{ "cells": [ { "cell_type": "markdown", "id": "c21b2ffd", "metadata": {}, "source": [ "# Superconductivity with KWANT\n", "\n", "### © Jalil Varela-Manjarres, University of Delaware\n", "[PHYS824: Nanophysics & Nanotechnology](https://wiki.physics.udel.edu/phys824) " ] }, { "cell_type": "markdown", "id": "81d1450c", "metadata": {}, "source": [ "Some of the following examples were taken and adapted from https://tkwant.kwant-project.org/doc/dev/tutorial" ] }, { "cell_type": "markdown", "id": "6441636f", "metadata": {}, "source": [ "## What is covered in this notebook\n", " \n", "\n", " Physics background\n", "\n", " - Conductance of a NS-junction (Andreev reflection, superconducting gap)\n", "\n", "- 1D SNS-juntion with and without Barrier\n", "\n", "\n", "- 2D SAS-juntion with A being and altermagnetic d-metal (Pending)" ] }, { "cell_type": "code", "execution_count": 1, "id": "f5ffb676", "metadata": {}, "outputs": [], "source": [ "import kwant\n", "from matplotlib import pyplot\n", "import matplotlib.pyplot as plt\n", "import tinyarray\n", "import numpy as np\n", "tau_x = tinyarray.array([[0, 1], [1, 0]])\n", "tau_y = tinyarray.array([[0, -1j], [1j, 0]])\n", "tau_z = tinyarray.array([[1, 0], [0, -1]])" ] }, { "cell_type": "markdown", "id": "223d1a42", "metadata": {}, "source": [ "The corresponding\n", "tight–binding Hamiltonian is\n", "\\begin{equation}\n", "\\hat H =\n", "\\sum_{i=-\\infty}^{+\\infty}\\sum_{\\sigma=\\uparrow,\\downarrow}\n", "\\left[\n", "e^{-i\\varphi_J(t)\\delta_{i,-1}}\n", "\\hat c_{i\\sigma}^\\dagger \\hat c_{i+1,\\sigma}\n", "+\n", "\\left(U\\delta_{i,0}-E_F\\right)\n", "\\hat c_{i\\sigma}^\\dagger \\hat c_{i\\sigma}\n", "\\right]\n", "+\n", "\\sum_{i=-\\infty}^{+\\infty}\n", "\\left[\n", "\\Delta (1-\\delta_{i,0})\\,\\hat c_{i\\uparrow}^\\dagger \\hat c_{i\\downarrow}^\\dagger\n", "+ \\text{h.c.}\n", "\\right].\n", "\\label{eq:H_SNS}\n", "\\end{equation}\n", "Here $\\hat c_{i,\\sigma}^\\dagger$ ($\\hat c_{i,\\sigma}$) creates (annihilates)\n", "a fermion with spin $\\sigma\\in\\{\\uparrow,\\downarrow\\}$ on site $i$.\n", "The time–dependent phase\n", "\\begin{equation}\n", "\\varphi_J(t) = \\frac{e}{\\hbar} \\int_0^t V_J(t')\\,\\mathrm{d}t'\n", "\\end{equation}\n", "is determined by the voltage drop $V_J(t)$ across the junction, which we\n", "assume to be located between the left superconducting lead and the central\n", "site. The parameter $\\Delta$ denotes the superconducting gap inside the\n", "leads, $U$ is a local barrier potential controlling the normal-state\n", "transmission probability $D$ of the junction, and $E_F$ is the Fermi\n", "energy. Within T-Kwant this Hamiltonian is treated almost as a standard\n", "normal-state tight-binding model; superconductivity simply doubles the\n", "local Hilbert space by introducing electron and hole degrees of freedom on\n", "each site.\n" ] }, { "cell_type": "markdown", "id": "b3af21f1", "metadata": {}, "source": [ "\n", "To make the notation more compact we introduce single-particle matrix\n", "elements\n", "\\begin{equation}\n", "h_{ij} = e^{-i\\varphi_J(t)\\delta_{i,-1}} \\delta_{i,j+1}\n", " + (U\\delta_{i,0}-E_F)\\delta_{ij},\n", "\\qquad\n", "\\Delta_{ij} = \\Delta (1-\\delta_{i,0}) \\delta_{ij}.\n", "\\label{eq:hij_Dij}\n", "\\end{equation}\n", "Strictly speaking, these expressions specify only the upper-triangular part\n", "of the Hamiltonian matrix; the lower-triangular part follows from Hermitian\n", "conjugation. With this definition the second-quantized Hamiltonian becomes\n", "\\begin{equation}\n", "\\hat H =\n", "\\sum_{i,j=-\\infty}^{+\\infty}\n", "\\left[\n", "h_{ij}\\bigl(\n", "\\hat c_{i\\uparrow}^\\dagger \\hat c_{j\\uparrow}\n", "+\n", "\\hat c_{i\\downarrow}^\\dagger \\hat c_{j\\downarrow}\n", "\\bigr)\n", "+\n", "\\Delta_{ij}\\hat c_{i\\uparrow}^\\dagger \\hat c_{j\\downarrow}^\\dagger\n", "+\n", "\\Delta_{ij}^\\ast \\hat c_{i\\downarrow}\\hat c_{j\\uparrow}\n", "\\right].\n", "\\label{eq:H_hDelta}\n", "\\end{equation}\n", "\n", "Using the fermionic anticommutation relations one can show that\n", "\\begin{equation}\n", "h_{ij}\\,\\hat c_i^\\dagger \\hat c_j\n", "= \\frac{1}{2}\n", "\\left(\n", "h_{ij}\\,\\hat c_i^\\dagger \\hat c_j\n", "- h_{ji}^\\ast\\,\\hat c_j \\hat c_i^\\dagger\n", "+ h_{ii}\\,\\delta_{ij}\n", "\\right),\n", "\\label{eq:fermion_identity}\n", "\\end{equation}\n", "which allows us to cast the Hamiltonian in Bogoliubov–de Gennes (BdG)\n", "matrix form,\n", "\\begin{equation}\n", "\\hat H =\n", "\\sum_{i,j=-\\infty}^{+\\infty}\n", "\\bigl(\\hat c_{i\\uparrow}^\\dagger,\\,\n", " \\hat c_{i\\downarrow}\\bigr)\n", "\\,H_{ij}\\,\n", "\\begin{pmatrix}\n", "\\hat c_{j\\uparrow}\\\\[2pt]\n", "\\hat c_{j\\downarrow}^\\dagger\n", "\\end{pmatrix},\n", "\\label{eq:H_BdG_matrix}\n", "\\end{equation}\n", "where $H_{ij}$ is the $2\\times2$ BdG Hamiltonian in Nambu (electron–hole)\n", "space." ] }, { "cell_type": "markdown", "id": "e735f26f", "metadata": {}, "source": [ "\n", "\n", "## Example 1:\"Superconductors\": orbitals, conservation laws and symmetries\n" ] }, { "cell_type": "markdown", "id": "77a45252", "metadata": {}, "source": [ "This example deals with superconductivity on the level of the Bogoliubov-de Gennes (BdG) equation. In this framework, the Hamiltonian is given as\n", "\n", " $$ H = \\begin{pmatrix}\n", " H_0 - \\mu & \\Delta \\\\\n", " \\Delta^\\dagger & \\mu - \\mathcal{T} H_0 \\mathcal{T}^{-1}\n", " \\end{pmatrix}$$\n", "\n", "where $H_0$ is the Hamiltonian of the system without\n", "superconductivity, $\\mu$ the chemical potential, $\\Delta$\n", "the superconducting order parameter, and $\\mathcal{T}$\n", "the time-reversal operator. The BdG Hamiltonian introduces\n", "electron and hole degrees of freedom (an artificial doubling -\n", "be aware of the fact that electron and hole excitations\n", "are related!), which we will need to include in our model with Kwant.