4fTYIQQBAcHc8899zR0KFI9MZodEy0WZDTdOyqSdCOSubnpaIjc3Kgav1IjFdgPHvqh6tfUerBVMRnWxUXUSoWljrznPw9z5+KddoiEuxfxw8dH2LstkWbDWpAl7MxZ9RsA3Vq6s+6R+rnW4WlwTK3+v6P/o0/zPlcoLd1MLl6C4Gbk7u5OcfHlL1A1BYqi8NRTTzV0GFI9sjX3RGWzYs1qwLX2JEm6JjI3Nw0NkZtl41e6Pho9CDvYSkFd9cdJrShkFRQz4Z3tnM8uIjVP4U03f9pmJ2H99hX2dImgR7wgJT6bn40lKDowGzRkFdTfL4VOXp3q7ViSJElS3Sv19MKYnEFBZmNa1VGSJElqSDIjSNdHXTZet7D67sL923gR6ueKu0nHkHY+PDE8FO0zjt7svVOO8YD/Gbo+1AGfYAvDC3W8YPZiXKAXpbb6G86tKAo9fXuSX5Jfb8eUJEmS6k6ppx/6ogxEXu0Nn5EkSZJubPLOr3R9XHwd/7/eFiz+cN968K64QPXoLs0Z3eXS8bZtsXaNJmH8eNof/xq/W/IQ857h+L4LbF95nIB9BXR3FZRYbWj16no5FZPWxPak7exO3o0bcg1QSZKkG1mJrz8G62k01kAKSwsxaowNHZIkSZLUwOSdX+n6dJ0KLXqAWyDkJEFaXI131bsraPXF2JIT4MBnKIpCaO9m3LugH/kt9HTMUfjixV84HZtehyfwpxGBjgm5fjhVzfhmSZIk6Ybh2akThqIMtMKV89mVl+OTJEmSmh7Z+JWuj0oNkVvh3ijH8ytMflVB+glUOoG1wJXUfSUUxTkazgazltwuFqK9bWi0Kja+/Rvff3SYgpy6HQN8V+hd+Lv4k18quz5LkiTd6Hr37IROOC6eJibLxq8kSZIkG79SbdHoHf9fYdkjhICTMbDjLdi+BK3JRlGKjbRf1aQv/dBZTK0onNMJpv6zD33GB3PiYCqfL9hN7M9JCHvdjQU2aU3sPrcbu5Czg0qSJN3QNAaMmjQAUlIyGzgYSZIkqTGQjV+pdpRPfHW5O7/WPIhdAyvGww/PQUYCzR8YTtCcoRg8SylJTPyzOpUKm02g1qroPTaYe57ri3eAC1s/+4M1r+8n9WxunZyGl8GL9KJ0cqw5dVK/dGVBQUH8/e9/b+gwJEm60SkKFpNjMsYL52TjV5Kuh8zN0s1CTngl1Q6NwfF/aVnjt7QYTvwEJzbDuQOQkQAFZWN3VRp4/AC4B6IBNJv/hd69mJyjR0l87HH831iMWgU2IaAgA1L/wD07kTvCzvKHWc3O2BBWvZRFl0759HloLHpj7X2MX+j/AqO+GoVN2MgrzkNBwawz11r9kiRJUv3x9CkEYcd6WjZ+JUmSJNn4lWqLpuzO7/Ef4PQOSNgKhZmgNUOL7tBhArgHOh5+nR3/O/fV4+pfSEFRMLk//EDxd+/SOVNhpEiHV6c6iylAe72F4OCW/HK2P4diRxM/fzf97wohtI8fiqJc92m0cGlBv+b9KLGXcDrnNADtPdujVtXPjNOSJElS7dH5u6JPyKY0xdbQoUiSJEmNgOz2LNUOjdFx9/f4d3B2L7QdBfeuhKdPw/3fwPj/wMAnocvd4Nv+kn31uPpbadHxMAAFX/6bkbsX8rr1bcfrtzwKj+xBzD1N8fRdcMdnDOp7nskh7+LiaeDHZUdYt+QAGedqZ6Iqs9ZcYcyvTdyYfzTNmDGDsLAwoqOj6dixIyaTibFjx5KRkUF8fDxDhw7FbDYTFhbGoUOHKuxrt9tZtGgRISEh6PV6QkNDWbFixRWP+fHHH9OpUyeMRiPe3t4MHjyY2NhY5+tpaWlERETg5eWFyWRiyJAh7Nu3r9r6li1bhl6vJysrq8L22NhYFEVh8+bNzm3r1q0jLCwMg8FAs2bNmDdvHiUlJTV9uyRJugmpvNzRF2WishoaOhRJAmRulrlZamiy8SvVDo0OZsbAE7/Dk7Ew6QMIHQVq7ZX37TQRBs5BN3EBAOf3uXN6szex0QHYH9oOty2kxO7OiTuncGLESBLGjKE4046v7iR3z+vFkL+0Iy0xj6iFe9i5Jp6i9BzyYmIoOX/+mk5leOBwdGodGpWjY8SNPPnVmTNneP7551m4cCFLly5l586dREZGEh4eTnh4OKtXr6a0tJTw8HCE+HMisccee4yFCxcSGRlJdHQ0EydO5IEHHmDjxo3VHismJoZZs2Yxbdo0Nm3axCeffEL//v3Jzs52lrnzzjv57rvveP3114mKisJutzN06FDi4+OrrHPSpEkAfP311xW2R0VF4evry5AhQwBYuXIlkyZNok+fPqxfv5758+ezdOlSnnnmmWt96yRJugkoRhd0JemobJYKv+MkqSHJ3Cxzs9SAhBA39aNXr15CunFkrV8vUt9/X/wU/oA40q69OD58hDjWp6840q69ONKxk0h65h/iSLv24vT4/sL+WnuRG/OzSP1gqThyZ7hYM+U18c7MzeLDiFVi64Cp4mivMJG3+xdhLy6+6jiOHDkicq254nDqYRGXESeOZx4XcRlxzq/jM+NFQlaCOJl1UpzKPiVOZ58WZ3LOiDM5Z0RRSVEdvDNXLyIiQqjVahEfH+/cNnfuXAGIFStWOLdFR0cLQBw5ckQIIcTx48eFoihi+fLlFeqbPn26CAsLq/Z4r732mujZs2e1r2/atEkAYuvWrc5teXl5wtvbW0RGRjq3tWrVSsyZM8f5fMKECWLUqFEV6goNDRWPPPKIEEIIu90uAgMDxYwZMyqU+fjjj4XBYBBpaWnVxiRJ1Sn/eagKsE80gvx2Iz/qKzef3Rklvpo4T7wT+a1IzUutl2NKdedyP5c3CpmbZW6Wrl1t5GY55ldqVNzGjwfguF8PTiVnEeTrSVFrC0EhAbSeNB5dmzbkfv89+XEZHIsDPvorALpWrejXOYdM3R/8mhHE4c6RnEuPJX/W3wme/RAuQ4ag9vBA7epa41iMGiNuejfswo6iKBxel0r2OSsgqHD/QJQ/F9iFQKc+h1ZVgzveV8G7pQsDp4Re9X5BQUG0adPG+TwkJASAYcOGVdqWlJREhw4d2Lx5MyqViokTJ1JaWuosN3z4cL744gtsNhtqdeUx0N27d2fevHnMnj2biRMn0q9fP3Q6nfP1PXv24OPjw+DBg53bzGYz48aNY/v27dWew9SpU4mIiCAtLQ1vb28OHjxIXFwcH330EQBxcXGcOXOGKVOmVIh32LBhFBUVcfjw4QrHlCSp6bC1GYFB+R4ULUmpF/A2ezd0SFIt+3llHGln8xrk2DI3y9ws3Xhk41dqlPyCA/hbvwecz6e0DuDVskTQfOFCst5/Cb3qDIbb7scU1gtNYAiKVzDNNXra2+z8uuoA+3/uwB6Pf3L+8x9pteh19N4etI3ZVuMY1Co1Aa4BzuendIUUXWHeq/yS/Eubxg3K3d29wvPyhHfx9vJtRUVFgGPsj81mw83Nrco6k5OTCQgIqLR9xIgRLFu2jLfeeos333wTFxcXpk2bxmuvvYbZbCY5ORk/P79K+/n5+ZGRkVHtOUyYMAGtVsuaNWuIjIwkKioKf39/br31Vme8AGPGjKly/7Nnz1ZbtyRJNzej0YTQOZauS0lOg6CGjUeSQOZmkLlZajiy8Ss1Snd092dkRz80KhXDFm+l1PZng9Jy+ygs7ifh26fgwhsQXfZCq1vh/mhUahVh4b3oMNpKzNJfSFCN5kLQYFrHfkFrqxW1Xn9NMdXk6u7R9KO46Fzw1Htix+7oYoGjmwU4GtRqRY1apUajaFApqlqZpbo2eXp6otFo2LFjBypV5WkBfH19q903IiKCiIgIUlNTWbNmDbNnz8ZisbBo0SKaN29OSkpKpX0uXLiAp6dntXW6uLgwduxYoqKiiIyMZOXKlUyZMsX5vpXvu3TpUnr06FFp/+Dg4CuesyRJNyeTTgNGx7rw2X8kwy0NHJBU667lzuuNSOZmSaodsvErNVomnePjqVYpjjV/L9Z3JnScAPmpjsfPb0B2xauIZjc9o+cO4lx8Flve/4XYTg+Svmg3gx/sgXeApU5i1qg05FhzyLHm1Ki8l9GLZuZmdRLLtRo2bBg2m43s7GxGjhx5TXX4+Pgwc+ZM1qxZw5EjRwDo27cv8+fPJyYmhkGDBgFQUFDgnLTjcsLDw5k6dSobNmwgISGB8PBw52vt2rXD39+fU6dO8de//vWa4pUk6eZk1KqxG6xgh8KkhukaK0m1QeZmSaodsvErNXpqRcFmv6TxqyhgaeF4AMSuhYyTVe7fIsSdsbcp7P33lySUjGPlS3vpPKQlfcYFYzDX7tjcQEsgJbYSFEVBQan0v81uo1SUYrPbSMpLoqi0qFaPXxvatWvHrFmzCA8PZ968eYSFhVFUVERsbGyF8TyXmj9/PhkZGQwZMgRvb28OHDjAtm3bWLRoEQCjRo1iwIABTJ06lUWLFuHl5cXrr79OYWEhc+fOvWxMY8eOxWQyMXPmTIKDg+nTp4/zNZVKxeLFi5k+fTo5OTmMHj0anU5HQkICa9euZfXq1ZhMptp7gyRJumGoVQqFLmZ0qdkUp5deeQdJaqRkbpak2iEbv1Kjp1JV0fi9lEYPNmu1L7uNGE5/d3eaPTaHk6ET+X0L/BFzih6hVno8Oha1unZW/dKr9ejVl+lWfdGY4ezibGz2xrmG8LvvvktoaCgffvghzz//PBaLhY4dO/Lggw9Wu0/v3r1ZsmQJX375Jbm5ubRq1YoFCxbwt7/9zVnm66+/Zs6cOTzxxBMUFRXRp08ffvrpJ+fEHtUxGAxMmDCBzz77jKeffrrS61OnTsVisfDyyy/zySefoFarad26NePGjaswsYckSU1PtsEdvTWd7BxBUWkRBo1c81e6McncLEnXTxGXdie9yYSFhYnLLdQtNX63/yeGQE8TS+8Lq77Qt8/Ar5/CPxIvW9eFf79K3rZtZFmNHPW5jWz3ECzF5xn57Fiatf5zEomjR4/SoUOH2jqFKp3NPUt+cT7uBnc0Ko3jUTYOWK2oUSkq56OxjQuWpJvd5X4HKIqyXwhxmV9I0pXUZ25e/Pz/4f9HIBmuIfT8V0v6Ne9XL8eVal995GZJkhqv2sjN8s6v1OipFAX7lS7SqHWXvfNbzu+pefg9NQ+A9nv3smfOW8S3mchXr+4ntIcH/cM7Yna7tgmxrpaL1oXCkkIyijK40kWo8kbwxY1itUqNVqXFz+QnG8eSJEnVaOkfgNuxFNLVvdmTtEc2fiVJkpow2fiVGj11jbs9F4MQjvHANWDu3ZsOt7XH+4sXOR04iuOM5OSRXfTo64IxxE5JSoqjvrKHEAKVXo/Gy6sWzgo8DB54GDwQQmAXdkrtpdiEDZuwYRd25/+Xfl3+PN+aD4CnwROdWnYfkiRJqoowuOOuPgyKiqRzFxo6HEmSJKkBycav1OipVAq2K/XOLx/D9e9WELERmnetUd3Nnv0nvvPmYpo4iea/7OJ4yN3sielMn5YWitJz0NitoDgmrBJCYLMLVEYjwmYHYUdlNqNUsaj81VAUxbn80dXIseZwNvcsNtE4xw1LkiQ1BsGBAbjpzwOgPVnYwNFIkiRJDUk2fqVGT62AzW6/fKGuUyHnHOz9ENLja9z4BVDpdPjNm4vLzl0Et3AjKTOVIrUHhSZfdEYNLh56NFo1pZmZlCQlYU1IcO6r9WuGxsf7Wk/tuqgUxyRddnGF90aSJKkJ6xDciiLLOSgGU3LtTG4oSZIk3Zhk41dq9DQq1ZW7Pbv5wy0POxq/tuKrPobL4MG4DB4MgCdw5MgRzO56CrKLyTiXj9FVh9liQddSBSrHo+T0GUounEfl7oZKW7tLJtVEeeO3oKQAs9Zc78eXJEm6EZjcvTG6pKKk2TDlyN+VkiRJTZls/EqNnkoFV7rxCzgmvYJravxeSlEUTBYdBhct+VlWCnOLKcovwcXdiMFFi6Io2D09KE1LozQ52TEmuKQEBGWTVwm0LVqgdnG57liqU75ch7zzK0m162ZfBaGpUZs8QWdDV5yBUup25R2kRk0IISd5lKQmqLZys2z8So2eWqVQYqtBA698fd3SK8z6fDIGoqY7JsnSW8Bgcfzv2gxufwWMHmi1WgoLCzGZTFi8jBhddeRlFJGbUURBbjGuHga0Pj7YsrOx5+WDSoVi0KOoHMsS2XJyKE1Lw15Y6Gi5l7XeNb6+1z1GuFz57M+y8StJtauwsBBtA/TmkOqI1kiJSo/Klo4ad9l4uoFdnJslSWpaais3y8av1OiplBrM9gygLvuBsJU4Gpsrp0NBOhg9wMXP0TXa4g+ndkBRFvS8D6y5UJQDucmQsAU63w1tR+Dr60tSUhL+/v4YjUa0OjXufiashaXkZ1rJSilwjAduHYJGW7kxaz2RgD0vD3teXtlJlN2+VhQ0frW3NJFKUWG1WckvyUer0qJRaZzdoSVJujpCCAoLC0lKSsLPz6+hw5Fqi6JQpPNCpUkBpQcr9x1kau8eDR2VdA0uzc3yIoYk3fxqOzfLxq/U6GlUCvEpecz6dD/N3Q10bG6hR6AHbXzMFROfpuzOr80K+alwbCN4tnE0cM/+4mgIl3Pxgwlv//n83EFYOtjZZdpisTg2nztHSUlJhXiEEJQU2bAWlgKgM6jRGTUVYhHlSy6VzxRtt1N64QJcuID63DlURmOtvDfphelYbVZOcMK5Ta2oUalUuOvd0ark3StJuhparRY/Pz/n7wDp5mD0CsBFk8oFtSuJJ4+DbPzekC6XmyVJunnVZm5uVI1fRVFuB94E1MBHQohFl7y+BBha9tQE+Aoh3Os3Sqm+TeoZQEGxjROpeWyLS6WwxLG0T0tPI8vv70Mbn7JxteVjfo+shz82Ob4e/hx0muj4uqTQMSN0ThKYfSoexDle+M8u0xaL5bI/ZPnZVn5Zl8DRXckYXbT0ndCaDgNaoFJVfSW60G7n1OQpqL29MXbqRMD776Goru8ubYm9hHN55ziXd47k/GTO5Z0jKS+JjQkbeabPM9zb4d7rql+SJOlmoGnVD/dfj3FBQO7p1IYOR7oOV8rNkiRJl9NoGr+KoqiBd4GRQCKwV1GU9UKII+VlhBCzLyr/GCAv3TYB47u1YHy3FgDY7IKTafms2neWD2ISOJyU/WfjV6WG9uMgcR8UZoJHELS46COiNYJXG8fjUs67xjW/kmx20zPsvg50GRLAzyvj2PrZH/y+NYlbp7QloJ1HpfLGLl3wfuQR8rZuJW/bNjI//wKNtzcaP19MPa7to6xVaWllaUUrSyvnNqvNysaEjRSUFlxTnZIkSTcdrQmLJhFKoDBZ/m6UJElqqhpN4xfoA8QLIRIAFEX5ErgDOFJN+XuA+fUUm9RIqFUKIb4u3NMnkA9iEiqPBQ7/7BorLh8vfPUzRfsEujJxTk9O/JrKzq/iWbfkAK27+9D/rja4+VSclMPnsUdxGTKYU1OmcmHhQuf21t98g7518LXFfgmdSodG0ZBakEqJrQStWnZ9liSpidOZ8NGfhxKwXP+CAJIkSdINqjE1fv2Bsxc9TwT6VlVQUZRWQDDwUz3EJTVC6rKuxTWaCKtGFdZwpuhqKIpCSC9fgrp6cfDHs+z/9jSnXkij27CW9BodhN7454+asUsXQnfvwpaTQ1FsLElPzCbtnXfwf2NxbZwJiqLgafDk82Of88WxL/Ax+dDM1Aw/sx/eRm+8DF74mHxo496GUI9QjJraGX8sSZLUaBk98Ndnos4qxGhvTH/6SJIkSfWpMWWAqgZKVteyCQdWCyFsVVakKJFAJEBgYGDtRCc1Khp1bTd+y+6OJv9WNl647ONYPolVzjnIuwBhD4KLT5VVAGi0asJGB9Ghf3N2rz3BgR/OcHRnMn3GBdNxYAvUascYX7WbG2o3N7TNmwNgPXWyds6jzIejPuS3lN9IykvifP55UgpSiM+KZ3fybnKLc53lVIqKIEsQt/rfytzec2s1BkmSpEbDszU6rcBQlEKp3tzQ0UiSJEkNpDE1fhOBlhc9DwDOVVM2HHikuoqEEEuBpQBhYWG11DqSGpPyO7+ltdX41ZlBY4RfVzge1XFtDr0irlid2U3P8IiOdB3akh2rjxPzZRy/b02k/6QQWnXxcs4MrWg0eNx7D9nR39TOeZRp7daa1m6tq3zNarOSUpBCXGYcxzKOsfXsVv575L880v0RTFq5dqIkSRVdaTLKsjJTgAU4Llr/JoRoXLPttRoAgLo0DZUhqGFjkSRJkhpMY2r87gXaKooSDCThaOBWSp6KorQDPIBd9Rue1JhoymZJrrU7vxo9PLYf8lNACJydDkTZP2otfDAISouuqlqfQFfumN2DU4fS2LnmBNHvHcK/nQcD7g7Bp6UrAFr/AOzZ2fzRtx+KVoui0TgeBj3NFyzAFBZWO+dYRq/W09K1JS1dWzI8cDjeBm8W/rKQgtIC2fiVJKmCmkxGqShKW+AZYIAQIlNRFN+GifYyFAW82qIWqQh1D5LS8/H3kneAJUmSmppG0/gVQpQqivIo8B2Oq8ufCCFiFUV5EdgnhFhfVvQe4EshhLyj24TV+p1fADd/x6Mq1rKuwtcwJlhRFIK7+RDY2YvYmHPs3XiSlS/vpX2/ZvSd0AbL+HHYsjKxFxYhSkocj9IScqK/If3jT7CePIn5llvQBQRcx8lVr7zBm2PNwdvoXSfHkCTphlWTySj/CrwrhMgEEEKk1HuUNWHyRKtOB0XFyq3HmX1X94aOSJIkSapnjabxCyCE+Ab45pJtz1/yfEF9xiQ1Tn9OeGWvpwOWL4V0bRNiAajVKroODaBdXz/2bzrNb1vOEr8/he4jA+nxyN/QGSr+OBafSCBvyxbytmzB9bbbCHjrzes5g2p5GBzLMk1aPwl/F39aWlrSwtyCB7s8iL9LNRcDJElqKmoyGWUogKIoO3BcvF4ghPi2fsK7CkYP3PWppAAZqecA2fiVJElqalQNHYAkXQuNs/FbTwcsnxCr9PrXyNCbtPS/K4S/LOhHUBdv9kWf4rP5uzmy4xz2i+5kt/r8M0K2bsE8YAC5339P+rLl133sqvRr3o/XBr3Gg10epL1nezIKM1gVt4pvTza+v10lSap3NZmMUgO0BYbg6J31kaIo7pUqUpRIRVH2KYqyLzU1tdYDvSKjJ766ZACSEg7z65nM+o9BkiRJalCy8SvdkOr9zq+igFp3XXd+L2XxNjLqr525a14vXD0NbPn0GCtf2svZIxkAqPR6tM2a4fv3OQCk/PvfCFuVE5xfF41Kw+3Bt/NYj8dYPGQxUeOiUCkq8kvya/1YkiTdcGoyGWUisE4IUSKEOAn8gaMxXIEQYqkQIkwIEebjU/2s+XXG6EFr1QU0Jfn4FqtZuffslfeRJEmSbiqy8SvdkNRKHYz5veJB9fD7avhoJLx/K7wdBm/1hJ+vb33eZq3duGteL257qBMl1lLWv3WQje/8RsY5R+PT0KEDLiOGA2D944/rPo0rURQFk8ZEQWlBnR9LkqRGzzkZpaIoOhyTUa6/pMxaYCiAoijeOLpBJ9RrlDVh8kCrz8dUmIp7iZnMwryGjkiSJEmqZ41qzK8k1ZRKpaBS4ExGAdZSG3qNuu4P2v0exzrAWiOYvR13gk/vgOM/wsA511W1oii0DfOjdTcfDm1JZN+mU3y5cA8db21Bn3HB+Dz6KHk/biZ7w0YMHTvW0glVz6w1sy5+Hb+l/Ia30Rsvoxf+Lv7c1+k+9OXjnyVJuunVcDLK74DbFEU5AtiAuUKI9IaLuhpGD3QuNoynUzC5hvDTyQNA/4aOSpIkSapHsvEr3bA6+7ux5tcktv2Ryl29Ari7VwChfq51d8Axr1Xe9ukkKMqqtUOotSp63BZI+/7N2Bt9ithtScTtOU/PUa0wqLRkr11Lwd69oFZhjTuOKCzE0LUr3jMjcR0+vNbieLLXk+w4t4P0wnSS85P5LfU3Mq2ZdPPpRp/mfWrtOJIk1Y6yJYmG4JiJeQKQg+OO7HohxL7rqftKk1GWrb7wZNmj8TJ6otIITCIHteKJWh2LEMK57rokSZJ085ONX+mGtfbhAfwcn8bnv5zmk+0nWRqTQNcAN+7qGUC/1l4Eepow6ur4jrBGXyuTYF3K6KJj0NRQugz2Z+eaE/yyLgHTyMW0s+7D334SxWZHFBYCUHziBBn//RS1hwf6Nm1Qu7ld9/HHtB7DmNZjnM+Pph9lysYp5JbkXnfdkiTVDkVRXIHROBq8owE3HJNR7QYswLPAPxVFSQbWlT22CCFKGibiBmZ0zGzvZnTM3eChFFJYYsOkk38KSZIkNRXyN750w1KpFAaH+jA41Ie0PCvrDp7jq/2JzF8f6yzjadbRzGJAo1YQAvQaFUadGn93Iy09TQR4GGnj40L7Zq5o1NcwBL6WJ8G6lEczM2Mf7krSH5ns+CqeA2f6crbVcPoLDsZzAAAgAElEQVRPDMFU/ATW+HiMvXqS9+NmTt/7F4w9ehD0xee1HodZawagoESOA5akhqYoyv/haPAOAXRAIfADjsbtRiFEalm5YODOsrKRwCwgT1GUTcAXQoh19R99AzJ5AuBpdvTIbmEt4dj5XHoGejRkVJIkSVI9ko1f6abg7aLnwVuDefDWYOJT8og9l01iZiGJmYVcyCnC0SsPim12cgpLOJqcQ1ren3dszTo1t7TxYngHP4a198XPYqjZgTV6KK27xm85/3YeTH46jOP7L7B7bQLr3zpIy55P0PdZf7z9XbAejyPjk2Xk/vAD1pMn0QcH1+rxXXQuACzas4hPDn+Cm94Nd707bno33PRuuGpdMWqMmLQmjBqj42uNqcI2d707Jq2pVuOSpCbqXSAV+AxHg/cHIUThpYXKZl5eAixRFMUDGI+jITwWx6RUTavx6xEEQDOfk5AJwblwNqNANn4lSZKaENn4lW46Ib4uhPi6XLFcYbGNxMwCjp7PZc/JdLYcS+XHoykAvHVPDyZ0a3Hlg6l1UFoE1lzQmkFVdxOoKyqF0N7NaNPdl9+3JbLvm1Os/k8s7fo2o++EDlgmjCf3hx8o2Lu31hu/ngZP5vWex4msE2RZs8i2ZnM65zQ51hyyrFkU22vW9dtF64K30Rsfkw8+Rh/aerTlwc4PyjF3knR1BgE7RPlVvRoQQmQC/wX+qyiKHuhWV8E1WgY36HkfLvs2oS3OxVPtQVZBUUNHJUmSJNUj2fiVmiyjTk1bP1fa+rkyoVsLhBD8cSGX2//zMydTa7jGrd4V8i7AKwGO51qzY5uLD7i2ANdm4Nq87P9m4BEMvu2vK261VkX3EYG0v6U5v353mkM/JRK/L4UuAwNw1Rix5+RcV/3V+f/s3XecVNXZwPHfuXf69r5sZWEXkF6WKlJEELGXxMRoTIwak9iSvJpoYmLUWJMY9dW8Go2JLRZsqKgggopKWYr05rK9wvY+5bx/zC4idRdmd3bh+X4+9zMzd+695xl0Z+aZc85zrhh6xWGfc3vdNHmaaPY00+Ruv/V8c9vkbqKqpYo9zXuobKqksrmSVWWrWLh7IWdnnE2/0H7dErMQJyKt9fLjPL8VWBWgcPqWyHQsVOJsriDEEsf7W3O5csrAYEclhBCih0jyK0Q7pRRDEsMB8Pp8nTvp1JshNgtaG6CtwX/bWgcNFVBfCiVrobHym+OtLri9BALQ0+kIsTLlokxGzEhh5YJc1i8rxTLxT2Qt38T0K32Y1p5bxttqWokw/UOgO+uDvA+45ZNbaHDLWptCiB4yaC7q47tx+Cqw+U7Bi7z/CCHEyUSSXyEOYBoKb2dHE4YlQPZVRz7G6/b3Di+8Fba/B942/1zhAAmLdnDGj4YyalYqS257ma2hEyn6wxdMuiiTrHEJKKN3DikOsfiLaDW6O9nLLoQQxytxOPQ/DefOEnyWyTQ15Qc7IiGEED2o57qGhOgjTKXwdrLjt3MXtEJECqRN8j/2Bn5pJIC41DBOH9fI6K8ew6jdw+JntvDa/TkUba/ulvaOV5jNvybzg6sfDHIkQvR9SqlblFJblFJlSqkcpdQzSqmfKaUmKKVswY6vVxl7JeH2QgBseWW4A/qGL4QQojc7puRXKWUqpWYppR5VSuUppTYope5SSmUHOkAhepphgK/zdWQ6r6O3txvWBe4Qd9ON9Iv1MO7LuxlVt5j6/DLefngdr980n7K1ud3W7rEYFjsMp8XJnuY9wQ5FiD5NKfUj4AEgBagBxgI/Bv4X+BKoV0qtU0o9FbQge5PBZxEXmee/W9dGdWP3vScLIYToXTqd/CqlwpRS31VKvYh/iYVFwM+BovZDfg+sVEoVKaUeV0rNUUpZAx+yEN3LYhh4vN2Q/Jrtfw7d1PMLoAyDhNtvJ/z0maSHVTOj7lUGV3/CnkYHrz+1m4+f20pDdfcvzdQZVsPK+QPPl2HPQhy/nwN7gCytdUdFvf8A9wAlgBUYAfwkOOH1MvZQUqafhfJ5iPdYqW12BzsiIYQQPeSoc36VUj/Dvy7gDMAGNAOL8a8P+K7WurL9uAzggvZjrwWuAxqUUu8D/9Van1zrCYo+y1Dd1PNrtvf8ers3+QyZPJmQyZP3PR4IJJ1+FrucY9j+5Sx2ri5n1KxUxpyZjt0Z3Gn/IdYQGt2NLClYQowjhqExQ7GZMkJTiC7KBF7XWpfvt2+31voupdTDwMtALXBfUKLrhcLGfx/765tRRgR1LZL8CiHEyaIz33wfx9/T+yL+hHex1rr5wIO01ruBh4GHlVJRwLn4E+GzgUHt5wrR65mGwuvrjuS3PanztILW4G6Cllr/1lwDDWVQV9K+FUNtsX+fzwvKgNPvgFGXHlPT/R+8G3X5FWRY8sgfdilrPvCx+dMiss8ZwPDTknu0MvT+0sPT8WovNy+9GfAvp3Tr+FuDEosQfZgFqNjvsQ9/by9a6xql1A+AbcACYH3Ph9cLRaVjepagHMnUNXuCHY0QQoge0pnkdxrwudad7wrTWlcDzwHPKaXswKhjjE+IHtelas9dYXP5bx+fAIYFfIf5wmVxQkQyhCdB2mT/cOmNr0PBF8ec/Lqys4n52XVUv/gSA7f/lrjQVPLGX8XyV718taSQiecNYND4nq8MfWHWhUxJmsLelr3ctPQm9jTJ/F8hjkEpEL/f4zoguuOB1npv+yisn+H/IVs4ozAoxWsdRVn1Qb/nCyGEOEEdNfnVWi8/nga01q3AquO5hhA9yVAKb3fM+R14Osz7CzTu8c/7dYSDIxIcEf4tLNGf8DoiD14H+Otl/iWTjkP8TTcRf9NNeBsaKP7lr4hY/VdaZv+A7faJfPTsFtYtKmDSBQNIHx6DCsA6xJ2VEJJAQkgCUfYoGj0y/1eIY7AaGLrf4+34i17trxT/aCzRzhq6B5TB/PfW8P3J6cEORwghRA8I2IQ/pdSdwHNa695VUlaILrJ0V8+v1QkTrjm2c01rwAplmaGhxFz1Y/Q/WtFvPsnsPyayd95MVrydy3uPb6BfZgRTLsokcUBEQNrrrBBrCHm1eby16y2iHdHEOGOIccQQ7YiWecBCHNlC4N9KqXitdUX74zuVUqdprT9TSpnAGUBLUKPsZSKiG6mqgaym4mCHIoQQoocEstrNH4BrlFLTtda7Ona2D3ueorVeGsC2hOg2hqHwdcec3+NhsQe0SnTI5Mm4Jkxg+7hsyu+5B3vmy8yZM4fKM85j1Xt5vP7gGjJGxTLp/IFEJ4UErN0jGRI9hJzyHO74/I6DnguzhhHtjObUpFO5beJtPRKPEH2F1volpdQCoOON6zHgF8CHSqllwAAgC3g+OBH2TrGDEti90kdkfVOwQxFCCNFDAl3q9SVgqVJqhtb66/Z9kcBHgBngtoToFt025/d4mNaArw+sTJO0p/9Jw2fLafh4CVVPPMGwdVczeFI/vlpSyLpF+bx890oGT+7HhHMyCIt2BLT9A/1mwm+4YcwN7G3ZS1VLFVXNVd/cb6liRckKFny9QJJfIQ5Ba92w3/0apdQc/Mnu3PbdHwO/DkZsvVXi+NnYP63C9DkprmkmOdIZ7JCEEEJ0s0Amvxp4CP9ag8uUUtPaK0AD9GwVHSGOg6kUbR5fsMP4NtPWLesDu7KzcWVnY0tPp/T229k+aTIJt/2W7O98h2HTkljzQT4blxWxc1U5I2YkM25ufxyh3bd8t8vqwmV1kRqWetBzj617jH9u+Cda6x6dkyxEX6S13gCMUkqlAC1aa6kmd4CEmDSUZzmGJZraJrckv0IIcRII+PomWusHgCfwJ8D9O3YHuh0huktMqI33N5Vx2T9X8PG28t4xBNq0Q00BfP4IrPl3wC8ffvY8+t1/H2ZoKDXz59O0ejWWphqmXpLF5XdNJmt8PF8tKeT5339BzsI83K3egMdwNKHWUDSanPIcCuoKerx9IfoirXWRJL6HZreH46MMjy2WNnfPv6cJIYToeYFMfvd1xWit7wOeApYBGQFsQ4hu9/SV4/ntWUPYvaeRq/6dwxkPf8ILK/Jpbgvil6PwfrB3Jyz+A7xzk3+d4AAy7HYiL7iAkNOm0vLVBvKv+CG7pk1n77+eJSzawawrh3LpHRNIGhTFygW5vHDHl2z6pAivt+d6yGOdsQBc9eFVnP3m2awuW91jbQshTkAWO15LKdqw0VhSHexohBBC9ADVheV7j3whpW4BntBaN+637w7gRiBaax2UOb/Z2dk6JycnGE2LPs7t9bFwYynPLN/NhqJaIl1WrpiUzo+m9Ccm1N6zwXjdUF8KK/4BK56AO/b45wEHmPb5cBcX05ZfQOnvfocRFkrEOediiY3BCA3DCAtlT5OLNataKCtsJiLOycTzB5A5Nr7b1wj2+rxs2ruJ3Jpc/vDFH7h36r0kuBJ4++u3+enIn5IWntat7QvRQSm1RmudHew4+rJe8dncuJcHfn85oc23MGi8YvZPZgY3HiGEEMess5/NXZ7zq5SKPdQQKq31Q4fYd7dSygfc0tV2hAg2q2lw/uhkzhuVRE5+NU9/lsv/Lt3FU5/mcvbIfpwzsh9TBsbisPbA7zqmFSLT/GsBA3hauyX5VYaBLTUVW2oqEeefT/XLL1P5978fdNwpQHz0MHIzL2TR082sTd7NlIsHkTo0OuAxdTANk1Fxo0gOTQag0d3Iy9tfZnH+YjIiMrh6xNXd1rYQvYlS6l/ATVrr+mDH0qc5o3CG50MzNJbUBTsaIYQQPeBYCl5VKKW+1Fqf2pmDtdZ/Bv58DO0I0SsopRjfP5rx/aP5urKBZ5bv5p31JbyxthiH1WBqZixzhiVy5tBEIlzdVwwK8M/9hW4pfnWg+F/9kvhf/RJfSwveqiq89Q346uvw1tTgrakhvrqajC1r2LF2L/m2y1jw6HqSB4Qy5dIhxKeHd1tcLosLgGVFyyhvLAegyS1LlYiTypXAbwFJfo+HYRAS1obOr6KpqhfUdhBCCNHtjrXac5xSKhoYjX/e8C6tdV7AohKilxoYF8q9F47gj+cOZWVuFUu2lvPR1go+2lrB7cZGpmbFMm9EP+YMTSDSZQt8AJb2a3paA3/twzAcDoykJA6V1rvLy2k4YzYJi9dSnDSVvLa5vHZfAwPGxDHx3AHdskaw0+JkbPxYviz5Ep/2zzlu8kjyK058SqmOsf0KSFFKHWn9sUIdqHlNJzCVOh5zbQktdYnBDkUIIUQPONbkNw0o3f98pVQu8CTwqNb6mLqllFJzgUfwrwn8tNb6/kMc813gTvwVpL/SWl92LG0JcTzsFpNpg+KYNiiOO8/TbCiqZeHGUt7bWMqt8zdwu6E4NTOWKyalM+uU+MAtzdPR81u5Dco3Q00etNSB9oLPB95WcLdAWz201kNrA7Q1+HuKJ18Pwy8KTBztrAkJZH3xOe7iYlJ27qLfb++geNgFFGyZQe76SgZPTGTCORmExwZuCRGlFP856z+4vW5KGkv4wcIf8P7u98mvyyfBlUBiSOI3tyEJJLoScVldAWtfiCDKw//Zp4HDVXxT7c/3Ayp6Jqy+y2WPptJWgmkOwePxYrEEpTyJEEKIHtLlglftc3g10AZ8BtQCKcB4/B+6W4F5WusurUWilDKBHcBsoAj/B/v3tdZb9jsmC3gVOF1rXa2UitdaH/HDvVcU1RAnDa01G4treW9jKe9+VUpxTTMTM6K554LhZCWEHX8Dm96A+T8+/PPKBKsTbKFgDwV7mP9+3mcw/BK45Jnjj+EwtM9H7tnn0LZ7N3FP/JMd1YlsWFaE9mmGTk0ie15/QiICXyjsjZ1vsLRwKeWN5ZQ3lVPVUnXQMWG2MKId0bgsLmKdsaSEpZAalrpvSwlLwW72cBEz0WcFq+CVUiod/+fs18BEoPIIhxf05p7f3vLZ/PUnT/Dv+StJdF/JxdemkTg2M9ghCSGEOAbdVvCqXRkwUWtdtF+D8cBvgJuAD5VS47TWXRmLOAH/8Onc9uu9DJwPbNnvmGuAx7XW1QBHS3yF6GlKKUamRDIyJZL/mTOYl1cX8tdF25n36Gf8bEYmP58x8PgKZGXNhjPvA1c0RKZDVDo4o/xJrzLAPMyf9OOT/L3C3UgZBmnPPM2u02dhVpYw5dKpjJqVSs7CPLZ8VsK2L0oZMTOFsXPScYQGbm70RVkXcVHWNz3ard5WKhorKGsqo7ypnLLGMsoay6hrq6PR3UhFUwXrKtbR4G74JnYU8a54kkOTCbeFE24P5yfDf8KAyAEBi1OI46W1zgdQ/qEkBfIZePxio1IpiHmTxDKo+Cpfkl8hhDjBHWvy+9r+iS/sS0R/rZT6En/v7A3AA124ZjJQuN/jIvy/bO9vEIBS6nP8Q6Pv1Fp/0MXYhegRVtPgiknpnDU8kXve3cKjS3by7oYS7r1wBJMGxBzbRe1hMPnnXT/PYvMvl9TNLAkJYLWy9+mnafj0U8zQUMbNO4thP01j7Yo61i0uYPOnxYyencaoWanYHMf6FnR4dtNOangqqeGphz1Ga01Naw2F9YUU1hdSUF9AUX0RpY2llDWVsaxoGf1C+nH9mOsDHp8QAfAfoDnYQZwIQiITIaoYVeKlPE8qPgshxInuWL55NgCH7ULSWs9XSn0EXErXkt9DTYo8cMiWBcgCZuAfav2ZUmq41rrmWxdS6lrgWoC0NFn7UwRXbKidv39vDBeOTeF3b27ke0+t4OqpGfz+nKE9F4Rp65EiWco0ib3mahpXrcJdVETD9u3Uvv02AKlAdGQau7MuYNU7Xta/u51TEqoZdc4QwrLHdHts34pTKaIcUUQ5ohgZN/Kg56e8NIVGd+MhzhQi+LTWR5j7ILrCEhqL09aGo6WciorA/xgnhBCidzGO4ZxdwJyjHLOa9l7aLijC//24QwpQcohj3tZau7XWu4Ht+JPhb9FaP6W1ztZaZ8fFxXUxDCG6x/RBcSz65TTmDkvk6eW7aXF7e65x094jPb8AcTfeSP8XXmDA228R+Z1L/DuVIv6WW0i96AymxO3k1Lo3Casv5KuyBF75vwI2f1aM1+vrkfg6w2V1saFyw75q0kKIE5QrhnCfD+UppskTuMJ8Qggheqdj+ZnzLeCPSql7tda3H+aYVA7utT2a1UCWUioDKAa+BxxYyfkt4PvAv5VSsfgT7NwutiNE0LhsFsakRfLB5jK8vh6sRWNa/VWfe1js9dfjGDoUMyaG8Dnf/GaWjH+dtE33Ps26jbDsxe2sfOZzBlYspV/zduKuvYao738fgOZNm6l9+220uw3tdqPdbvB42u970B4P+LyAIu6mG3GOGnXccYfZwtiwZwMLdy/knAHnHPf1hBC9lD2MaK+PFqMUnzmepRvLmDlClj0SQogT1bEkv3/Fn4D+Ril1KvAw8KHWuhlAKfV9/EOeD7cMwyFprT1KqeuBD/HP5/2X1nqzUuouIEdrvaD9uTlKqS2AF7hFa733GF6DEEFjGv4R/t6eLMRqsUPZBnj3l/4h0KYVrCEQGgehCRASD2EJ/iJagVqWCf9SSB1J7KEM/sm5xL/yGqXVu9i4px+bHN8hr6WMQW+sYDAKw2aj5rXXaN64ETMiAmW1+jeLZd99LBaUYdC8aRPmc88T9b02ME0MpxP74MEoo+sDXB6a9hAXLriQiiapJyTECU0prrEm8qSzhAjg8892SfIrhBAnsC4nv1rrRqXUNOC/wOnAVMCnlKoAwoCQ9kO7Mt+349oLgYUH7PvDfvc18Kv2TYg+yWhPLr3eHkx+M6ZB6VewZYF/+LPPDe5DFGM/+28w/ic9FpY1IYH4G68nHhjp0+xaW8EX/25mreN8dr2zmwG5/yW6Zgfh8+aR/Le/HvFauRddRN1771H33nv79iU/9ijhs2d3Oa6BkQNRKJn3K8RJIOqMu9mw50+cVgyRO3Lxf60RQghxIjqm6g5a60rgDKXUbOBy/J8U6e1Prwfu0lq/E5gQhTixWMwg9PxO/oV/25/XDY17oLECGirgxUugrrjnYjqAMhRZ2QkMGD2XrR/vJucjC+vDbyIp3cGki45eQiDtySdpy8tDe73o1lYKf3odFQ8+RM2rr5Fw223YB2R0PhalcFld5JTl8Nzm53BancxMnUmsM/Z4XqIQ3UYpdQvwYyAaf32Mr4AcYA2wXmvdFsTwejUjaza7U29hRkEzjj21wQ5HCCFENzqu0oZa68XAYvCvO9jeMyuEOIKOnl9fT875PRTTCuH9/BuAxQne4H8/Ni0mw+dkMmRmBps/LWHNB3m88fAG+o+MZcK5GcSlhh3yPEtcHJb9CtxF/+QqWjZtpvGzz6gZlEXcjTdi2O2djmNI9BDWlK9hbcVaAArrCvlVtgw6Eb2PUupH+EdbNeAvFDm2fftR+yGe9ulCq7XW1wYjxt4uxOrA5y0BQoMdihBCiG501ORXKRWutT7q4ndHSnyVUhFaa/k5VQiCNOe3Myw28AQ/+e1gsZqMmpXKKaf2Y8PHRaz/qIBX/7yagWPjGH9OBjFJR/6SmnDLLWit2XnqVKqe+RfePXtJeuD+Trf/7JnP0uZro8XTwgVvX0Btm7yFiV7r58AeYITWulwp5cO/FnABcBX+GnMjgJG0LwMovm1O1DBazCKUcxK+NjeGzRrskIQQQnSDzlSC2aOU+lAp9XOlVOrRD/dTSg1TSt2ulFoJLDn2EIU4sZgdc36D3fN7INMO3u5fC7irbA4L2fP6c8U9k8me15+CLVW8fPcqFj2zmZryQ8xb3o9Siv4vvYhj5Ehq336b1tzOF4dXSmE37UTYIwi1hsr8X9GbZeJfBrB8v327tdZ/xJ/0LgJeB8YFI7i+4NSYkVQ5C/GZdv7x3OfBDkcIIUQ36Uzy+xwwCvhfIE8ptUYpdYdS6lvriSilDKXUNKXUX5VSu4ANwD345x+9FujAheirDKOXJr+WnlsL+FjYXVYmnjeAH94zhbFz0tj9VSUv3bmCJf/ZQt2e5sOeZ+vfn6hLLwVgzxP/OKa2Q62hfFL4Cee+eS4bKzce0zWE6EYWYP/S5D7ACqC1rgF+gL9A5bCeD61vCHXGUBJRBEDtjvKjHC2EEKKvOmryq7W+GuiHv6jVX/FXc/4TsFYplaeUelQp9W+gHFgK3AxUAX/APwQrS2vd5crPQpyoLL01+e1YC7gXJ8AAjlArky/M5Ip7pjDy9FR25lTw4h9WsPTFbdRXtRzynMiLL8Jwuah7913aioq63OaVw65kWso08ury2LBnw/G+BCECrRSI3+9xHf4fngFoXxLwfeBnPRxXnxEamsDuuDKUz01odX2wwxFCCNFNOrUApvb7Qmt9q9Z6CDAU+D3+D9xf4F/3dy1wPZCqtZ6gtf6z1npzdwUuRF/V0fPr621zfm2hsOVtuDsW7oyAP0VBzrPBjuqwXOE2pn4niyvunsyw05LY9kUpL/zhSz59eQeNtQcP3068+y4Ayv7wR5pycrrU1tyMudx72r0ANHsO38ssRJCsxv+53GE7/oJX+yvFPwRaHEJozCD2hvsIaSwh1AOLt0jvrxBCnIg6lfweSGu9TWt9n9Z6MpAExGmtz9Ra/0NrXRLYEIU4sXwz5zfIgRzovMdg7v0w8/cw/bf+OcAVW4Id1VGFRNqZ9v3BXH73ZIZM6sfmT4t5/vdfsnz+TprqvingFTZjBiGnnUbT2rWUP/gQXS1ObzNsWJSFyqZKqlqqqGuro7UXzpEWJ6WFwHilVPx+jycopU4DUEqZwBnAoYdGCEKd0WilcLUW4LYksKtCen+FEOJEdFxLHQEcUGBDCHEUZvtPTr1u2HPSaP/WYc2z4Ok7yV1YtIOZlw9h7Jnp5Ly3mw1LCtn8WQkjZ6QwZnYajtAQ0v75FIXXX0/DR0vY++STxF53Xaevr5Qiwh7BS9te4qVtL/n3ofjL9L8wp/+c7npZQhyV1volpdQCoONN5TH8o7I+VEotAwYAWcDzwYmw93NZXAAosxSPGUJZSUOQIxJCCNEdjjv5FUJ0jdFbqz0fyLT3inV/uyoizsmsHw1l7Nx0Vr+