\n", "\n", "For this we restrict ourselves to a simple spinless system without\n", "magnetic field, so that $\\Delta$ is just a number (which we\n", "choose real), and $\\mathcal{T}H_0\\mathcal{T}^{-1}=H_0^*=H_0.$\n", "Furthermore, note that the Hamiltonian has particle-hole symmetry\n", "$\\mathcal{P}$, i. e. $\\mathcal{P}H\\mathcal{P}^{-1}=-H.$\n", "\n" ] }, { "cell_type": "markdown", "id": "397a00e1", "metadata": {}, "source": [ "### N-S Junction " ] }, { "attachments": { "image.png": { "image/png": "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" } }, "cell_type": "markdown", "id": "4f51a523", "metadata": {}, "source": [ "Let us consider a system that consists of a normal lead on the left,\n", "a superconductor on the right, and a tunnel barrier in between:\n", "\n", "![image.png](attachment:image.png)\n", "\n", "\n", "Care must be taken when transport calculations are done with\n", "the BdG equation. Electrons and holes carry charge with\n", "opposite sign, such that it is necessary to separate the electron\n", "and hole degrees of freedom in the scattering matrix.\n", "In particular, the conductance of a N-S-junction is given as\n", "\n", "\n", " $$ G = \\frac{e^2}{h} (N - R_\\text{ee} + R_\\text{he})\\,,$$\n", "\n", "We implement the BdG Hamiltonian in Kwant using a 2x2 matrix structure\n", "for all Hamiltonian matrix elements.\n", "We start by declaring some parameters that will be used in the following code:\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "9a31d977", "metadata": {}, "outputs": [], "source": [ "a = 1\n", "W, L = 10, 10\n", "barrier = 0.0\n", "barrierpos = (3, 4)\n", "mu = 0.4\n", "Delta = 0.1\n", "Deltapos = 4\n", "t = 1.0\n", "sep=4*t-mu" ] }, { "cell_type": "code", "execution_count": 4, "id": "3bce6cf7", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Start with an empty tight-binding system. On each site, there\n", "# are now electron and hole orbitals, so we must specify the\n", "# number of orbitals per site. The orbital structure is the same\n", "# as in the Hamiltonian.\n", "lat = kwant.lattice.square(norbs=2)\n", "syst = kwant.Builder()\n", "\n", "#### Define the scattering region. ####\n", "# The superconducting order parameter couples electron and hole orbitals\n", "# on each site, and hence enters as an onsite potential.\n", "# The pairing is only included beyond the point 'Deltapos' in the scattering region.\n", "syst[(lat(x, y) for x in range(Deltapos) for y in range(W))] = (4 * t - mu) * tau_z\n", "syst[(lat(x, y) for x in range(Deltapos, L) for y in range(W))] = (4 * t - mu) * tau_z + Delta * tau_x\n", "\n", "# The tunnel barrier\n", "syst[(lat(x, y) for x in range(barrierpos[0], barrierpos[1])\n", " for y in range(W))] = (4 * t + barrier - mu) * tau_z\n", "\n", "# Hoppings\n", "syst[lat.neighbors()] = -t * tau_z\n", "\n", "kwant.plot(syst)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "6d678e96", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "0076a445", "metadata": {}, "source": [ "Note the argument ``norbs`` to `~kwant.lattice.square`. This is\n", "the number of orbitals per site in the discretized BdG Hamiltonian - of course,\n", "``norbs = 2``, since each site has one electron orbital and one hole orbital.\n", "It is necessary to specify ``norbs`` here, such that we may later separate the\n", "scattering matrix into electrons and holes. Aside from this, creating the system\n", "is syntactically equivalent to :ref:`spin example `.\n", "The only difference is that the Pauli matrices now act in electron-hole space.\n", "Note that the tunnel barrier is added by overwriting previously set\n", "on-site matrix elements.\n", "\n", "The superconducting order parameter is nonzero only in a part of the\n", "scattering region - the part to the right of the tunnel barrier. Thus,\n", "the scattering region is split into a superconducting part (the right\n", "side of it), and a normal part where the pairing is zero (the left side\n", "of it). The next step towards computing conductance is to attach leads.\n", "Let's attach two leads: a normal one to the left end, and a superconducting\n", "one to the right end. Starting with the left lead, we have:\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "d8091778", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#### Define the leads. ####\n", "# Left lead - normal, so the order parameter is zero.\n", "sym_left = kwant.TranslationalSymmetry((-a, 0))\n", "# Specify the conservation law used to treat electrons and holes separately.\n", "# We only do this in the left lead, where the pairing is zero.\n", "lead0 = kwant.Builder(sym_left, conservation_law=-tau_z)#, particle_hole=tau_y)\n", "lead0[(lat(0, j) for j in range(W))] = (4 * t - mu) * tau_z\n", "lead0[lat.neighbors()] = -t * tau_z\n", "\n", "\n", "kwant.plot(lead0)\n", "plt.show()\n", "\n", "\n", "k = np.arange(-np.pi, np.pi, 0.01)\n", "fig = kwant.plotter.bands(lead0.finalized(), momenta=k, show=False);\n", "ax = fig.axes[0]\n", "#ax.set_ylim(-2.0, 2.0);\n", "ax.axhline(0.4,ls=\"--\")" ] }, { "cell_type": "markdown", "id": "167a5556", "metadata": {}, "source": [ "Note the two new new arguments in `~kwant.builder.Builder`, ``conservation_law``\n", "and ``particle_hole``. For the purpose of computing conductance, ``conservation_law``\n", "is the essential one, as it allows us to separate the electron and hole degrees of\n", "freedom. Note that it is not necessary to specify ``particle_hole``\n", "in `~kwant.builder.Builder` to correctly compute the conductance in this example.\n", "We will discuss the argument ``particle_hole`` later on. First, let us\n", "discuss ``conservation_law`` in more detail.\n", "\n", "Observe that electrons and holes are uncoupled in the left (normal) lead, since\n", "the superconducting order parameter that couples them is zero.\n", "Consequently, we may view the electron and hole degrees of freedom as being\n", "conserved, and may therefore separate them in the Hamiltonian.\n", "\n", "In more technical terms, the conservation law implies that the Hamiltonian\n", "can be block diagonalized into uncoupled electron and hole blocks. Since\n", "the blocks are uncoupled, we can construct scattering states in each block\n", "independently. Of course, any scattering state from the electron (hole) block\n", "is entirely electron (hole) like. As a result, the scattering matrix separates\n", "into blocks that describe the scattering between different types of carriers,\n", "such as electron to electron, hole to electron, et cetera.\n", "\n", "As we saw above, conservation laws in Kwant are specified with the\n", "``conservation_law`` argument in `~kwant.builder.Builder`.\n", "Specifically, ``conservation_law`` is a matrix that acts on a single *site*\n", "and it must in addition have integer eigenvalues.\n", "Of course, it must also commute with the onsite Hamiltonian and hoppings\n", "to adjacent sites. Internally, Kwant then uses the eigenvectors of the\n", "conservation law to block diagonalize the Hamiltonian. Here, we've specified\n", "the conservation law $-\\sigma_z$, such that the eigenvectors with\n", "eigenvalues $-1$ and $1$ pick out the electron and hole\n", "blocks, respectively. Internally in Kwant, the blocks are stored in the order\n", "of ascending eigenvalues of the conservation law.\n", "\n", "In order to move on with the conductance calculation, let's attach the second\n", "lead to the right side of the scattering region:" ] }, { "cell_type": "code", "execution_count": 6, "id": "c6160c79", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Right lead - superconducting, so the order parameter is included.\n", "sym_right = kwant.TranslationalSymmetry((a, 0))\n", "lead1 = kwant.Builder(sym_right)\n", "lead1[(lat(0, j) for j in range(W))] = (4 * t - mu) * tau_z + Delta * tau_x\n", "lead1[lat.neighbors()] = -t * tau_z\n", "\n", "\n", "k = np.arange(-np.pi, np.pi, 0.01)\n", "fig = kwant.plotter.bands(lead1.finalized(), momenta=k, show=False);\n", "ax = fig.axes[0]\n", "ax.set_ylim(-1.0, 1.0);\n", "\n", "#ax.axhline(0.0,ls=\"--\")\n", "ax.axhline(0.1,ls=\"--\")\n", "ax.axhline(-0.1,ls=\"--\")\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "40e8a148", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#### Attach the leads and finalize the system. ####\n", "syst.attach_lead(lead0)\n", "syst.attach_lead(lead1)\n", "\n", "syst = syst.finalized()\n", "\n", "#plt.figure()\n", "kwant.plot(syst)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4117c26b", "metadata": {}, "source": [ "The second (right) lead is superconducting, such that the electron and hole\n", "blocks are coupled. Of course, this means that we can not separate them into\n", "uncoupled blocks as we did before, and therefore no conservation law is specified.\n", "\n", "Kwant is now aware of the block structure of the Hamiltonian in the left lead.\n", "This means that we can extract transmission and reflection amplitudes not only\n", "into the left lead, but also between different conservation law blocks in\n", "the left lead. Generally if leads :math:`i` and :math:`j` both have a conservation\n", "law specified, ``smatrix.transmission((i, a), (j, b))`` gives us\n", "the scattering probability of carriers from block :math:`b` of lead :math:`j`, to\n", "block :math:`a` of lead :math:`i`. In our example, reflection from electrons to\n", "electrons in the left lead is thus ``smatrix.transmission((0, 0), (0, 0))`` (Don't get\n", "confused by the fact that it says ``transmission`` -- transmission\n", "into the same lead is reflection), and reflection from electrons to holes\n", "is ``smatrix.transmission((0, 1), (0, 0))``:" ] }, { "cell_type": "code", "execution_count": 8, "id": "0ba4f19d", "metadata": {}, "outputs": [], "source": [ "def plot_conductance(syst, energies):\n", " # Compute conductance\n", " data = []\n", " for energy in energies:\n", " smatrix = kwant.smatrix(syst, energy)\n", " # Conductance is N - R_ee + R_he\n", " data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] -\n", " smatrix.transmission((0, 0), (0, 0)) +\n", " smatrix.transmission((0, 1), (0, 0)))\n", " pyplot.figure()\n", " pyplot.plot(energies, data)\n", " pyplot.xlabel(\"energy [t]\")\n", " pyplot.ylabel(\"conductance [e^2/h]\")\n", " plt.axvline(0.1,ls=\"--\")\n", " \n", " pyplot.show()\n", " " ] }, { "cell_type": "code", "execution_count": 9, "id": "00bfb93a", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_conductance(syst, energies=[0.002 * i for i in range(-10, 100)])" ] }, { "cell_type": "code", "execution_count": 13, "id": "b6a6d3f5", "metadata": {}, "outputs": [], "source": [ "def plot_reflection(syst, energies):\n", " # Compute conductance\n", " data_refle_ee = []\n", " data_refle_hh = []\n", " data_refle_eh = []\n", "\n", " \n", " for energy in energies:\n", " smatrix = kwant.smatrix(syst, energy)\n", " # Conductance is N - R_ee + R_he\n", " data_refle_ee.append(smatrix.transmission((0, 0), (0, 0)) )\n", "# data_refle_hh.append(smatrix.transmission((0, 1), (0, 1)) )\n", " data_refle_eh.append(smatrix.transmission((0, 0), (0, 1)) )\n", " \n", "# data_trans_ee.append(smatrix.transmission((0, 0), (1, 0)) )\n", "# data_trans_hh.append(smatrix.transmission((0, 1), (1, 1)) )\n", "# data_trans_eh.append(smatrix.transmission((0, 0), (1, 1)) )\n", " \n", " pyplot.figure()\n", " pyplot.plot(energies, data_refle_ee,label=r\"R_ee\")\n", " #pyplot.plot(energies, data_refle_hh,label=r\"R_hh\")\n", " pyplot.plot(energies, data_refle_eh,label=r\"R_he\")\n", " pyplot.xlabel(\"energy [t]\")\n", " pyplot.ylabel(\"Reflection\")\n", " pyplot.legend()\n", " pyplot.show()\n", " \n", " \n", "def plot_transmission(syst, energies):\n", " # Compute conductance\n", " data_trans_ee = []\n", " data_trans_hh = []\n", " data_trans_eh = []\n", "\n", " \n", " for energy in energies:\n", " smatrix = kwant.smatrix(syst, energy)\n", " # Conductance is N - R_ee + R_he\n", "# data_refle_ee.append(smatrix.transmission((0, 0), (0, 0)) )\n", "# data_refle_hh.append(smatrix.transmission((0, 1), (0, 1)) )\n", "# data_refle_eh.append(smatrix.transmission((0, 0), (0, 1)) )\n", " \n", " data_trans_ee.append(smatrix.transmission((1, 0), (0, 0)) )\n", " #data_trans_hh.append(smatrix.transmission((1, 1), (0, 1)) )\n", " data_trans_eh.append(smatrix.transmission((1, 0), (0, 1)) )\n", " \n", " pyplot.figure()\n", " pyplot.plot(energies, data_trans_ee,label=r\"T_ee\")\n", " #pyplot.plot(energies, data_refle_hh,label=r\"R_hh\")\n", " pyplot.plot(energies, data_trans_eh,label=r\"T_eh\")\n", " pyplot.xlabel(\"energy [t]\")\n", " pyplot.ylabel(\"Trasmission\")\n", " pyplot.legend()\n", " pyplot.show()\n", " \n" ] }, { "cell_type": "code", "execution_count": 14, "id": "9e1578de", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_reflection(syst, energies=[0.002 * i for i in range(-10, 100)])" ] }, { "cell_type": "code", "execution_count": 15, "id": "a5dc6e9b", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_transmission(syst, energies=[0.002 * i for i in range(-10, 100)])" ] }, { "cell_type": "markdown", "id": "8a054ea9", "metadata": {}, "source": [ "## S-N-S Junction in 1D system " ] }, { "attachments": { "image.png": { "image/png": "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" } }, "cell_type": "markdown", "id": "1e8cd719", "metadata": {}, "source": [ "![image.png](attachment:image.png)\n", "\n", "\n", "We consider a short, ballistic S--N--S junction with a single perfectly\n", "transmitting channel ($T = 1$). The left and right superconducting\n", "electrodes have the same gap $\\Delta$ but different phases, $-\\phi/2$\n", "and $+\\phi/2$, respectively. We focus on subgap energies $|E| < \\Delta$.\n", "\n", "For energies inside the gap, quasiparticles cannot propagate in the bulk\n", "of the superconductors and are instead Andreev reflected at the\n", "interfaces. An incident electron from the normal region is retroreflected\n", "as a hole with the Andreev reflection amplitude\n", "$\n", "r_A(E) = e^{-i \\arccos(E/\\Delta)}.\n", "$\n", "At the opposite interface, the hole is converted back into an electron\n", "with the same magnitude of phase shift.\n", "\n", " We neglect \n", "(i) normal reflection at the interfaces and \n", "(ii) the dynamical phase accumulated in the normal region (its length is\n", "much shorter than the superconducting coherence length). A closed\n", "electron--hole orbit inside the junction then consists of:\n", "\n", "\n", "- two Andreev reflections, one at each S/N interface, giving a total\n", " Andreev phase $2 \\arccos(E/\\Delta)$;\n", "- the superconducting phase difference $\\phi$ picked up between the\n", " two electrodes.\n", "\n", "\n", "The quantization condition for an Andreev bound state is that the total\n", "phase acquired by an electron--hole loop is an integer multiple of $2\\pi$:\n", "$\n", "2 \\arccos(E/\\Delta) + \\phi = 2\\pi n, \\qquad n \\in \\mathbb{Z}.