Xx9pF+Wz8pIhRs1IZPSuVxDvuYNdHS6h962289fWYYWEYYWGYYWEomw0MA2WaYBg4TjkFa2Livms/cvoj7Kzeidvnps3bxl9y/sLXNV8H8dUK4ae1btjvfo1Sag7+ZHdu++6PgV8HI7a+wDRMTGWyPraAfl6oXbMLLht99BOFEEL0KZL8CtHDOtb53VpWx4iUiCBHcwQWW5/q+T1QVGIIc34yjHFz01n17m5y3stj49IiRp+RRr9rfkbjW69R/cKL6NbDv0bn2LH0f+nFfY9HxY1iVNw3he4fX/+4LIEkeiWt9QZglFIqBWjRWu8Jdky93QWZF7C09m0u3eQlvUbW9RZCiBORJL9C9LCxaVGkx7i4df4G3ttQym3zhjAkMTzYYR2sj/b8HigmOZSzfjqCyoJ6Vr2Ty8oFuThCxzDmjvMZMSMFEy+++nq8dXVotxt8PvD52PPUP6n/4APqFi0ifM6hhzU7LU42793M/B3z0WjcXjez02cT54rr4VcpTiZKqXCtdV1njtVaH7K8uVIqQmstGd5+piRN4fUd83E1laEttmCHI4QQohtI8itED4sKsbHol9N47ot8Hvt4J3P//hkT+kdzwZhkZp0ST0K4I9gh+lnsUJ0f7CgCJi4tjLN/MYqy3bWsemc3X77xNes/KmTcmekMOy0Je0zMt46PvfYa6j/4gNLbbid0xgwM28FfhlPDUskpzyGn/Jvq0Xtb9nLDmBu6/fWIk9oepdRS4G3gHa11YWdOUkoNA85v30wgu/tC7HsyIzNBKRwthbREDA92OEIIIbqBJL9CBIHdYnLNtAFcMi6Fl1cX8srqAm5/cyO8CUP7hTMmLZKRKRFMHhBLWowrOEF626B8EzRVgSv66Mf3EYkZEZx342hKdtWwakEuy1/bydoP8xnbngRbbCYAjqFDcY4bR/OaNTQsXbF6JlMAACAASURBVIZrwnjMyEhU+5xtgH+d+S+qW6r3Pb5owUXUtXaqQ06I4/EccA4wG3hMKbUeeAtYoLX+quMgpZQBTOWbhDcDUMDXwNM9HXRvNyByAInOeAxfAV7LJPbuaSImNkjvv0IIIbqFJL9CBFFUiI2fzRjIddMHsLOigSVbK/h0RyULvirhxZUFAKRGOzl1YCxTMmOZMjCG2FB7zwQ3/CJ/8ttSe0Ilvx2SMiO54FdjKd5ezer3dvuT4EXtSfBUfxKc8sjf2Tn1NIpvugmAqB9eQeLtt++7hs20kRCSsO9xqDWURncjXp+XBre//lCEvRfP6xZ9ktb6auX/FWYycAFwHvAn4E6lVCGwAAgHzgY6/njXAM8Cb2mtN/d81H3DgKhMyqNLMYDc9SXEnJEZ7JCEEEIEkCS/QvQCSikGJYQxKCGMn80YiM+nyd3TwOe79rJ81x7e21DKy6sLUQpmDo7n8klpTB8Uv694VreITPffet3d10YvkDw4iuTBUd8kwa/u1xM8NYmkBx/AU1lJzfzXqXv/fXRzM9FXXok98+AvxSG2EN7NfZd3ct/Zt2/hhQtJDU/tyZckTgLav1D1F+3brUqpIcCF+BPhXwAeYBn+HuG3tdYlQQq1T4l2RLMzYS1DKrzsXLWb8ZL8CiHECUWSXyF6IcNQZMaHkRkfxpVT+uPx+thYXMtHW8t5ZXURV/07h4zYEB64eCQTMrqpV9Zsn+Pq7bsVn7ti/yR41bv7J8FjGDY3CSM0jKp//Yua199A2ewk/O52lGF86xo3jL6BNeVrCLGFsGXvFpYVLqO0sVSSX9HttNbbgPuA+5RSCUBzZ4tiiW9EO6JZn+Ame3cxusgArUF144+MQgghepQkv0L0ARbTYExaFGPSorhp1iAWbSnjzgVbeGTJDl68elL3NLov+e37FZ+7InlwFBceMgmezLB3Lqbg4gupfvFFPBUVpDz26LfOnZk2k5lpMwHYvGczywqX0eRpOqgNn/ZR3VJNZXMlFU0VVDZVUt9WT5uvDY/Pg0/78GkfGu2/1RpDGVgMC1bDisPiYFjMMLITpV6ROJjWujyQ11NKzQUewV8k62mt9f2HOe4S4DVgvNY651DH9HaxzliKwjyEN+ymPGQCvuoCjOj0YIclhBAiQCT5FaKPsVkMzhmZxEsrC2jz+LqvIdPqvz3Bhz0fzuGS4JE/+CNR7z5G44oVVD72vxguF0aIC8PlwoyMJGTKFJTFgtPqBGD+jvl8XPAx1S3VVLVUUdlcSWVzJR6f57BtKxSGMlBKYeC/9Wkfbt83/y1inbEs/e7Sbv93ECc3pZQJPI6/uFYRsFoptUBrveWA48KAG4GVPR9l4IyMGwlK0aor8RhOqr/8gJizfxrssIQQQgSIJL9C9FGmoWhx6+5rwNJeWMtzcgx7PpwDk+AVy2pwxlxOauwC3P94EvOAJDb50UcInzOHOHsscTqMzduXE2dEEGOG0V+FMd4cQIw5iigjlEjlIjxzCPEjxhNmC8Nm2LAYlm9VlN6f1hqP9vDwmod5ZdsrPfHyhZgA7NJa5wIopV7GXzl6ywHH3Q08CPxPz4YXWIOjBgOQH9ZICFBeahBz5FOEEEL0IZL8CtFHGUrh9XVj8tsx7PmD28DRXrHYEQERKTDrjm/2nSSSB0dxwaBIinfUsOqdXHa0XkDxyO8yZmY/Bo8MhYZadp93PiW/vY2S396Gbmri8X1nV7RvB7Mk9SPx4487FYNSCquyEmGLoM3XhtvrxtrRQy9E90gG9l9HuAiYuP8BSqkxQKrW+l2lVJ9OfkOsIZjKpCwqn8EtTZQVGwwNdlBCCCECRpJfIfooi6Hw6m5MfuOGwKC50NrwTcGXvbtgx/sw6EzImt19bfdSSilSBkeRPGjsviR4+Vv5rFtqY+zc/iTc/Gt8JYXtQ6FD/LcuJ8rhxHDYUXY7ymbfd792wTtUP/88O047jQFvvYUlpnN9TKG2UAAuePsCHBYHDtOBzbRht9hxmA6shhWLYcFi+N/i959DfNmQy/xDO4XonEMNQ9j3xtO+lvDDwI+OeiGlrgWuBUhLSwtQeIGllCLGGUNVRBVhFfmUV8cHOyQhhBABJMmvEH2UYSi83TjlF0c4XHbA0NrSr+DJaSddEawDHSoJ/uyVHYREDGHs3LkMndoPi9U86nUscXH46uupfestKh58EDM2Fu124xw1ioizzz7seaenns7O6p00uZto8bbQ6m2lxdNCbUst5d5yPD4Pbp9737xiU5kopShtLCXUGirJr+iKImD/cuUpwP7LJoUBw4Fl7cP1E4EFSqnzDix6pbV+CngKIDs7uxt/uTs+Vw2/imeL7yN8bR4FLYNxt3mx2o7+9yyEEKL3k+RXiD7KVAqvrzuz30M12j4U+iSfB9zhW0lw+5zgz17ZwdoP8hg7N52hU5OOmARbExOJ/82tNCxdSu2776GsVrTXS/VzzxN+1lkHLaXUoV9oP+6ccmeX4537+lwa3Y1dPk+c1FYDWUqpDKAY+B5wWceTWutaILbjsVJqGfA/fbXaM8C5A8/l/qj7cbTmozGo3LiNpHHDgh2WEEKIADj0NyshRK9nmt085/eQjXYsf3RyVoA+HKUUKUOiufDXYzn/5tGExzn57JWdPP+7L1n/UQHuNu9hz7VERZG14ktO2byJIevXEX/TjQDUvvlWwOMMsYZQ3VJNRVMFZY1lVLdUB7wNcWLRWnuA64EPga3Aq1rrzUqpu5RS5wU3uu4RbgvHqeIoDM8HoHzRa0GOSAghRKBI8itEH2UqRU/nvifr2r+d9a0k+JdjiOrn4vP5u3j+d1+w9sN82loOvbzR/tWdoy7zd6pV/P1hdl96Ke6ysoDFF2GP4POSz5n12ixmz5/N9Fems71qe8CuL05MWuuFWutBWuuBWus/t+/7g9Z6wSGOndGXe307DHWdzc6kBhzNeygttkHbwet1CyGE6Htk2LMQfZRpBLPnV4Y9H0nHcOiUwVGU7KohZ2EeX775NWsX5TN6ViojZqZidx767ddwuYj9+c9pWrWKppwcKh99DMfgQUReeimGw3Fccd024TbWlq/FMAzKGst4asNTlDaWMjh68HFdV4gTzdjoeSxLeZZxq76mxHEKuqYAFT8k2GEJIYQ4TpL8CtFHdftSR4fSsaxOcw142sBi69n2+6CkzEjOu3E0ZbtrWbMwj5ULdrNucSEjZ6YwalYqjpCDlyqKu/EGfM3N7Jw2ndo33qAWsCQkED537nHFkhWVRVZUFgB5tXk8teEpGtwNx3VNIU5Eo1JiedI2iZCGXZQlTqS2qJJISX6FEKLPk+RXiD7KEoyeX6sTlAEf3+3fbKHgiISIZEgaA7PvloT4MBIzIjj7F6OoLKgnZ2EeOQvz+GpJISNmpDD6jFScYd/+dzOcTrI+WYa3uppds86g+OZfErZxFsoamHV9O5ZLemnrS4RaQ5mROiMg1xXiRDAtKxaPewC7YxYDULKzhsixQQ5KCCHEcetVc36VUnOVUtuVUruUUr89xPM/UkpVKqXWt29XByNOIXoDo7vX+T0UqxN++DbM+wvM/D2MvRIypoG7CVb+H1RuhfX/hVevhPrAzVU9kcSlhXHWdSP43h0TSB8ew9pF+Tz3uy/4fP5OGmu/PZzccLmwJicTOnMmAGX33kv5Qw/RsnXrcccRZY9iVtosdtXs4j+b/3Pc1xPiRKKUwmlEszG1Aqu7gYJPNkJPv98KIYQIuF7T86uUMoHHgdn41xVcrZRaoLXecsChr2itr+/xAIXoZUyDnu/5BX+ymzHt2/t2LoYXL/FXgV5yF9SXwLALYNiFPR9fHxGTHMqZ1wxnfGkjaz7w9wJv/KSYoVOTGDsnjdCob+b3xv/6VzSvXUvtm2+hW1tpy88n8Y4/ABpls2GJiupy+6Zh8veZf+cXS35BZVNlAF+ZECeGEDOWtZmK6R99TVl4BjTugdC4YIclhBDiOPSmnt8JwC6tda7Wug14GTg/yDEJ0WuF2C3UNrt5dMlOmtoOXUW4x3TMBfa0gqfFf1+WQ+qU6H4hzP7xMC67cxJZ4xPY/Ekxz9/xJcte2k7d3mYA7JmZDFq5giHr1xFy6qk0fLSEXdOns2v6DHZOnkLT2rXH3H6INUTW/hXiEK6dkk2dSsStdtNoS6CxaHewQxJCCHGcek3PL5AMFO73uAiYeIjjLlZKTQN2AL/UWhce4hghTnhXTx1Awd4m/rZ4By+uzOfXswdz8bgUTEMd/eRAM+3+W28b0N4b7ZGK0F0RmeBi1g9PYfy8/qz5MJ+tn5ewdXkJgyclMu6sdCLiXAAk3H47TatWAgpfSzMV9z9Axd/+hj0rC9fYsUSce26X2g23hVNQX8DEFycS44whzhnH7RNvlwrQ4qQX7rTgqR9JWcg2nEDplhIypeaVEEL0ab0p+T3UN/YDx3S+A/xXa92qlLoO+A9w+kEXUupa4FqAtLS0QMcpRK8QF2bnH5ePIyevij8v3Mqtr2/gX5/v5rZ5pzB9UA8Pzdu3BNJ+vb2yFvAxCY91MvMHQ8g+qz/rFhWwZXkJ21aUMWh8AuPOSidqQAb2ARkAaK1p/Gw5rV9/TcvmLdS9t5CwOXNQNtu31g4+kh8P/zGJIYnsbd5LRVMFi/IXsaJ0hSS/4qSXGReGrzWOooiPGNzURvGGEjIvCnZUQgghjkdvGvZcBKTu9zgFKNn/AK31Xq11R3fSP4Fxh7qQ1voprXW21jo7Lk7m54gTW3b/aN742RQev2wsTW1ervzXKq54ZiVfFdb0XBAdw573T3gl+T0uYdEOpn1vEFf8eTIjZ6bw9doKXvrTShY9vYm9xf7liZRSpD3zNFnLlhJ3ww346urYPmo024aPoO799zvVTnJoMlePuJrfTPgND057EIAmd1O3vS4h+oqB8SH4WhMpSPARXpdHSXlosEMSQghxnHpTz+9qIEsplQEUA98DLtv/AKVUP611afvD84DjL3kqxAlAKcXZI/txxtB4nv8yn8c+3sX5j3/OqJQI5gxLZGBcKM1uD7VNbjw+jcNq4rSauGwm6TEhDIgLwWE1jz2Ajp7fjvm+IMlvgIRE2Jn6nSzGnpnOV0sK2LismJ05FfQfGUv2Wf1JyAgHIPLii1A2G76mJvb84x9U/ec53KVlRH3vUgyXq1NtmYaJ0+KUOcBCAE6rieGJZ1c/cH2xi5LIubQ2e7A7e9NXJyGEEF3Ra97BtdYepdT1wIeACfxLa71ZKXUXkKO1XgDcqJQ6D/AAVcCPghawEL2Q3WJy9WkD+O74VN5cW8x/VxXw0Ifbj3qeoSA12kVKlJOUSBfJUU4iXVasptG+KWymgdNmEuG0EumyEem0EuawYDENsIcBoN+4FqW9/ouWbYSCFRCeDGGJ3/QOi2PiCrcx+cJMxsxJZ8PHhWxYWsT8B3JIGRLFuLP6kzwokujLfwBAy6ZN1C9eTPP69Vji44k45+xOtxNqDeXVHa+yqmwVaeFpDIwcyKDIQWRGZZISmoJpHMePJEL0IUopfnf2UB7fNJbykJ2g5lGybS8ZYxKCHZoQQohjpPQJvm5ddna2zsnJCXYYQgRNbZObgqomQuz+xNVqMWhxe2lp81HX4mb3nkZ2lNeTt7eJouomiqqbqazvfLEqu8VAa5iov2K8sZVTVAGzzQOrDysITYCo/pB9FYy6NKCv8WTU1uJh06fFrP+okOa6NhIHhDNubn/SR8SglMLX3Mz2MWPBasUMDcVwuTBCQoi76UbCZs067HU/KfyE5cXLKWwoJL82n6KGon3POUwHAyIHkBmZSVZkFplR/tt4V3yn5xifCJRSa7TW2cGOoy/rS5/Nv1+wmtplVzO0/gFOGWVnxvUzgx2SEEKIA3T2s7nX9PwKIbpHhMvKCFfEt/aFO77phR2eHHHgKbS4vTS2enB7NW6vjzavD7fXR2Orl7pmNzXNbVQ3uqlv8dDU5sEwFBZjAD7jIp7atYffFFew9vpBUFfcvpVAbTGsf8E/HFqS3+Nmc1gYOyedkTNS2PpFKesWFfDeExuISQ5l3FnpDBwbT9KDD9C6Ywe+piZ8jY3UL/mYqn//BwAjJBTHsKGYYWHfuu701OlMT52+73GTu4nc2lx2Vu9kZ81OdlXv4suSL1nw9YJ9x4TZwsiKzCIrKovMyEx/chyVRYT94P+3hOhrop0RlLgiiSj6muKNIVCxDeKl7LMQQvRFkvwKIQ7isJrHPAe41ePjq8JaSBjq3/bXXA01+QGIUHSw2ExGzEhh6GlJ7FxVzpoP8ln09GYi4nMZe2Y2g28+B9Pir21YdMMN1C/+iKbVqwEIO/NMUh75+xGv77K6GB47nOGxw7+1v6alxp8M1+xiV/UudtbsZGHuQurd9fuOCbGGEOuMJcYRQ6wzdt82JXkKw2KGBfhfQojucd6oJP6bk8l3araTG30BTSUFuCT5FUKIPkmSXyFEQJlK4T3cdAqLTQphdRPTNBgyuR+DJiaSu66SNR/ksfT5bax+dzdj5qQx9NQkkv/2N9ylpfgaGii//wEaly+n8KfXYYSHE3nxxYRMOtTS6ocW6YhkfOJ4xieO37dPa015U/m+hLi8qZw9zXvY07yHHdU7+LLkS+rd9SwrWsaL817sjn8GIQJuQGwIe5unYmt+BYDirZVkjQ5yUEIIIY6JJL9CiIAyDIXXp9FaHzwP1LSDp/PziUXXGYYic1w8A8fGUbC5ijXv5/HZKzvJWZjHqFmpjJiegiPNQvRVP6bq2X/jqaykdeVKvHW1XUp+D0UpRWJIIokhiUxNnnrIY3697NfsrNl5XO0I0ZMMQ2FT4eTFFGF6mslfmUvW94MdlRBCiGMhya8QIqAshj/h9WkwD6yBJD2/PUYpRfrwGNKHx1Cys5o17+ez4q1c1i0qYMSMFEaePoX0GTMA/3Dotry8HokrxBoiSymJPuehiybxhMvGj1bvpJjMYIcjhBDiGEnyK4QIKLM9+fX69L773zxpk57fIEjKiiIpK4qK/DrWfJBPzsI81n9UwLBpyYw5Iw1rUjINn3/xrd56b0Mj1c8/BxYLZngEZkQ4tvR0HKecclyxhFhDqGqp4o9f/JHTU0//VnEtIXqraVnx3Lp8AA2WHbRYRlJXUEx4WnKwwxJCCNFFkvwKIQLKUN8kvwcx7dBaD4vuAGcUOCL8awRrDYPm+PeJbhOfHs5ZPx1BVUkjaz/MZ8PHRWxcVsSAmGHE+d6lZcMGzJgYlNVGwyfLqHzk0W9fwDQZ9MXnmBHHXsV5eup01lWs4/3d77OhcoMkv6JPCHNY8NQPZ0PycgY1Qu78hYz+1TXBDksIIUQXSfIrhAiojmHPhyx6lXEabHsXVj4J3gN6gE//PUy7pQciFNFJIZzx46GMPyeDdYsL2Lq8mK8n/pHcO98nvWARoY2l/gMNg6zln6Hb2qj/+GPK77qbqhdfJO7nPz/mtif1m8TL57zM75b/jlVlqwL0ioToXoahcLRm8/ng+Qz/sprcjW1IzSshhOh7JPkVQgSUYRyh53fwWf5Na/C0QEsttDbAE5P8t6JHRcQ5mXHZYLLPTGX1C6vYYRlPecIEkmJaGdqvjqQhMViio/3HnnMO5XfdTcPSZYRMmoxr7JjjajvUGtotc3+b3E3sbdlLdUs1Na01VLVUUd1STYO7gQmJE5jY7/iKeomTV7jdhU+dRr1tKz7vaFpyd+MYkBHssIQQQnSBJL9CiIDqKHJ1yOS3g1Jgdfq3MMBiB6+7R+ITBwuNcTHzphlMbnSzcVkRGz4u4qNNdvo1RzA2fg/pw2Mww8OJuOgiat94g/zLLiPrs0+xxMUde5u2UOrb6pkzfw6R9kiiHFFE2COIskcR6Ygk0h6J1bAC4NM+3D43Hp+HVm8rzZ7mfVtda92+5ZT2tuyl2dN8yPYUCqthleRXHLOhSeEsK41iY7+tZJdNoWDZJgZJ8iuEEH2KJL9CiIAyTQM4SvJ70Em2g4dBix7nCLEy/uwMRp+RxtYvSli3uID3nthAdFIIY89MZ+CddxIyaSIlt/6GsrvvIeXRR465rQszL6TN20ZVSxW1rbVUt1ZTVF9EdWs19W31RzzXVCZOixOnxUmoLZQ4Zxwj4kYQ64wlxhFDtCOaaEc0UY4oohxRRDuicVlcBy+9JUQXPHXFONaUm1z37jWML/GSv3EPg4IdlBBCiC6R5FcIEVCm6ljqqAvJr0XW/+1NrHaTkTNTGTYtmV05Faz9MJ+Pnt3CirftjJ4+HIsjhKaVK2lcsQIzOhpLdLS/UFYXksuUsBR+nf3rQz7n9rmpba3F4/OgUBjKwGJYMA0Th+nAalglkRU9TinFqPjhtFpbMdtyKW4JRft8KMMIdmhCCCE6SZJfIURAtXf84jlCz6/Pp2lo81Db5Ka8roXBHoPc/AqKN5Yyb0S/HopUHI1pGgyemMig8Qnkb9rL2g/zWf5mHvap95G0cyEtV/8Cq6cJgMjvfpd+d/0pIO1aDSuxztiAXEuIQLIaVm5RGeSFbCXGex51OwqJGJIe7LCEEEJ0kiS/QoiAMtt7QS775woAPF5Nm9eHx+vbd7/N62P/juGPbBqjcTsF7z8M9angbfPPAfa2tW8eyJgGQ+YF4yWd9JSh6D8ylv4jYynZVcPaD/PZ7TmXwqxzyUr3krjyeeqXLMFwuTDCQjHDwjCjYwifMxtlswU7fCEC6ruTfs51u/5GTMV5fPTfN7jozptlJIIQQvQRkvwKIQJq0oBozh2VhM+nsZgKi2Fgs/hvLabCZhrYLQbhTivhDitxYXZSvhiEo2AZI5qehEX7Xcyw+OcDe1ohf7kkv71AUmYkSZmR7C1uYN2iAratLmd73JUkWtaTtmAxrqr8fceqv/+d8LlnBjFaIQLPERLPJbaNlLbWsGe3l+e2PMeVw64MdlhCCCE6QZJfIURApUS5eOz7XVwGJ/M1bnl+GXnVbbz2i+n+hNewQsdculevhIqtgQ9WHLOY5FDO+PFQJpybwfolhWxdblISNYaMkTGMGh9G3eVnU37ffdS+9RbJf/0LRkhIsEMWIjBsIZzjaeKf7ny0YygLtz0rya8QQvQRUqVBCBF8FhuNthiqCQN7mL8A1v5FZKQadK8VHutk2qWD+OG9U8g+qz8lO2t56+k8Np3zEDUZk6hftoya198IdphCBI7VBYDbUorX4iD0K3XUCuVCCCF6B0l+hRC9gqEUvsMVybLYZB3gXs4ZZmPieQP44b1TOPWSTBotUaxyzGH1uN+y4ekPaavYE+wQhQgMm38UQ110LaanmVFFI9i6d3uQgxJCCNEZkvwKIXoF01B4D7c8Use8X9Hr2RwWRp+RxhX3TOb0H56CkdCPzUOv4uWHNrFxWRHuNm+wQxTi+LT3/M4aHYvyluNgBO+sfDHIQQkhhOgMSX6FEL2CqRTew/X8mnbp+e1jTIvBKVP6cclPkhmx6SnsVi+fvryD5277gpXv5NJc3xbsEIU4NhY7KIPxyXYiJ2XitoWT9HlLsKMSQgjRCZL8CiF6BcM4wrBn0wqeFqjOg7pSaGvq0djEsTMjIonb8xVzxtZy4f+MJXFgBDnv5fGf279g2UvbqamQ/5aij1EKrCHQ1kTM5CzweQjPjWJD5YZgRyaEEOIopNqzEKJXMNURhj07wv0Frx4Z9c2+IefA92SoYW9nRkYAsPepJ8lcdBFJmZFUlzWyfnEBW78oYfNnxQwYHceY2WkkDogIcrRCdJLNBe5GThsaz3pvGc7QUaxd/gYjLxwZ7MiEEEIcgSS/QohewTSPMOx5wrUQPQDcLf4keN0LULK+ZwMUx8QMDcWWkUHb7t3UffAB4XPnEpUYwswrTmHCeQPYuLSITZ8Wk7uukn6ZEYyZnUb/EbEoQwU7dCEOzxEJ9WXYLSZ1YXacLXGMu/8ZqqbsJTohJtjRCSGEOAwZ9iyE6BWOOOfXEQHDL4YxP4DsqyBxpCx91IfE3XwzAMW33Ir2+fbtD4mwM+mCgfzw3ilM/U4WDVWtLPzHRv5710q2LC/B45biWKKXCkuEnYugpoCKERlovOyJHsPjN/wZfbgRLEIIIYJOkl8hRK9gGkdIfg862AZeKZjUV4SfOYfEO/8IbjfbRo1m+4SJ7Jwxk6/Pmsfuiy+h9p//x6hZqVx+9yRm/2QoptVg6QvbeO53X5Lzfh4tjVLsTPQyo77nvy3bxAOXjaEhvpqSxHGcu2kRNVtk2SMhhOitZNizEKJXMJSis7kvplWqP/cx4fPm4WtowFtXj6+pCV9zE76mJlo2bab6hRcImTwJw+UiIymCrNvHU7S9mvWLClj5di5rPshn6Kn9GDUrlfAYZ7BfihCQdab/dt3zRAw6kzGnprPrzUbqw1MpvOqHhH36KRa7I7gxCiGEOIgkv0KIXsE06HzPr8V+0qz729zmpbC6ieKaZuqa3dS3eKhv8aDRXHVqBg6rGewQO8UMDyfm6qsP2l/13HOU33sf+ZdfsW9f6pP/R+r06aQOiWZPUT3rFhewaVkxG5cVkzkunjGz04hLC+vJ8IX4Nlc0WBywfSF8/TEzps1kx9tLWTIhm0sXzeeT+29m1h//L9hRCiGEOIAkv0KIXsEwFC0eL9c9v4akSCcZcSFkxYcyMiUCl+2AtyrTBtoLPi8YfSP5O5oWt5fcykZ2lNezraye7WV1bCurp7T28OuHjkiO4LSsuB6MMvCiLrsM55gx/l7h2jqKb76Z8gcfovqVV1E2G8pmZeLppzPpnhl89fH/t3ffcXLV9f7HX59zpmyv2U3vCSkEEkgg9F5Vip2miChiQb145SL6Ey5eroheBa+IoiiKepGgQFQUQi9CCAmhJAQS0gnp2ZIt087398eZTTZhQzYmuzOZfT8fj5NT5uzMZ76bme9+zvd7vt9VLHx6DYvnrGPI+GoOOW0YQyfUYKbBsaSXmcFnH4PbjoKNi4mPPZURYeOevAAAIABJREFUk/qRWHgsjcV/IvWiBuQTEclHSn5FJC8cN7aO59/axJINW3nizfW0p8KBkXzPOHBQBUeMquX4A+qYNqKauB8Nf+jFX4UtMPGKcCmqCEdhrRiYw3eye23JDK+sbuClVQ28tHILi9Y2s2pz67Zu31HfGF1XxvSRNYypL2NoTQlDqoupLI5RURRh6cYWzrv9eVKZ4L1faD9gkQjFBx20bb/l/PNoX7CQ1Jo1uGSS9Nq1tC9YyKi/ns4xHxnLYe8bwYKn1/DyY6v4y49fpnZwGYecOpQxh/XH9zWMhfSi+onhfL9zfgnTL2f84YNY+coWXhh/BMcseI75S19lyqiDdv88IiLSa/Iq+TWzM4BbAB/4pXPuxl2c9xFgBnCYc+7FXgxRRHrI0WP68cCXjgEgCBxrm9pZtLaJuSu2MGf5Fn797DJuf2opxVGfL/aHLwE8+O9dPteCKdeyfvxFpDIBrckMbakMyXRAxDeivkfM9zCDwDkyQbguivqMritldF3ZPulKnAkcb29pY9mmFpZvbGHZxhaWZ7dXbWnb1sV7ZL9SJg2q5NwpgxlTX8a4AeWM7FdK9D0SuXVNiexr7HWYeWfgtdfusL/uxu+x+c47eXPaYYy4dwbxkSM59PThTD5pKG/OWctLs1bxyJ2v89z9Szn4xCEceOwg4iXRHEUvfYpZePFt81vwzkuMOHgKzjfWVJ1McfI5Hrr2Cqbc9USuoxQRkU7yJvk1Mx+4FTgVWA3MMbOZzrmFO51XDnwZmN37UYpIb/A8Y1BVMYOqijlpfH8AWhJpnntrE08t3sC9b8b5afuvKKeVcmulglbKrY1yWvlR9Kc8+eJL3PT8uH/ptc1gaHUJY+vLGNu/nAkDw2S0sjhKRVGU4pjP1kSa9U0JkpkA5xzN7WlWbm5leTbBXbaxhVWb20h2yk5LYj4jaks5cFAlZ00exJShVRwyrJqa0ti/UD7hutv3SO/Hai/9NF5pKRtvvZXNv76TsuOPIz5uHLEhQ5hw1CDGHzGQFQs2Mf+RVTx331u8+OByJhw9kMknDaWinwbHkh52zq3w27OhvZFozGfC4f2JzDWemVjK0a+uo7llC+Wl1bmOUkREsvIm+QUOB5Y455YCmNndwDnAwp3O+w5wE9B1k4+IFKTSeIRTJvbnlIlhMrxiU5hgZpyjKOJREotQHPPwf/FrPj6+niMOO4qY71ES8ymJRYj64VRKyUxAMh0mpZ5ZuHiwNZHmrfUtLF7fzJL1W1m8bitPLd5AKtP9BDMe8RhRW8qY+jJOnTiAkf1KGFFbysh+pdSVx/fZvam+Fz5PX0h+I3V11F72WRr+9Cca7rmHhnvuwYqKOGD283jxOOYZIw7qx4iD+rFhZTPzH80OjvX4akYfWs+UU4bRf2RFrt+GFKriqnCdbAVgwlGDWPTcWhrGXkzZwp+y/NG/cNDZn8xhgCIi0lk+Jb+DgVWd9lcD0zufYGaHAEOdc381MyW/In3Y8NpShteWvvuBSIzaIqN22J63towfUAFsv184mQ5YtrGFFZtaaG5P09Seoi2VoTQWoa48TnG2e3RpPMKQ6mIGVBTheT0/+FKkI/l1hZ/8AnjxOGMee5TMpk003Hc/G374Q9Zeex2DbvzuDufVDSvn1EsO5MhzR/PKY6tZ8Mwalsxdz8AxlUw5ZRgjD+6H9cLvR/qQaPY7KBUmvwPHVFJZV0xbahytcdj