\n", "$\n", "Solving for $E$,\n", "\n", "$$\n", "\\arccos(E/\\Delta) = \\pi n - \\frac{\\phi}{2}\n", "\\;\\Rightarrow\\;\n", "\\frac{E}{\\Delta} = \\cos\\!\\Bigl(\\pi n - \\frac{\\phi}{2}\\Bigr)\n", " = (-1)^n \\cos\\!\\frac{\\phi}{2}.\n", "$$\n", "\n", "Even and odd $n$ simply correspond to the two branches of the spectrum,\n", "so we can write the Andreev bound state energies as\n", "$$\n", "E_\\pm(\\phi) = \\pm \\Delta \\cos\\frac{\\phi}{2}.\n", "$$\n", "\n", "This is the dispersion of Andreev bound states in a short,\n", "perfectly transmitting Josephson junction\n" ] }, { "cell_type": "code", "execution_count": 16, "id": "b5531e4d", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lat1d = kwant.lattice.chain(norbs=2)\n", "\n", "def make_sns_1d(phi,\n", " LS=4, # SC Left\n", " LW=1, # Central region\n", " RS=4, # SC Right\n", " mu=0.0, Delta=0.1, t=1.0):\n", " \"\"\"\n", " SNS 1D finito (sin leads):\n", " - onsite normal: -mu * tau_z\n", " - hopping: -t * tau_z\n", " - SC izquierda: Delta * e^{-i phi/2}\n", " - SC derecha: Delta * e^{+i phi/2}\n", " \"\"\"\n", " syst = kwant.Builder()\n", "\n", " Ltot = LS + LW + RS\n", "\n", " for x in range(Ltot):\n", " # S1: x < LS\n", " if x < LS:\n", " Δ = Delta * np.exp(-0.5j * phi)\n", " onsite = -mu * tau_z + (Δ.real * tau_x - Δ.imag * tau_y)\n", " # N: LS <= x < LS+LW\n", " elif LS <= x < LS + LW:\n", " onsite = -mu * tau_z\n", " # S2: x >= LS+LW\n", " else:\n", " Δ = Delta * np.exp(+0.5j * phi)\n", " onsite = -mu * tau_z + (Δ.real * tau_x - Δ.imag * tau_y)\n", "\n", " syst[lat1d(x)] = onsite\n", "\n", " # Hoppings 1D (vecinos a distancia 1)\n", " syst[lat1d.neighbors()] = -t * tau_z\n", "\n", " return syst.finalized()\n", "\n", "syst_test = make_sns_1d(0.0)\n", "kwant.plot(syst_test)\n", "plt.show()\n", "\n", "make_sns_1d(0.0)" ] }, { "cell_type": "code", "execution_count": 17, "id": "946784b7", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import scipy.sparse.linalg as sla\n", "\n", "Delta = 0.1\n", "t = 1.0\n", "mu = 0.0\n", "LS, LW, RS = 100, 1, 100\n", "\n", "phi_list = np.linspace(-2*np.pi, 2*np.pi, 101)\n", "E_num = np.full_like(phi_list, np.nan, dtype=float)\n", "\n", "k_eigs = 12 # nº de autovalores alrededor de 0\n", "\n", "for i, phi in enumerate(phi_list):\n", " syst_f = make_sns_1d(phi, LS=LS, LW=LW, RS=RS,\n", " mu=mu, Delta=Delta, t=t)\n", "\n", " H = syst_f.hamiltonian_submatrix(sparse=True)\n", " evals, evecs = sla.eigsh(H, k=k_eigs, sigma=0.0)\n", " evals = np.real(evals)\n", "\n", " # ordenamos por |E| y tomamos el más cercano a 0\n", " evals_sorted = sorted(evals, key=lambda E: abs(E))\n", " E_closest = evals_sorted[0]\n", "\n", " E_num[i] = abs(E_closest)\n", "\n", "E_analytic_abs = np.abs(Delta * np.cos(phi_list / 2.0))\n", "\n", "plt.figure(figsize=(5,4))\n", "plt.plot(phi_list, E_num, 'o', label='|E_num(φ)|')\n", "plt.plot(phi_list, E_analytic_abs, '-', label=r'$|\\Delta \\cos(\\phi/2)|$')\n", "plt.xlabel(r'$\\phi$')\n", "plt.ylabel(r'$|E(\\phi)|$')\n", "##plt.title('SNS 1D corto: ABS numérico vs analítico')\n", "plt.grid(True)\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "d511053d", "metadata": {}, "source": [ "### Phase dependent current\n" ] }, { "cell_type": "markdown", "id": "5d8839dc", "metadata": {}, "source": [ "In a Josephson junction the current is the rate of change of the number\n", "of Cooper pairs, $I = 2e\\, d\\langle N\\rangle/dt$, while the phase\n", "difference $\\phi$ is the variable conjugate to $N$. In a Josephson system, the phase $\\phi$ is\n", "canonically conjugate to the number of transferred pairs, which is\n", "encoded in the commutation relation\n", "$$\n", "[\\hat \\phi, \\hat N_R] = 2i,\n", "$$\n", "(up to conventions for factors of 2). This implies that the dependence\n", "of the Hamiltonian on $\\phi$ is equivalent to coupling to the number\n", "operator. One can then rewrite the commutator as a derivative with\n", "respect to $\\phi$:\n", "$$\n", "[\\hat H(\\phi), \\hat N_R]\n", "= -\\,2i\\,\\frac{\\partial \\hat H(\\phi)}{\\partial \\phi}.\n", "$$\n", "Combining this with the Heisenberg equation gives\n", "$$\n", "\\hat I = 2e\\,\\frac{d\\hat N}{dt}\n", " = -\\frac{2e}{\\hbar}\\frac{\\partial \\hat H}{\\partial \\phi},\n", "$$\n", "so that for an eigenstate with energy $E(\\phi)$ one obtains\n", "$$\n", "I(\\phi) = -\\frac{2e}{\\hbar}\\frac{\\partial E(\\phi)}{\\partial \\phi}.\n", "$$\n", "Experimentally, the AC Josephson relation $d\\phi/dt = 2eV/\\hbar$\n", "confirms this conjugate nature of phase and particle number:\n", "a DC voltage $V$ makes the phase wind linearly in time, and the\n", "resulting time-dependent current $I(\\phi(t))$ is the measurable\n", "signature of the transfer of Cooper pairs." ] }, { "cell_type": "markdown", "id": "bfb7a26c", "metadata": {}, "source": [ "In thermal equilibrium, the supercurrent in a short Josephson junction\n", "can be expressed in terms of the phase-dependent Andreev bound state (ABS)\n", "energies $E_n(\\phi)$ as\n", "$$\n", "I(\\phi) = -\\frac{2e}{\\hbar}\\sum_n\n", "\\frac{\\partial E_n(\\phi)}{\\partial \\phi}\\, f\\!