8wN+V/IqI5JF8Sn67+otk2192ZuYBPwI+tdsnMrsMuAxg2LBh+yg8Edkv+DHI7JtpkGIRj3EDyhk3IL+m1fGyLchBH2j57WCeR6Sujspzz2HDj39M4/33U3/V14nU1Lzr3LLqIo768BimvX8Erz/7Di8/uoq//+xVppw6jKM/PCYH0UvBKsr2KnjzITj4Y5gZ448cSOPMNl4YV8eR8xbikkkstue3N4iIyL6XT0NjrgaGdtofAqzptF8OTAKeMLPlwBHATDObtvMTOedud85Nc85Nq6vbv6cBEZE9FIlBJpXrKHpUX+r2vLNofT2D/vsGABYfdzxBW9suz40VRZh88lAu+s4RnPaZA5lwVH6PAi77obL6cG3b/5waf+QAMFg16CjibUke+d1feWjBWp5ZvJH5qxpIF+JIdSIi+4l8avmdA4w1s5HA28B5wAUdDzrnGoF+Hftm9gTw7xrtWUR24McgvW9afvNVR8tvX+n2vLOKM8+k5dlnaXxgJuv++7tEhw7Fr67Cr6qiZNo0ItU7dnn3fI+x0/rnKFopeAMnQ9PbsH4R1I6mrLqIoRNq2Lp4Oltjf2Ph3ffxozfj206/9qyJXHL0yBwGLCLSd+VN8uucS5vZl4CHCKc6+pVzboGZXQ+86JybmdsIRWS/4Mdh2VMw+3aYflmuo+kREb/vdXvuzKJR+l3xZdrmv0zjzJm4xPaLHRVnncXg79+Uw+ikzynrD4sfhp9Oh+mXw5nf48BjB7Fq4WYWHXIEp732EidfMpnWWAkX3TGbdxrbcx2xiEiflU/dnnHOPeicO8A5N9o5d0P22Le7Snydcyeo1VdE3uXgj0GQhnm/zXUkPcbPtvym+2jyCxAbMpjRD/2D8S/PZ9xL8xjz+GMUTZxIesOGXIcmfc1Zt8DHfwd142H2z2DpE4w8uB+p4laWVh8CLS1U3/FjDh9ZQ1VxlHkrtvDPJRtzHbWISJ+UV8mviMheO+arMOqEfTboVT7qGFE66KPdnnfmFRcTHTiQSF0dqZUrafzLX9n65JO0vvQSibfeIr1hA0GicP8/SI5VDIIJZ8HRXw33H7kOzzNsYiP92sfz/IQBNM38C81PPMHoujJeXLGFz/xW1+5FRHJBya+IFJ5IvKDv++1o+e2LA169l/jYMaTWrGHN17/Oqs9dzorzL2Dp+z/A4mOP443JU9jwvz/JdYj7JTM7w8zeMLMlZnZ1F49faWYLzewVM3vUzIbnIs6cm3I+DDgY1rwEy5/mEx85CzzH6kkfAODtb36T33xqKl88cTStyQztqUyOAxYR6Xvy5p5fEZF9xo9BJpnrKHqM7++Y/DrnSAcO58LpmbqjoTXJI6+vZ+6KLXzl5LEMqCzqsXh7S93XvkbNJZeQaWwiaG4i0xQuQVMTmaZmSg49JNch7nfMzAduBU4lnJVhjpnNdM4t7HTaS8A051yrmX0euAn4eO9HmwfOvQ1+djTc/wVqvvoqBxw2gCXzp3Dr+4v54t82k37tVQZU1gLw4vItHDO2326eUERE9iUlvyJSeAq85TeS7fZ800Nv8P2H3iCZCejoAV0S86kuiVFdGg3XJTHqy+MMqy2hf0URaxvbeXjhWp5funlb8jx1eDUfmTokV29nnzEzIrW1RGprcx1KITkcWOKcWwpgZncD5wDbkl/n3OOdzn8euKhXI8wn/Q+EisHQuAoaVnDQ8UN4c/Y6SoefDfyRrfPmcsiZHwPg6SUblPyKiPQyJb8iUnj8wp7rtyQW4Zr3jWdNQzuxiEfM94hFPAxoaEuxpTXJlpYkW1pTrNzcyrqmdtpT2+cWHVVXyueOG8XBQ6q4/Hdz++yo0dItg4FVnfZXA9Pf4/xLgb/3aET5zAzO+Qnc9UF4+of0P+sW6kdUwNojebvmHhK/v5PJF3+KfmVxmtoK9ztKRCRfKfkVkcLjxyC5FX7/MZj2aRh3Rq4j2ucuO250t891zrFha4L1TQkqi6MMrSkB4J3GNqDvzhcs3WJdHOvyP4yZXQRMA47fxeOXAZcBDBs2bF/Fl39GnQjFNfDqDOzsH3PoacP4x+1NPHLkNC7+2xyW/PSHVBZPp1HJr4hIr9OAVyJSeEadAAMnw9In4JW7cxxM7pkZ9eVFTBpcuS3xBQ2cJd2yGhjaaX8IsGbnk8zsFOCbwNnOuS7vOXDO3e6cm+acm1ZXV9cjweYFMxh+FKRaIdXOyCl1VNYXM7L0IjaWQ9uvfkelH9Ca1IBXIiK9TcmviBSe0SfC556EfmMhXbgDX+0t31PyK7s1BxhrZiPNLAacB8zsfIKZHQL8nDDxXZ+DGPPPhLPDdcNKPM845NRhpNdHeOyEqUQTaY5c9CyJTrciiIhI71DyKyKFy48V9Hy/e0vJr+yOcy4NfAl4CHgduMc5t8DMrjezbIbH94EyYIaZzTezmbt4ur6jZlS4fu1PAIw7YgAlFTH6V13AwqFw2rP34lpbchigiEjfpORXRApXgY/6vLe8bPIb6J5feQ/OuQedcwc450Y7527IHvu2c25mdvsU51x/59yU7HL2ez9jHzB4arh++geQ2Eok6jP55KFkVhXx4BGjiKWSfPihX+Q2RhGRPkjJr4gULj9a0KM+762OKZPSavkV2bc8DyacBUEaVvwTgEnHD6aoLEpd6v3MGWtMWvYyzY89luNARUT6FiW/IlK4/Li6Pb8HTwNeifScM78frhtWABArinDo6cMZ2jCeGSeMZX2Fz+ovfonWuXNzGKSISN+iqY5EpHBF4rD+dfj58WErsBfZcfGj4PnhdqQoPN8F0LIREs1wxndhwEG5fhc9puOeX83zK9IDyvqHF+Cevw3WzIfTb2DS8YOZP2slR274JNee/x1u+32UTb+8g5KpU3MdrYhIn6DkV0QK1yGfAOfCrodBKlxn0uF9wJ33gxRkkpBqD3+uuBo2vgErnivs5NfU7Vmkx3geHPkFWDwL5v8OBkwiOuEspp4xjKfvSVI0cDSLplcz7omnSGzcRLxfba4jFhEpeEp+RaRwjTsjXPZUohm+O6Tgu0x7nmGmAa9Eeswp18ExV8JNI+EfV8M/rubAqZfzfPn7mL7yLG6tu5+bMwG/++jl3Hzsp4lEfOIRn+vOPpAzJg3IdfQiIgVHya+IyM78WLjOFP4cwRHPyAQO5xzvNLaztqmdVDpgw9YEaxvbWd+cYF1TO41tKdpTGdpTAcl0QMQ3Yr4XJtCAI/ynojhKXXmMiuIo5fEI5UVRSuMRMkFAazJD4KAk5meXyA7bNaUx6srjOS4RkX2sqAIufxY2LYbHv4s/92ccf/IHeeT+YVQOqOGZE4Zy/BOvEXOLefPgk/jji6uYvWyTkl8RkR6g5FdEZGdeNFynCz/59cyYMXc1f3hhJQ2t7x4ZOx7x6F9RRHVJlHjUp7woQjzikQ4cyXQQJs6AZ2ECvHpLK/NXNdDUniKZDvYoFjN4+KvHMbZ/+b55cyL5on58uGxdD3+7kgNafsWLQy/miFVn8fPDvsPUDcOZNuM2zj1xEo+Vxdm4tfC/e0REckHJr4jIzjwvTID7QMvvsWPr2NDczoSBFUwcVMHQ6hKivke/8hgDKoqoLI5i2XuD91QinWFre5qtiTQR36Mk6mMGbakMrckMbckMLYk0rckML69u4OZHFrNha0LJrxSuwy6F1/6MNazg5PMn8aeb5jJlzSncfNgjfOuNCKu/8EU+eNg5/KThWL5y8hjG1OuzICKyLyn5FRHpih/rE8nvLy+e1mPPHY/4xMt8ast27Mpc1cW5pfEINz+ymGDPGotF9j/VI2DBnxnw2v9j7KGfhpdP53eTn2fdvd9g1E0zOHP237ivcjxvbWhR8isiso9pnl8Rka64DLxwOzS9k+tI+gQ/WxtlNPiWFLqDPwb9DoB5v+HIsfOJ+D7HLv0otyy6nZLrr8ELMpy0ci5LN7SwNZHOdbQiIgVFya+ISFeqhoctvy/+KteR9Ameac5h6SNGHQ+fuA/Mo/zJrzC9ZibDGw4kWFrGx/55GYkJo7jgzUf4092PMOnah5j58ppcRywiUjCU/IqIdOXSh8N1qjW3cfQRvhcmvxklv9IXlNTAZx+DyRdwsPs1/eoynLLqQtLtjv85sQmAH7xxLyUuzaJ3mnIcrIhI4VDyKyLSleIqKK6GdGHP9ZsvOlp+00p+pa8YdAiccDWeBZx07Cb89hiXbL2K+RVb+O1JHvF3VnPZogdpaHv3KOwiIvKvUfIrIrIrfhwySn57Q8TPdnvWPb/Sl5TUAFA359+YXP88ra/EuWnET3n11JGsHFPB6W88xZp772fyfz7MJ+6YrZ4RIiJ7ScmviMiuRGJ9Yq7ffOCbuj1LHxQvh4/dBQd/nOn8kJrKNtb+1TE6Ppb/OakFgP+Y+weOrMjw9OKNbGrRxTgRkb2h5FdEZFd2bvnNpMLRn4NM7mIqUJ6nll/poyaeDWfeRCQe59TINbQ3tzH5sYG8U2P85wXhn2lf/sW/c+6Sp2hsVRdoEZG9oXl+RUR2JRKHpU/CbUdD81po3QQ4OPSTcPb/5jq6gqKWX+nTIjH44gv0W/ca059q5LkXp/Gtt+bxX2MW8J3z4Bt/K+Vzr83k+c+u59bzr2BYbSmj68t430EDifpqxxAR6S4lvyIiuzL+/bD4YSgbAEOmhesnbwwTYdmnNNqz9HmVg6FyMFPGOFY1v8Q7b1zMDyc+y5UjH2D2L77AoJueY9q8p5j3xAR+UnMggYOKoignjq/PdeQiIvsNXS4UEdmVE6+By56AC+6Gs26BE78BQ6drBOge4Cn5FQHCz8Jpn5lEsd/C2jnTGVU0llte/h/6f/9SiiZP5vL5f+bRiw8EYMNWfReJiOyJvEp+zewMM3vDzJaY2dVdPH65mb1qZvPN7Bkzm5iLOEWkD/Nj4b2/sk9t6/ase35FKC6PcfqIP7K1Lc65iz4OzvjUI5fyy3OKCdra8H77SwAemP8298xZRToT5DhiEZH9Q94kv2bmA7cCZwITgfO7SG7/4Jw7yDk3BbgJ+GEvhykifZ0fg4xGgN7XOro9L9/YwrNLNrJgTSPrm9oJ1BIsfdSAA0dwTPmvaX2njusWnkgNEWamXuSpKRFa//wnvsAy5q1o4Ko/vcKk6x7iE3fM5toHXmPGi6toaNV3lIhIV/Lpnt/DgSXOuaUAZnY3cA6wsOME51xTp/NLAf1VJCK9y49p7t8eUBT18Ax+8fQyfvH0sm3Hi6M+B/QvY9yAcsbUlzG6rozB1cUMqS6hLJ5PVZjIPva+7zPptCSb7nqFBbPP4UdvbGLexHX8Zvo7HDsHzrr/Vi695hs8PP4E/vnWJlZsamHG3NX85rkVfProkXz7LHWOExHZWT795TAYWNVpfzUwfeeTzOyLwJVADDipd0ITEcmKqNtzTygvijLj8qNoak9RFPFpbEuyoTnBso2tLFrbxGOL1nPPi6u3nT+8toQnv35iDiMW6XkWiXHcJw+lef3jPL/sU5yy/OfcMnQtn/+Cz09uy7Duxhs5+46xnH/+kQCkMgGHfmeW5gMWEdmFfEp+rYtj72rZdc7dCtxqZhcA3wIuftcTmV0GXAYwbNiwfRymiPRpfgy2LIfbT4BkK6RawQXh8Uh8+zpStOOxqqFw8nXgd/raTSfCxwWAqcOr3/PxhtYkb23Yys+eXMozizf2UlQiueX5Hqd/5Xju+595PL728/w89U2W1aznW1cO4D9+vgW75NMMuO46qs/7OFHfY0RtKc+9tSnXYYuI5KV8Sn5XA0M77Q8B1rzH+XcDt3X1gHPuduB2gGnTpqlrtIjsOxPOgqY1EC2BqhKIloJ5YVfodCK8HzjdDukkpBrC9bpXw5+dciHUTwi3n78N/nE1VA2D+gPD4/3Ghvt146G0X+7eY56qKokxdXgNo+vW8+SbG3IdjkiviRVF+MAXJ/PnH8xlwZbvcG7662yeUMTVF3v85+8ycN11tC9YQNmJJxD346xvTrBqcytDa0pyHbqISF7Jp+R3DjDWzEYCbwPnARd0PsHMxjrnFmd33w8sRkSkN008J1z2xKK/wd0X7DhQ1pblYYvwkMNg3UJYMguCdPhYrAyuWqpW4V3wPTQQlvQ5pVVxzr3yUO77wTxmNlzPBa9fw5DqzVz16Rq+fa8xZsYMGmbM4Kr3fZCPxY5mc0tSya+IyE7yZrRn51wa+BLwEPA6cI9zboGZXW9mZ2dP+5KZLTCz+YT3/b6ry7OISN7xY+E63Sn5zSQhXgEf+RV88Xm45h24Yh4c/jlIbg27U0uXfDNNiSR9UnlNEef82xT8sirub7mZo0d9gw+3b+WaCyEz6y6iw4ZR/uB9/Nu8P/Lk72dy9wsrmbtic67DFhHJG3mT/AI45x50zh3gnBvtnLshe+zbzrmZ2e2vOOcOdM5Ncc6d6JxbkNuIRUS6wY+G684tv+nkji27kRjUjoa6A7Y/Ll3yPMM5tf5K31RZV8K5X5tKtLSY+588mNM2jgTg/Mcu4defGUb64AmctnIOp975XR65+Vd85GfPaeojEZGsvEp+RUQKkp9NcjM7tfx2JMW7O1d24Fs4PqJaf6Wvqqov4cNfn0p5bRGzN32LL68YzRGlw/hb+xx+/YURjP7H37GSEr42749c+8872NCs0Z9FREDJr4hIz+vo9vyu5DfWvXNlB76fTX7V8it9WGlVnA9+7VDqhpaTXPNlPvfOBxlcOphZK2ZxX/tsRt47g9TocUxf9zpvf+piHr/hxyx/anauwxYRySklvyIiPa2jhTfRvP1YJrm9lbeziJLf3elo+Q3U8it9XFFplHOvnMrYynnMXjCKT6y9Gj8T5b9m/xcMH0y/u37H4xOOp3TVMgbcdRttl32K1Vd8mbZXX8116CIiOaHkV0SkpxVVhOs/XQrfHQY/OxZWzd5Ft2clv7vje2r5FekQifmceuCzHFF2F5teS/GFZd+jsq2eD8/8ME+u/wvH//IKJs2bw31f+B7zB4yn+ZFHWHHxp8g0NOQ6dBGRXpdPUx2JiBSm6hFw0Z9h/cJwiqMtKyDVBqOOf/e5Hcnv4/8NVcMhXt5pqYBYaZgYF1fBqBN67z3kEa+j5TfIcSAiecIOuZCpSy+ldmgVjy49g49tvoqnm2fw343/DQa/f9/vKZk4nm+s+Qyfq27i3F9fz5LTz6B0+nSqL7yQksMPw7KfKxGRQqbkV0SkN4w5OVx2p/+BMHhqOPfvyuch0QRuF1neVcugpGbfxrkf6Gj5TSv7FQmNfz+MPY0Ra//BeRX3Mav415zw1gW8P/pxbi37f1z44IV8a+oPOWVCfx5YHWfV5A/xueINBA8/TPPDD1N5ztnUX3UVkdraXL8TEZEepeRXRCSfVAyCzz62fd+5sJU40RwmwolmWPwwPPHdcD7gPpj8ep5GexbZQbQYLpwBm5dR+uMpnH3QX5h3yJeZ89dlXBq7gYcH38XMFXdy/TnXk0mM47QfJTjz/EM4c1CUtdd/h8YHZtL8xJPUXHgB/S6/HIt1MRifiEgBUPIrIpLPzCBWEi7l/cNjm5aE60wqd3HlUMRTt2eRLtWEc/566VamnTWCkZP78fhdizh5ySdZuXEhF6+6jJMmnUi0KsFNj6R4bcI4jrniWww99UzSP/0xG396G4nFSxj841vUDVpECpKSXxGR/U3HfcHpvjl3Z8doz/NXbaFqU4zWZJqWRIZ4xGN0fRmj68pyHKFIDg04KBxboGUjtYP68aGvT+WVx1fhzYQhL49j4bpnqRz8MC3eHH7+1BX8/KmlABQd9mW+UvE3Tpg1i6Xvez+lRx5B/2uuwSL6U1FECoe+0URE9jeR7BRJmb1MfhNboWU9bF0PLRvCZNoFEGTCgbVKaqC4Zvs6kh9dIcuLwqrr8t/N6/LxWf92HGP7l/dmSCL5o3IYvPE3+P5ouPBevLGnMuXkYRxw2ABe+MtS/GeOY8KmI5gz4CHWHXwr/cqGcHK/r7Bms/FQ3UdZmYxw8eb5bPnD/5FcvoJB37sRv6YG8/1cvzMRkb2m5FdEZH/TMUVSehfTIaUTYcvPprdg61rYugG2rtue6G5dFx5LtezZ60ZLw6QYFybJzoWJeLQYoiUQK4N4WTgydawsOzJ1Kownk4B0O5ifPT/7M5GibKJdm11qwlGtiyrDKaJi5eDtOCvfqRP788fLjiCZCfDMKI1HKIn5vLBsM9+6/zUa2vpmd3ARAD7083CwvN9/JBwb4O15MPxISqqGccJ5o5l0/BCe/vMi/IVnkVp7KvMGzOLWARfzszN/ypThg7lizSm0HvQJPjPju7T8858sPvY4ooMHM/CGGyg9Ynqu352IyF4xV+ADhkybNs29+OKLuQ5DRGTfWfY0/OYDMPmCMEFs3Qytm6BtM7RsgqbV7x4hurgGyvpDWV24Lq2Hsk5LaV2YiJof3mecbAmfr3Vzdr0F2hvCQbbMCxcIE9t0OyRbIdkctiYnmsPzki1hoh4pCrtqR+LbB/BKt4XrVOuuR7MGwLLJcMX2qZ7MC2N0jjARd+BF2JKO8M9V7Rw2bgT1dfXh+ZlEGFN7Yzgi7sSz97r4zWyuc27aXj9RH6a6uRfMvALefCi82LWNQflAqBrKOqbwwqrDWLm2loTfyqL62bw24Cm2xltJN0/kELuE28YmSa5YwcbbbsO1tVF+6imUn3Y6sVEjiVRXE6mvV7doEckL3a2b9Y0lIrK/qRwcJqkv/yFM8Iqrt7ec9jsgnFe4dgzUjIaKgWFi29FanG86kuG2zdCyEdq2hKNatzdCe3adaAq3O0a77kh4zQAL10GGaKKBcbaRqreXw/LmMME2P2yNLqqEQYfk+M2K9KKz/zdcb90A6xdAwypoXLVt3b/xIc7y7mBd7QieaTuX+DvHMvmdE3inbjHzah9jZewJKk6/DoCqD3+Id775LZpnPULzrEe2vUSkvp4R9/yR6IABvf/+RET+BWr5FRHZHyVbwtbUfE1qc2DO8s189GfPcdelh3Ps2DrIpMHLtmTvQ2r53Xuqm/NEJh32FHn1XrbOupXX/E/x2qbDSKSKaIk20jy4nZIx/RkyZDQDK4o4YUgxySVLyGzZQuP9D9A8axYWjVJ2ysnERoyg5NCplB4xHYvqe0lEepdafkVEClmsNNcR5B0vm+RmguxFXV9VnMh78iNhT5HDP0tZ42qO2DSHw0r+wG/bxrOs/SSGrZiIvxyWxeYyq3Qdi46rYuLE/hw7+TjKTz6ZttfG3wBnAAATDUlEQVQWsP4HP6Bt/ss0//0fbAKiw4ZR9aEPUfXhDxGpq8vxGxQR2ZH+MhARkYLgd8z/W+A9mkT2uaJKOOtmAPzX/8Ilf7yI4Avf5IHNa3jsiZeoWjOMw7aMxR7weOHvm1k64SFOOnI6gw84gOF3/hqA1Lr1rP3O9bTNnceGm29mw803U3bCCVS870z8ykr8ykqKJk3SPcIiklP6BhIRkYIQySa/6YySX5F/Wd14ALw7TuWDwAcjxST7VfNKtJK13nSeT42h+NUx/P3lV3EEJGqaKRluVI+MMfE/Ps9BQybSOmcOTQ8+SMOMe9n6xBPbntqv60f1eedRfNBBeOXlxMeOxS/TvNwi0nuU/IqISEHo6Pasll+RvdBvLHz0Tti4GIJ0OL5A80baFy5hUPoZjqy6n2cHxliWOJzirQcwuGUosZeGsukln6dZx19iSwj6pakaMZXaG49iSKnPkEgR8dcX0vp/f2Dj//5kh5eLDR+OFRfjlZZSc9GFFE2ciFdRQaS6OjfvX0QKmpJfEREpCB3dnjPvNXOSiOzegR/cYTcGHEN4P3105TrOuOtg/MxfwSAog41lJTzjHcw/vAlUtIyg/4aReGtK2QJsJuCZ+Bq2BvWsn/xVEgcnidFKXWI94zYsoTTTTmmynVGL5vL23LnbXrN51HiC6mq88gpsxCjileWM/MjZlNfV9mZJiEiBUfIrIiIFwc9OPZxRy69Ij/A946ARA+DyZ2DTEmhvwGtvpL6tgQ+1N/KhTUtIrbiHLcVtvM0A1qRHsdCNYmNmBDWtg5jcXodHOVALNpRNgyewPN5CcyzJrAOPIdraSCbZQkXzJiateYuSzRsY2NxI0RMPAbDylu+zvrSaVKyYdLyIoKgYV1yMV1KCX1JKtLwUv7QUSkqhuBjKyklNmkKkvJyiohjFMZ/iqE9JzKco6m/b77hwJiKFT8mviIgUhG3dngMlvyI9qu6AcOlCFKhPJ6hv28IhrZs5ceta/r7maba0z6bpjUdpba0mWX8mQXMR1hTHaypiQHMVpanB4RP4QBWsq4J2v4UXYw20RRuJJ5qpbWqmKigjlkwTaWsk0tZIbPMWilavori9iZJ0gqjLdBlXwovQHonR4MdIRGK0++GSiMRwRcV4xcVESkuIlJYQLS0hXlZGUXkJxZXllFVVUFZVRlF5GfGyUuJlJcTKy7DiErziIsz3e6acRWSfU/IrIiIFYXu3ZyW/IjkViUP5ACgfQEn/iXx49Enh8fR/wOyfwfKXoWIIlEWhMkrGPFqCKJtqj6Rhwmdp2tzK1oYErQ1R2hpLSTQOoDWdJCjyaXIxKAYqd3zJwAIykSRpP0ngJwm8BLFUO9FUG16QwAva8dPtRNIJIukkkVSSaCpBRTJBNJkktqWJ+Lp24okERakEXpDEC1J4LryPoi27dCXpe7RHfRKRCImYTzoWJR2PkIpGScUipGJRksVxUkUx1g2tp62ylGg0SiweJRaPURyPU1Qcp7ioiJKiOCXFRcTiMfxIDD8aDddeBN/z8c0n4kXwzcczb9u27/lELDwn4kWIelFifoyoF8Uzr6d+0yL7HSW/IiJSELbN86tuz/uUmZ0B3ELYJvdL59yNOz0eB34LTAU2AR93zi3v7ThlP3DGjVBWDw0rIZPKLkl8F1Cx6K9UbHoVVvwRzAAHDnABxB0uDm9EIvxfSQVBphwyFVimHEuX42XKsEwpXqYYC4qwTDF+poiMX4SjEj9ThJ+OE0SjpKJ7FnJABmcZHOECaRwZzKWBDObCbQsyeEEaL8jgZ7cjmQx+EOCnA8obAiIZR//VAeaC7M+mMdeS3Q8w5zAX4FxAotO+uQCHw1mAI8iuHc4cjvD7zpmD7DFzjsDIrh2GwxlkPHAWFq8zoNMaM/AsLHoz8A0D8COYZ5hvmHmY52F+eE5gEOBwZgRA4IHDAzPikVKi0TjOwHmWfQ0IfMN5hnlhjOHiSIfvLFu6jkzHMQs6HQNnPg4jY0YaSANBNvaA8LWchQuew/M9/IhPxI8SiUSIRKJEoj6RWIxYJEY0FiEWjRGLxYjH4xRFoxTF48T8CBE/gm9edr394oPv+UQtgu9v3/c9H8O21UPmGYaHYdltyxazYdlzvE7n4EHHnmde+DNmOOfIuAzpIE0qSO1yncwkty2JTIJEkCCVSYXb6XZS6RSJTDvJdMfxdlwQELgAF2TC1wky4ByBy+CCAOccFmT/jzmHcy78PLrw19mx9jA8F/6OPTw8Fx7DhfVyxHn4ziNiHr4zfOfhY/h4RPA4cPyxHHrgKf/ad8q/QMmviIgUhG3z/Krld58xMx+4FTgVWA3MMbOZzrmFnU67FNjinBtjZucB3wM+3vvRSt4zg2O/1vVjjavhnz8JR5i2bKZk3rZtM2O8C/jPIA1BBlwmXAdpyGyF9KZsMp0I1+kEZJLbl3SSjIuSshLSVkKaonBxRaTTkE5DKhMl4yKkgwipTIR0xicIjEzgbV87n4yLEBAJt4kQuAgZotnjsezaJ+OiBHhknEcCj8B5BIGPw+tyYX9roXU7rTsPNphi103le8AjHHCtp3Qk0K07HM1kl0QPvvK/wO08mqPD3PbtHdcGxDAXBbZPJxbBEQFKtv3Yzj/X8dOd9nfxGtvulH/XBef3etxt+ze8fOR446mnOPQWJb8iIiJ7JB4J/3D89swF3PbkW8QjHumMI+McgXNcctRIPn3MyBxHud85HFjinFsKYGZ3A+cAnZPfc4Drstv3Aj8xM3NOTfCyByqHwJk37v68veBnl73iXJhcB9mW6yANqVZY/zqk2jol5R0JemL7z4Ub27ddAK2bskl+p0TYIjg8AvywBa61Aec8AjxcohXXugVnHpBNpD0f8HCWXXvhcbIJdUdraXOkhqSLknFGJpuUhwtYeyNBQPiYg8AZLpPCTzTjHAQu7FXjgnA7cOEFR988PM+IeN62C5ApAtYGLXiAZcIWTXPgBRBJtuBn0kSTTXgBeIELWw8d+A48FyZ0YeshWDbfM5dt2Q7A0glItnYqTssWsWU7DHQ0a4fbQXbtgAAL35vLthRjBM4Pj+OFxzrK2oXnOxe2aIchhM+z46/TOjYxHNaRke48jpp1xEb2ok62cwO27dzwJYzArONdbHuaHfc7P27Z17WwzADb1iq749p2eu3OsYSPuk77734TznY+bjusOsq543fgMJwXnuC2va5tKwsH+HXl9CYlvyIiUhBqy+L88GOTWbS2mXca20mlAyK+Zf9AMwZVFec6xP3RYGBVp/3VwPRdneOcS5tZI1ALbOyVCEV6kxlEYryrPbJq2N4/Ne/Ol/aluh587pwIgh17AATp8IJCR++AIB0+7hz4UfBj4EXCtR8FLwpeL7a2B0F40aQj1kw6u5/JdifOkEimaGxL8MaaRjY1t5JKp0ml0qTTaZLpNC7IkAognXGkHeF2AOnAbetyHnROPLMLtuN+4MKeFeaFj5ll983DZbteh50v/E69L7zwPM/bdj4Ynu8T8SNEIhGifnghxLOwW3dH/WuWvVjihRcTMoEjHQSkA8f0kTW99ztAya+IiBSQDx06JNchFJqu/hbfuUW3O+dgZpcBlwEMG7b3iYKI9HFetnXb38MbuXPF88CLA/FdnhIH6oH6Eb0UUx+0n91cICIiIr1oNTC00/4QYM2uzjGzCOE4vJt3fiLn3O3OuWnOuWl1dQXXBiUiIvsBJb8iIiKyK3OAsWY20sxiwHnAzJ3OmQlcnN3+CPCY7vcVEZF8lFfJr5mdYWZvmNkSM7u6i8evNLOFZvaKmT1qZsNzEaeIiEhf4JxLA18CHgJeB+5xzi0ws+vN7OzsaXcAtWa2BLgSeFf9LSIikg/y5p7fbk6n8BIwzTnXamafB25C0ymIiIj0GOfcg8CDOx37dqftduCjvR2XiIjInsqnlt9t0yk455JAx3QK2zjnHnfOdUzF9TzhvUciIiIiIiIi7ymfkt+uplMY/B7nXwr8vUcjEhERERERkYKQN92e6eZUCQBmdhEwDTh+F49rOgURERERERHZJp9afrsznQJmdgrwTeBs51yiqyfSdAoiIiIiIiLSWT4lv7udTsHMDgF+Tpj4rs9BjCIiIiIiIrIfypvkt5vTKXwfKANmmNl8M9t5rkERERERERGRd8mne367M53CKb0elIiIiIiIiOz38qblV0RERERERKSnKPkVERERERGRgmfOdTmbUMEwsw3Ain30dP2AjfvouQqZymn3VEbdo3LqHpVT9+yrchrunNNUAntBdXNOqJx2T2XUPSqn7lE5dU+v1s0Fn/zuS2b2onNuWq7jyHcqp91TGXWPyql7VE7do3IqTPq9do/KafdURt2jcuoelVP39HY5qduziIiIiIiIFDwlvyIiIiIiIlLwlPzumdtzHcB+QuW0eyqj7lE5dY/KqXtUToVJv9fuUTntnsqoe1RO3aNy6p5eLSfd8ysiIiIiIiIFTy2/IiIiIiIiUvCU/HaDmZ1hZm+Y2RIzuzrX8eQLM/uVma03s9c6Hasxs1lmtji7rs5ljPnAzIaa2eNm9rqZLTCzr2SPq6w6MbMiM3vBzF7OltN/Zo+PNLPZ2XL6o5nFch1rrpmZb2Yvmdlfs/sqo52Y2XIze9XM5pvZi9lj+swVENXNXVPd3D2qm7tHdXP3qW7evXyom5X87oaZ+cCtwJnAROB8M5uY26jyxp3AGTsduxp41Dk3Fng0u9/XpYGvOecmAEcAX8z+H1JZ7SgBnOScmwxMAc4wsyOA7wE/ypbTFuDSHMaYL74CvN5pX2XUtROdc1M6TaGgz1yBUN38nu5EdXN3qG7uHtXN3ae6uXtyWjcr+d29w4ElzrmlzrkkcDdwTo5jygvOuaeAzTsdPgf4TXb7N8C5vRpUHnLOveOcm5fdbib8YhyMymoHLrQ1uxvNLg44Cbg3e7zPl5OZDQHeD/wyu2+ojLpLn7nCobp5F1Q3d4/q5u5R3dw9qpv3Sq9+5pT87t5gYFWn/dXZY9K1/s65dyCsWID6HMeTV8xsBHAIMBuV1btkuwzNB9YDs4C3gAbnXDp7ij5/cDNwFRBk92tRGXXFAQ+b2Vwzuyx7TJ+5wqG6ec/o//57UN383lQ3d4vq5u7Jed0c6cknLxDWxTENkS17zMzKgD8BX3XONYUXBaUz51wGmGJmVcB9wISuTuvdqPKHmX0AWO+cm2tmJ3Qc7uLUPltGnRztnFtjZvXALDNblOuAZJ/S/3vZJ1Q3757q5vemunmP5LxuVsvv7q0GhnbaHwKsyVEs+4N1ZjYQILten+N48oKZRQkr19875/6cPayy2gXnXAPwBOF9WFVm1nGhrq9//o4Gzjaz5YTdPE8ivNqsMtqJc25Ndr2e8I+1w9FnrpCobt4z+r/fBdXNe0Z18y6pbu6mfKiblfzu3hxgbHbEthhwHjAzxzHls5nAxdnti4EHchhLXsje93EH8Lpz7oedHlJZdWJmddmryphZMXAK4T1YjwMfyZ7Wp8vJOfcN59wQ59wIwu+ix5xzF6Iy2oGZlZpZecc2cBrwGvrMFRLVzXtG//d3orq5e1Q3757q5u7Jl7rZnFML/O6Y2fsIr+D4wK+cczfkOKS8YGb/B5wA9APWAdcC9wP3AMOAlcBHnXM7D7zRp5jZMcDTwKtsvxfkGsJ7i1RWWWZ2MOFABz7hhbl7nHPXm9kowiupNcBLwEXOuUTuIs0P2a5V/+6c+4DKaEfZ8rgvuxsB/uCcu8HMatFnrmCobu6a6ubuUd3cPaqb94zq5l3Ll7pZya+IiIiIiIgUPHV7FhERERERkYKn5FdEREREREQKnpJfERERERERKXhKfkVERERERKTgKfkVERERERGRgqfkV0RERERERAqekl8RwcyuNDNnZhfkOhYRERFR3SzSE5T8igjAodn13JxGISIiIh1UN4vsY+acy3UMIpJjZvY6MASodM4FuY5HRESkr1PdLLLvqeVXpA8zs++ZmQPGA2VAJtvFypnZRTkOT0REpM9R3SzScyK5DkBEcmou8BvgYuCfwKxOjz2Zk4hERET6NtXNIj1Eya9IH+acu8fMqggr2N84527PdUwiIiJ9mepmkZ6jbs8i0jGgxrycRiEiIiIdVDeL9AAlvyJyKJACXs11ICIiIgKobhbpEUp+RfowM4sABwELnXOJXMcjIiLS16luFuk5Sn5F+raJQBHqViUiIpIvVDeL9BAlvyJ925Ts+qWcRiEiIiIdVDeL9BAlvyJ9W2123ZTTKERERKSD6maRHqKpjkT6trnZ9Q1mNgloARY452bkMCYREZG+THWzSA9Ry69IH+acewq4grBivQK4lu3drURERKSXqW4W6TnmnMt1DCIiIiIiIiI9Si2/IiIiIiIiUvCU/IqIiIiIiEjBU/IrIiIiIiIiBU/Jr4iIiIiIiBQ8Jb8iIiIiIiJS8JT8ioiIiIiISMFT8isiIiIiIiIFT8mviIiIiIiIFDwlvyIiIiIiIlLwlPyKiIiIiIhIwfv/S+396BI54OoAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16,6))\n", + "# spin excitation\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_mc_t50, label=\"mc solve (50 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t100, label=\"mc solve (100 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t200, label=\"mc solve (200 trajectories)\")\n", + "plt.plot(tlist, sz_mc_t, label=\"mc solve (500 trajectories)\")\n", + "plt.plot(tlist, sz_t, label=\"me solve\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "# photonic excitation\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_mc_t50/nph/0.5, label=\"mc solve (50 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t100/nph/0.5, label=\"mc solve (100 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t200/nph/0.5, label=\"mc solve (200 trajectories)\")\n", + "plt.plot(tlist, nph_mc_t/nph/0.5, label=\"mc solve (500 trajectories)\")\n", + "plt.plot(tlist, nph_t/nph/0.5, label=\"me solve\")\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", + "plt.legend(fontsize=15)\n", + "plt.show()\n", + "plt.close()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We observe that progressively, as the number of trajectories is increased, the value given by the average over the trajectories gets closer to the master equation value." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(12,4))\n", + "plt.subplot(121)\n", + "plt.plot(tlist, sz_t)\n", + "plt.plot(tlist, sz_mc_t)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle s_z \\rangle$\",fontsize=fs)\n", + "plt.subplot(122)\n", + "plt.plot(tlist, nph_t/nph/0.5)\n", + "plt.plot(tlist, nph_mc_t/nph/0.5)\n", + "\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle n_{ph} \\rangle$\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting single quantum trajectories\n", + "\n", + "By setting:\n", + "my_options = Options(average_states = False, store_states = True)\n", + "\n", + "we can inspect single quantum trajectories and their behaviour." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(14,5))\n", + "plt.subplot(121)\n", + "for i in range(len(sz_stoch_t)):\n", + " plt.plot(tlist, sz_stoch_t[i],alpha=0.1)\n", + "\n", + "plt.plot(tlist, sz_t,\"b\",linewidth=3)\n", + "plt.plot(tlist, sz_mc_t,\"y\",linewidth=2)\n", + "plt.plot(tlist, sz_stoch_t[4]/nph/0.5,\"g\",linewidth=5)\n", + "plt.plot(tlist, sz_stoch_t[6]/nph/0.5,\"r\",linewidth=5)\n", + "plt.subplot(122)\n", + "for i in range(len(sz_stoch_t)):\n", + " plt.plot(tlist, nph_stoch_t[i]/nph/0.5,alpha=0.1)\n", + "plt.plot(tlist, nph_t/nph/0.5,\"b\",linewidth=3)\n", + "plt.plot(tlist, nph_mc_t/nph/0.5,\"y\",linewidth=2)\n", + "plt.plot(tlist, nph_stoch_t[4]/nph/0.5,\"g\",linewidth=5)\n", + "plt.plot(tlist, nph_stoch_t[6]/nph/0.5,\"r\",linewidth=5)\n", + "plt.xlabel(r\"$t$\",fontsize=fs)\n", + "plt.ylabel(r\"$\\langle X \\rangle$\",fontsize=fs)\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We obseverve that the single trajectories can provide information about the phase of the system. In presence of a phase transition the quantum trajectory jumps between possible choices of the degenerate steady state. " + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "QuTiP: Quantum Toolbox in Python\n", + "Copyright (c) 2011 and later.\n", + "A. J. Pitchford, P. D. Nation, R. J. Johansson, A. Grimsmo, and C. Granade\n", + "\n", + "QuTiP Version: 4.3.1\n", + "Numpy Version: 1.15.4\n", + "Scipy Version: 1.2.1\n", + "Cython Version: 0.29.8\n", + "Matplotlib Version: 3.0.3\n", + "Python Version: 3.7.3\n", + "Number of CPUs: 2\n", + "BLAS Info: OPENBLAS\n", + "OPENMP Installed: False\n", + "INTEL MKL Ext: False\n", + "Platform Info: Darwin (x86_64)\n", + "Installation path: /miniconda3/lib/python3.7/site-packages/qutip\n", + "==============================================================================\n", + "Please cite QuTiP in your publication.\n", + "==============================================================================\n", + "For your convenience a bibtex file can be easily generated using `qutip.cite()`\n" + ] + } + ], + "source": [ + "qutip.about()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/test.rtf b/test.rtf deleted file mode 100644 index 165ce91..0000000 --- a/test.rtf +++ /dev/null @@ -1,8 +0,0 @@ -{\rtf1\ansi\ansicpg1252\cocoartf1671\cocoasubrtf500 -{\fonttbl\f0\fswiss\fcharset0 Helvetica;} -{\colortbl;\red255\green255\blue255;} -{\*\expandedcolortbl;;} -\paperw11900\paperh16840\margl1440\margr1440\vieww10800\viewh8400\viewkind0 -\pard\tx566\tx1133\tx1700\tx2267\tx2834\tx3401\tx3968\tx4535\tx5102\tx5669\tx6236\tx6803\pardirnatural\partightenfactor0 - -\f0\fs24 \cf0 Test} \ No newline at end of file