\\bigl(E_n(\\phi)\\bigr),\n", "$$\n", "where $f(E)$ is the Fermi-Dirac distribution and the factor $2e$ reflects\n", "the charge of a Cooper pair.\n", "\n", "For a single perfectly transparent channel ($T=1$) in a short junction,\n", "the ABS spectrum is\n", "$$\n", "E_\\pm(\\phi) = \\pm \\Delta \\cos\\frac{\\phi}{2}.\n", "$$\n", "At zero temperature, only the lower branch $E_-(\\phi)$ is occupied\n", "($f(E_-) = 1$, $f(E_+) = 0$). The current is then entirely carried by this\n", "state:\n", "$$\n", "I(\\phi) = -\\frac{2e}{\\hbar}\\,\\frac{\\partial E_-(\\phi)}{\\partial \\phi}\n", " = -\\frac{2e}{\\hbar}\\,\\frac{\\partial}{\\partial \\phi}\n", " \\bigl[-\\Delta \\cos(\\phi/2)\\bigr].\n", "$$\n", "Taking the derivative, we obtain\n", "$$\n", "I(\\phi) = \\frac{e\\Delta}{\\hbar}\\,\\sin\\frac{\\phi}{2}.\n", "$$\n", "\n", "This expression is valid for the short-junction limit\n", "and for the phase interval where the branch $E_-(\\phi)$ is the\n", "ground state (typically $0 < \\phi < \\pi$). More generally, one\n", "must account for the $2\\pi$-periodicity and the possibility of\n", "level crossings, which leads to a current-phase relation with\n", "a cusp at $\\phi = \\pi$." ] }, { "attachments": { "image.png": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnQAAAJKCAYAAAClGdgSAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAH3qSURBVHhe7d1dcqpA1zf8lbfuw6cK9ggkI4CMAByBZATgCCQjEEcgOb+rxBEERyCOQKx6zsURBM+fKt+DK3A1DSoq3/x/VVbtoMlOtOlevfrr7XK5XAgAAAAAOuv/4y8AAAAAQLcgoAMAAADoOAR0PRVFEem6Tpqm8U8BAABAz7xhDl3/BEFAmqbR+XwmQRAoiiL+JQAAANAjyND1jOM4STBHRHQ+nykMQ/5lAAAA0CMI6HogCAKyLIskSaKvr68kmIshoAMAAOg3BHQ94Ps+fX9/0+l04p8CAACAAUBA1wOWZdFqtaLJZEKCIPBPAwAAQM9hUUTPRFFEkiSlhl232y1WuwIAAPQYMnQ9I4oiKYqSuhYEQeprAAAA6BcEdAOAbUsAAAD6DUOuPWRZFn1/fydfz+dzsm079ZoyxKtrnxEEQWY1LgAAQJvJskyiKPKXK6UoCjmOw1/OQEDXQ7Zt02KxSL6uKqDzfZ/G4zHJslyosJUtCAJkHxsShmFl2+GEYYgV2wAAf1RVJd/3+csZCOh6qO6ArmhhA7gnb1FPbDQaERElwd5oNCJd10mSpMy8UYCioigi0zRzyxxvuVyirEFpbNum3W7HX6bRaESKotBmsyF6IKCjC/TOfD6/EFHy+Pn54V9Siu12eyGii6qq/FMAD/v9/b3Ispwqu0R0kWX5slqtLheubM/nc/5HADzkWpkTBOGyXC4vv7+/qevb7Zb/EQBPMQzjarm7MO0rPdDGYlHEANQ93g/wqCiKSNM0OhwOybXRaETb7ZaCICDTNFOvByiDaZqpMkdEZBgGhWFIlmWh7oRKmKZJ6/U6dW02myXljv7mzT0KAR0ANM6yrFTDahgGBUGQ2T+R/xrgWaZpJkNaRESCINDPzw+5rotADiqj63oqmIvLneM4qXLH/rtovYeADgAaZVlWqoKbzWZoVKFSfIZEVVUKw5B0XU+9DqBMfCei7HKHgA4AGuO6bmqLndVq1ciKaRgO13VTwZxhGOT7PjoQUCm+47pcLksvdwjoAKAR/D6Gs9kMc+WgUq7r0nQ6Tb42DINc1029BqBsfMfVMIyn93C9BQFdD7HpW1VVC4+/A9QliiLSdT3ZKqKpvQxhOPgOhKqqCOagcp7npToRk8mksnKHgK6HFEWhy+VCx+Ox2N41ADXTdT3ZT04QBJRTqBy715wgCOR5Hv8SgFLFexzGRqNRZcEcIaDrN0mS+EsAjeM30yx7HgkAj19F7XkeyhxUjt+wuupyh4AOAGoTBEHqFBPsvA9V8zwvc7Y1pqFA1TzPS61onc/nldd1COgAoDbsHKbJZFLJxGCAWBRFqTImy3IlxyACsMIwTA211lXuENABQC0cx0mGWgVBqHQuCQD9lbl4rmb8NUDV+KHWV+u6osO0COgAoHJhGKZ6qDhWCaoWhmFqeH82m2GoFSrHdlyppKHWot+PgA4AKmdZVtJjHY1GtQw/wLCxQ16CIKDMQeWiKEqVs9FoVOu0EgR0AFApfnLwq8MPAPf4vp/KkvDnZAJUwbbt1FBr3eUOAR0AVIpfCIFhL6gam51TVRUnkEDlwjBMraZWVbW0M1qLQkAHAJVxXTe1gTAmpUPVbNvGQgioHd9paGIkAgEdAFSC3zLCsixsdg2VCsMwFcAZhlF4QjnAs/gh/vl83khdh4AOACrhOA4WQkCt+DlMKHNQB/54rzoXQrAQ0AFA6aIoSmVK0LBC1cIwpPV6nXxtGEYjWRIYFnZaCZW4EOKZ860R0AFA6fjsHD+/BKBsfKeB/xqgCmw5a2IhBAsBHQCUip/HhGAOqobsHDSBz8413YlAQAcApWLnMQmC0Nh8EhgOfkVh0w0rDAOfnWt6SyYEdABQmiiKyPO85Osqj/hquvKEduDnayI7B3XwPK+27FzR8oyADgBKw86dQ3YO6sCWOaq4YQWIsZ2IqrNzCOgAoHZsJVdldg4gxg63IjsHdeD3nWtLJwIBHTwtiiL+EgyY67rIzkGt+EnpKHNQh7bNnYshoIOnBUHAX4IBYys5ZOegDnzDilMhoGphGLYyO0cI6ACgDPwE4aoyJehEQIzPzrWpYYX+Yof425SdIwR0AFAGfpVhVdk5DPNDjG1YR6NRqxpW6C+23LWtE4GADgBeEgRBaggCGwlD1fgy17aGFfrJ9/0kK9zGTgQCOgB4CZuda2MlB/3Dlzl0IqAObHauqmklr0BABwBPi6IodeQSMiVQNX7zagRzUAe+rmtjuUNABwBPY3usgiA0ejA1DIPneamNhNuYKYH+YTsRVc4TfgUCOgB4Gjv0pet6Kys56Bd+I2GUOagDW9e1MTtHCOgA4FlBEGDbCKgVvwdYWxtW6JcwDOlwOBC1fJ4wAjoAeAp/liGOXIKq8Ysh2tqwQr/wRxq2FQI6AHgYJqZDE9q+yhD6qSt1HQI6AHgYOzEd20ZAHfjFEChzUAd2aslkMmn1nE0EdADwsC5MEIZ+wWIIaAJb7tq+ih8BHQA8JAiCZIIwIaCDGoRhSJvNJvkaZQ7qwg63IqADgF7BYgioG85thSaww62qqrY+K4yADgAe0pUJwtAfWAwBTeD32Ww7BHQAUBg/Mb0LlRx0G3sgOqHMQY2aHG4NgoC/dBcCOgAoDBPToW5smZtMJhjih1qwnVdZlmsvd1EU8ZfuQkAHL0OjPgxRFKUmptfdY4VhajJLAsPVxaklCOjgZYqi8Jegh9gKbjQaoXGFyrFZEkEQOtOwQvd1sSOBgA4ACuliBQfdhjIHTWh6uPVZCOgA4C7sAwZN6OKwF3RfVzsSCOgA4C62gpNlGcPsUDk2S4K956BOCOgAoLfYlYbIlEAdutqoQrfxHYmmO6+j0Yi/dBUCOgC4KQzD1FFfaFyhDmxAh82EoS5t60g8Mn8PAR0A3IR9wKBuXZ2UDt3n+37y766NRiCgA4Cb2ICuDT1W6D8shoAmsGe3tmG49VEI6ADgKraCIwR0UJO2DXvFsDCj39pa7opCQAcAV7HDD5PJBKeCQOUw3ApNYQO6LgbvCOjgac+cNQfdguFWqBuGW6EJ7OIvQRA6Wd8hoIOnBUHAX4Ieafvq1q7Nb4Fiup4lgW7q+nArIaADgGvaONzK/k5t+H2gXG3bAwyGg61bENABQK/0occK3YIyB02Ioig52rCrw62EgA4A8rAVHKFxhZpg/hw0oS8dCQR0AJDBVnBtGW6FfsNwKzSFHW7t8rxNBHQAkNGH+STQLX3JkkD39KXsIaADgIy+VHDQHShz0ATf95PMcNdHIxDQAUAKv7Frlys46Aa2zAmC0OlhL+iWPnUkENABQEqXD6eGbupTowrd0qeyh4AOAFL6VMFBN6DMQRPYs6pVVe38aAQCOgBIsBUcztGEOvDDrQjooC5tXvz1zNGaCOjgZdheoD+wDxjUrc2NKvRbm8+qfuZoTQR08LKup6nhvzD0BXVDmYMmsGdVj0ajXoxGIKADACKugsNwK9QhDMNkiJ86vqkrdEsfM8MI6ACAiMuUoGGFOrBlrut7gEG39DEzjIAOAIiwXQk0oI+NKnRDfFZ1n/Y9REAHABRFUaqCw0IXqFoURbTb7ZKvEdBBXfrakUBABwC9reCgvdiMMIZboU59nV6CgA4AejlBGNoNnQhoSl/LHgI6ACjcYw3DkBzHIU3T6O3tDXPt4GlsJ+JWmcsTBAGFYchfBrgrCIJkI+s+nA7BQkAHMHDsTv3XKrgoisg0TXp/f6evr69k7hMCOngGu13Jo1vkuK5LHx8f9P7+ToqipDaHBbjnkc2EXdclXddJURR6e3sjURRJ07Ray9wj9wYCOoCBuzfcGkURaZpG6/U6dX02mz2cWQEgbhf8vDJ3C3sk0uFwoOl0io4FFFZ0uFXTNJpOp7TZbJL9Oc/nM+12u6dOcXgWAjoAKOxeBec4TlKhxVarFTmOk7oWcxyHbNt+6ixCGIZ7w62WZdHb21uqbLLPbbdbUlU1ubZer3PLLgCLzQzfOh3C9/3UCuzRaESqqpKqqjSZTMi27dTr2wIBHcCABUFwt4JjG19BEGi1Wt3MiHieR4vForWVHjSPzXDwAZ1t2/T9/U104zxLTdPI930yDCO5ttlsrnYyAKhA5zWmKAqpqkqj0YhWqxWFYUi+75Pv++R5Xu60lDZAQAcwYI/MJ1FVlYIguBnMETNE8P39nQoGAWJx9oPNstFf52GxWCRf39sP0XXdVFCXl9EDiLHl41Y9Jooi+b5PYRjefF3bIKADGLB78+fobwh1tVqR7/u5GTwem5kzTRNDr5Bybbg1XngTk2X5aplkOY5Ds9mMvwyQwm5kXfbm6W2p4xDQwdPaUojhOWEYJnPjbh1/oyjKQ71USZKSzMvpdKp1RRi037WAzrbtZPif/gK1IkRRJMdx6HK5ICMMVxUdbn2UKIr0798/siyLf6p2COjgafxEeeiWaw1rGdgsHQI6YOWVuzAMk3lzhBXUUIFbe22GYfh0giKeT9eGKSYI6AAGqqoeK/1VmPEw2OFwuDq5HYYnHvaaTCbJNbYDMJlMCmfnAIq6Nr3Etm1SFIX+/fv3VOeTzzI3CQEdvKzIvCpon2sVXBAEpQRgtm2TIAhEBSa3wzBcy5LEWY75fP5Uowpwi+/7yebpsiwn5c22bVosFnQ+n0kQhKc6tmwQt9vtGi2/COjgZQjouudaBWeaJn18fDxVsfFEUaQgCGi73fJPPY3dGwq6J2+4lf7my10uF7Jtu5QtIeIVigB0ZTQi3l4pZlnWU2WPnTNMDa+0RkAHMEDXKrj4NIgyAjr6q+z4+SowXHFAV/YqQ954PCZFUUrJNEP38aMRURSlFjGMRqOXFjWwWbrNZvP0fLxXIaADGCA+U8JXcK9UbgB5oihKFlJVGczRX9b5fD6X1jGB7mLLXdyRcBwns6L6mexcTNO0VJauqY4EAjqAgWErOPqrjNgKTlVVDKND6dhORNUBXfzzsW0OXBuNiM1ms1ICf7acNTXcj4AOYGDYyizuVbKVUdMrtYoYjUb8JWg5NqB7JRtSBNtAI6AbNn40gpgtt2RZLq2+kySJVqsVTSaTUgLEZyCgAxgYvoLzPC/Jzk0mk8rmvLmuW9rcEmQQu4ctd47j0Nvb20MbVj9C1/VkhfVut3u63DW9rxi8jp8/R0S0XC5pMpmQ7/uldi5M0yztrNdnyiwCOoCB4beOiPf8EgShsmyG7/s0nU5JkqTGhiOgOfwwf7zCusqywAaLCMyGKQiCpLPKrua3LKu0wKsqz2zcj4AOYECCIEgaU/oL6CRJqqS3yop/7vl8riwrA+11LaCqqrwRAjq4kp3rMwR0AANybf6c53mVTlRXFCU1BIYGdliufd5VNrKKoiRlvKlVh9CsvAURfYaADmBA+OHWOrEVKo52GpYmAjr666xMJpPSJr5Dt7AbkVfZYeX5vt9IHYeADmAg+HlMVQ535WEb7yY334R68eUuZhhG5WVQkiTyPK/2zgs0jz+x4e3tjSRJqqXesSyLvr6+at/PEwEdwEDwFVzdK0U1TUuGXQnDYIORl50TBAFZM6hUXrk7nU611DtxR+X7+zv396gKAjp4iSzL/CVoKb5iMU2z1kZVFMXU/8f/PtBPeZ+zbdu1dyhgWPgObKyOoVc2I1xnHYuADl5S9ZAJlIdvWM/nc+pw6jpYlkU/Pz80mUyw2nUg2HI3mUzoeDzWPhQFwxKGYepor5ggCLW0Wez0kt1uV+n2PCwEdAADwO7HxGrixAVd18nzPGRoBoCfP+c4TiOfe3xW8bWsTREYjegOvvMaq3oRToxd1U83fp+yIaADGIBrFUpdFRwMExtAjUajRoI5+vs9vr+/yTTNp7MldWR2oBzXAvc6RwXYuvXZMvcoBHQAA9CGCg6Gh+1INBXMEdOgns/nWibFQ7PyOrCqqta62rnO/yuGgA6g56IoSu3HFBuNRrVMEIbhYhvWurIUedhyjoCu3/jTcGJ17wvHnif8Smfmke9FQFeDIAjIcRzSdZ1s2ybbtl+u3DzPI9M0SdO01MOyLLJtu7IzOaF78nqrVPPqKxgefmL66XRqLCPMDpdeux+gH/JGI2azWe2dV1EUKQgCWi6XL5X7RwI6ukBlfn9/L4ZhXIgo9zGbzS6/v7/8t921Wq0yPyvvsVwu+W8tFRFdVFXlL0PL5JVBWZb5l9Xq9/f3oqrqZbVa8U/dFP/+KHftt1wuM+WOGmxynvkdttstylzHyLKcquf2+z3/kk6I/4btdss/dRUydBWJoogURaH1es0/lYgn6T6qSGZFEITaeyTQTnxGQhCExjO4QRDQbrej6XT6crYa2okvd/S3bUlT2P8bw679xK+q1nV9UO0gArqKmKaZGm4YjUY0n88zS983m81Dlcu17ScEQSBVVWk+n9N2u6UwDBuZlAntwpcXQRDI9/1WVXJ1z22BeuQFdM90YMvClrOHhrGgM/LK3JAgoKtAGIa02WySr2VZpiAIyLZtCoKAZrNZ6vWPFEL+tfFGnVEUke/7ZNs2aZqGJfZAxJUXQRAoDMNWBHNsZ6PpbCGUL29i+mg0anSbHEmS6Hg80na7Rf3YU/z8ubYE7rquk67rlZ8ji4CuAnyhcl03VYE4jpPa0JUP0m7hXytJEvm+T77vV15YoHvY8qLreqsasvgeOJ/PGHbtGb4OpJZkYiVJwshFj+W1j22w2Wxos9lUfg8goKsAO4SqqmpuRoQdengkEOML7Pf3N02nUxqPx/Tv3z+SJAnH6kCCzRS3pXKLsQ0rArp+4espVVUbzc5B//HTS9qo6tEIBHQVYBuna71B9nrROXR5wxi80+lE39/fpCjKQ4Hio+Kffe3vg+blZUna5NlODbQfu+9hGxbhQP/xnQhqUSc23o/udDpV2nlFQFeBRz+we0FaLC/wEwQhMyePiOhwOFSa3o1/l8ViQW9vbzcfiqKk9sqzbRsNeA3yKrhbbNsmSZJIkqRKy05M07Rk5WFeFhu6ie9IuK57tWGNz/RF9g5exdd3TR41x2PrN/7+KBMCugoUSfvyAU2RIJBv9CaTCYVhSI7j0Ha7TR0GTDWkd4s6HA602+2Sh+u6mZsPyvdoxREPWZxOp9o+H8/z6Hg8tqbihdexZccwjJvBmuM4dDqdaLPZ1FbmoJ/Y6SWU016yfN8nURRJUZRCbe+r2N+Fb/vLhICuYtc+PD7bVqRBUxSFLpcLHY9Hulwu5HleMsld0zTyfT8V1J1Op8z/UwXDMJLfqcgjDMOblTy8jt+lvwjXdckwDJrNZpnOgOd5lWVWi5R96A42MLu3Z2Y8ZaPOY+jCMCRJkkgUxVoac6heXmfgVhsThiGdz2c6HA4Pd3yfUdfUJAR0FVBVNfl3XkGjG9dvib/nWgOoKEpmqKyKBpgXD9NBe+QF8vcqFVEUyXVdchwnsxrWNE1aLBaNLrjJ+5ugXfiNXe/VC7Zt0/F4pDAMM2XOsizSdb30z93zPDqdTnQ+n2tpzKF6eZ/jrYDONE2azWa5G/AHQUCmaeb+zGfVtQAMAV3FDodDJngLwzD3sPRbXNel8XhMb29vZJrm1UJxrwKFYeDLHCsIAhJFMQngHnGt3NWhjs4JvOZWIxhFEem6nnnNtTrr+/ubNpvNzYb5GWw5unWfQHfwn+NkMsl0EHiO41AURZmOrm3btF6v6fPzs7TOhCiKyaECfABZJgR0FeALCJ/VuDcMkYctBOv1mhRFyS1sfMG+V6ihn/hyQEwZ8jyPzucznc/nwgFdnPmtsjKC7ssrdzHXdWmz2dDn52ehjsF8Pie6EfA9i60T0UnovjAMU1lhQRBSI1WWZdHb2xtpmlbo82bLW5ntp2VZZBhGodNSivyeufjDXeF1Pz8/mQOpZ7PZ5cId9sweIMyaTCYXIroIgnD5+flJro9Go9T3CYKQOnh4v9+nnh+NRslzZWP/jvl8zj8NDfr9/c2Usbj8xc9PJpOLqqoPHfz8+/vLXyrFarUqVI5wUHr78XUUa7lcJtePx2PquWuqKHN8HXwLylz7xfVH/FitVslzfJvItpe3VFHuHsGWu0fqaGToKqDrembF6ff3NzmOkzt8wF4LgiBZrcNnUPhsyvl8Jl3XybZtsiwrkxnM+7+g//gsiSzLqR6rKIrkeR75vp8pM7eU2Vtlxdkafv4ndAu/EIc9DYeYeUvb7bZw1q2KMqdpWqp+fjobAq3A1neyLGcyYIIgJGepFx1hqKLc1QEBXUX44IuI6OvrK7PnnCAIqSHZWwVJ0zRarVapa6fTiRaLBX1/f6d+tizLTw3tQvfxQ/FVBEpRFJFt25ng8RlxmT+fz6X8PGjGvblxoiiS4zgPdSJ4QRAUGq69h230+fsFuoUtd3wSQ/nbYD8Mw0G0hwjoKqLrOq1Wq0ymjmUYRmZ1lyRJyeobWZYz8+9M06Sfn59M75c1mUzI/9tnB4aHDYpUVU3mjpQZLFmWRYvFgsbj8csZjro23YRq8eXrlcAtj+M49PHxUTjLcott26SqKgmCgHqywwLu9KQyygYvDMObCxHbBAFdheJCsFwuaT6fk6qqNJvNaLVa0fF4JNd1cyuTePVNEAS5laKu6xSGIf38/NB8Pk8eq9WKfn9/U/vTwfCwK6jjHqtpmjQejzMdhGex2ZcyKzpkS7qLD+jibZT4rMmzvr6+iB44WecWURTJ932KoqiSIADqwXcA+axwGXzfp/V6XVqGLwzD6uo5flIdQBFYFNFO/ITveBJwPFmdX4DzrN/f34uqqqnFFs9iF3HcmniOCertxU8+FwQh9bmyE9WfNZlMLoIg1FrfoMy1m6qqqXIX10uyLBdeAHFPvIhsMpnwTz1FEIS79wQWRQBAbpaEmOGvvIzvM+IMRxnz80RRTKYQlJntg/rw5Y4foirjc/U8L5m7CUDcaMRoNCLXdWm329HhcCitnMSLyPhs4DN8308yzPw9UwYEdPCyKtLc8JxrlYTjOPTz81NaJVc2DHt1GzuENBqNyLZtUhSFZrMZjUaj0joSADG+rpMkiTRNI1mWaTQalTbUX5UyOjk8BHTwMgR07XFtboYoiqTremvnVsYNPgK7bmIbV3ZusOM4FIYhAjooHV/XKYqSbLgfL2Ros0dPiyoCAR1AT/ArvqimPbaiKErO8+Ur2aJ0XafJZNLaDCJcx+4/J8tyLcFbvGDs1Q6A67o3MyV13D/wHD5DV3VnNQzDZCHNs6r+HRHQAfQEX8FRiXPmbnEch06nE51Op6cDMkmSyPO8lxtoqB9b7uoY5oqiiD4+Pl7OcHieR9PpNNmrLM+zHRSoHl/fVT1SZFkWjcdjkiQp838XpShKaiuzZ3/ONQjoAHoir3I4HA6518uk6zqpqkqqqpa2LQp0B1++NE17KVt7jyiKpKoq0YsBZJwt4U/kgfbLG424l219VVzWzufz1Q5AEWwn+5WfkwcBHUBPXGtAq6zk6K/X6fs++Q8eJQb9wAZ0i8WCdrsdnU6nUlYFXuP7Pq1Wq6czwjwEdN3CdyLob05alR1K0zRpv9/Tdrt9qSPB/o7X6mzWI6MWlQd08biz7/uFfnkAeBw7jykmCALNZrPWTw6G7rpW7iaTyUuNXhGvlmt2PtPhcEg9B+2WF9DVQVGUlzutmqbRz89P4XvkkXl3pQd0YRgmu4O/vb3R+/s7jcdjGo/H9PHxQW9vb6RpGtm2jQAPoCT8vTSZTCiKolL2iatL+HfeYtUZRSgP37DKskxRFHViPiQ/nwnlrjvYcjefz2m73dJ2u+1MfafreiX3SCkBXRzEKYpC7+/v9PX1RZvNhn9ZYrfb0WKxoI+PD5IkiUzTrDQ9D9B3fMPaxBBSHEC6rvvU3BDXdWmxWNycpA7twpe7Koe8rvH/Nrh+JiBjG9Rnvh/qx86fi1fGa5qWzN2si+M4rYtbng7o4sqbDeKeSVufTidar9f0+flJoiiihw7wBD5D14QgCOjr64um0+lLPeXz+Xx3btSrwx5QDj6gq7NBjem6Tl9fX3fLTB62HDXxu8Pj2DJXdoarKNu26evriz4/P/mnGvVwQBcfvSJJ0tNB3DXn85kWiwW9v79njo4BgOv4LRyayJQoivLSEV5s48oHCtA+efPnuiYuc7IsI6DrCLZueHY04FXs7/BMXVeVhwK6OJBbLBaZJcNlW6/X9P7+3kjDBNAlecHPer3OvV4lURQpCIJSVh+W2VGEauSVryYyxZZlkSAIT7UVmqbRcrls3dAZXMeWu9PpRJqm1R5UlZHZDYKAbNsuNSAtFNBFUUSapj0UyMX7UqmqSpPJhAzDSF1jJ6Pe8v39TcrfcR4AkJV3b6iq2shwhCiKZJrmU5UcP4ya93dBe+QFdGU2TkXFjeKz5d2yrKfKK9Qvb/+5w+FQe7mzbZuWyyX9/PzwTxUWx1RlzncuFNBZlpUZ0omNRiOaz+f08/NDv7+/dLlc6HK5kP+3VYnv++R5Hrmum7oWRVHy2u12S/P5PNksknc4HEjTtNo/NIAuYBvWyWSS3H+PLHdvC7ajh/u93fICOoAq5ZW5yWTydDD/CsuyCm07kocNTMvMDhcK6NbrNX+JDMOg7XabbDXwysHf8TYmvu/T8XgkwzAyGbzz+Ywee0s9+7lDOdj7oomKrUzs749y1V78/LnZbEbH4/HlveEAbuFjAEEQSs1w1aWqzmqhgC4mCAIZhkHH45Fc180MkZRBkqTkCI/5fJ4J7KAd2DkLXQ8iuoxvWNsi7ug9OreFLUsoV+3FZkpkWSbHcUiSpEaHLoMgIF3XO9nAQzF8hs5xnM53/K6Nfj6jUEB3PB5pu91SFEXkum4tN228hUkURbTf7+nn56eSABKe82hDDdXge6xtuUfiPeXe398fKivx3JTtdss/BS3Clru2lDld12mz2dB0On2ozAVBQJqmIRBsOb7zKstyKzLCnuc93JGoqrNaKKCTJKnRm1ZRlKfHqgH6jA/o2oKtsPhe9S2iKJJlWY3WN3Af+5m2pQyyZeaRgM7zPNrtdg8HglAvvh5pSx1hmiZtNpuHVvaLophs8UQ5f9uzCgV0ANBOZVUEZdN1nbbbLa1WK3TGeiaKotS2MrvdrhVBneu69PPzQ6vV6qHGnn1tW+8nyH42bRpqFQTh4c3Un9lm5x4EdAAdxs6/EAShslT+MzRNI9M0W1Xxwuv4hrVNdF1/aRiuzBWHUC6+3LWlXgnDMJm/+QjTNK+uEeD/1qIQ0AF0FJ8VsSyrNZUc9Bff2DS1bURZ2HuG/9v4r6EZ/Pw5QRBeCtzLJIriU+sK2I3YH8ko34KADqCj+MamLRUc9Btb7rq6bQSLDUb5TWuhHfi6znXdXnReJUkqtd6uJKAL/o600HWdFEWht7e35KFpGvm+nyy0eHTcGQD+g83QGYbxVC+xamEYkqZppD1wPE98xGAVc0zgdez8uTZuGxFvqfXIJHV26KtoOYX6sAGdYRgPD2/WIY57qtpjrohSA7ooikjXdfr4+KDFYkGbzSb3TEbf9+l0OtFut6Ovry9SFAU3EcCD2EqujcEc/TWuu92Odrtd4UyO67p0Op3o+/u70coRsvhMSRvLnW3btNvtaLFYZKYlXMNm6dAWtU8X6jrt7yivJoPN0gK6+LzXzWbDP5XBfyCHw4EURUHlDVBQFEWpOSVlzcEoG/t7Ff0d2fqhaIMM9eADujZ6Zj4f3yZBe/Dz59oqHq4vc6PgR5UW0Om6npuNy6PremZ1x/l8LnUsGaDP+Ia1bcNeMU3T6Hg80vF4LBzQsX8LArp26cLn4bpucr540eDOtm2SZZlGoxGCu5bh67q2Jn5kWSYiunomfR1KCejiYRWWLMu0XC5T1+iv9ySKYu7wy2azwbJxgAL4hrVow9WER4+EYgM/DH+1C9u4jkajwkF6neJThh4Z+pIkiYIgoDAMHyqrUD0+oOPrvrYIgoD2+33m970liqIkJiqjrisloOMXNgiCQL7vk2VZmWg17n3ruk6GYaSeI+wDBFAIv9KwT9iGmK28y6jw4HlBEKRWgT4SMAE8iw/g2joaQU90rIMgoMPhQOfzOTfJ9ahSAjp+qJXdD+tWb8d13SRNGVuv16mvod36Fkx0BZsRf7QSaTtJkjIdQUJA1zi+YcUqZKgafyrJZDIpJfBpC/6eetXLAV3eL8Sm4W8FdISMXOf1LZjogrx7ru1830824CwSmDmOQ4IgFHot1IPNCsuyfLdub1oUReS6bifvF/gPfviyK5unP1NvPfM9vJcDurwJio/Mq5AkKZOlA4Dr+ErukfutKa7r0vl8ptPpVKiHHa96L6OSg3Kw5a4L2TnLsmg6ndLHxwf/1FV57Rk0h6/r2t6JoL+pCO/v74XukbK3y3k5oMuLlh+5KfiUKgDcxmcc8u7BtonPLRyNRljN3kH8NjldaFhjRaeF+L5P//79I0mSHmrDoDpdC+jCMEy2bitShti/p4x6/OWATlGUzA1zaxiV/4D4KHY0GqW+BoA0/h7qQoZO07Qk49b2Shmy+DLHf91GruvSz89PpgN0Tfw3nU6n5HuKfi+Uj0/2dGEkT5IkmkwmZBhGZrFoHrYuLGP60ssBHeU0KJZlJelDPriLJ3NHUUSmaWYWQaD3DnAdnymhkioCgFv4wKaMbEIddF0v3IHg/0biznYt+nOgHHynoSv1nOd5D501GweqRV9/SykBHZ9lO5/PpCgK2badO5yq6zppmpYJ5ggBHcBNfCWXtxoUoGz8Njl9rKfvbWiNgK5e7GcgCMJDZ/N2ieM4pKpqKfdUKQGdpmmZPeXO5zMtFovUtdi1M16XyyVuGoAb+IYGe4FBHdhtcrqy0vBRbNtTZP4TVItfhNPX2EDTNPL/dgGI8fV8UaUEdPQXZb4yxm0YRibTBwBpfIauawGd67r09vZW6F6PA4cyVn/B8/gyV0YmoU5BEJBt25npPzx2SK+PAWvXsJ0IflpXF0RRlLl3inq2Q1FaQCeKIvm+T5PJhH/qrtlsVmgCIcDQsZVcF8+djBvV7+/vu5VW8HcyAeqGZrHZgi6WOdu2abFY0OfnJ/9UChvEdWW+Vl/xGaqulTn6+53H43GtHaDSAjr6uyE8z6PVapVZ+ZpnNBrRdrslx3HQIwK4g6/kupadI6ahlGX57j0fB3zP9nKhHOz738UyFwcDgiDc7ESwOzZ0MYDoE/6e79rnEXdGKedvecSju36UGtDFTNOkMAzp5+eHDMMgQRBIlmVSVZVUVaXZbEb7/Z7CMOxkKhWgCXzF0MV7x7Is2m63meA0TzzPNm++LdSHLXddzFzZtk2TyeRu4kAURXJdlwzD6FwA0Tdsmeviwi9FUWg+n5Oqqi+NMDxaDisJ6Ojv5tB1nVzXpSiKKAgC8n2ffN8nx3E6WTEANIkPgrqYLRFFsXAg+sqcXChHGIaprTuKfnZtEo8cFRn6itssaBZb1z0a1LSFbdvk+36hejqOjV5VWUAHAOViK7ln5qp2DZtNKaOyg8ex73sX589B94Rh2NlTSZ41Ho9pPB6/lM0jBHTwqltDGFAeftf0IWS42bI1hEq9jbo+3Ardw3feupgVfta9ldj3IKCDl6CSrwc/3Nr1Si4MQ3Ic5+YkdXaoAgFdM9hy1+UyF0URua770HAqf89BPfj3vev3vud5mSD1GnYXg2cgoIOnYG+wevEVQpcbV/pbHPH19XXz79B1nQRBGMTwchvxWeFbn1XbBUFA0+mUptNp4WGtW50NqE6fhvnDMKTPz0/Sdf1meSpr4cdDAV0YhmTbNjmOgwZ94PD516vrq754tm2TYRg3g4R4MnvRBhjKxWZKBEHodDZeUZRkCwg+A8SKoqjQJsRQjT51IohpJ8/n881yx+I77494KKBTFIUWiwV9fX3R+/s7KYryUAobAJ7Tl6GvWFx33AvWNE3rdA+9y/o0fy7e+H4+n988E9RxnGQTYnRa68cHPV2v69h9N2/dQ2X9nYUDOn75Ov3tDzWdTkkURbIsCzcAQAXYTSqpB40rdAMb0JXV4DRJkiSybftmB4G9t+51NqB8fHaq6+VOFEW6XC4UBMHNBYR8mXx2Ll3hgE6SJJrP5/xlor904vf3N72/v5OmacjaAZSob71W6Iaun6X5DLbRxYbW9evT/LlHlPV3Fg7o6G/ey3a7vTmHZ7fb0XQ6TXpDyNoBvIat5IocmQXwqqF2IspqWOE5fZtaUpSmabRcLmk+n780AvNQQEd//7Hv+7Tf78kwDP7pxOl0osViQe/v76TrOiaZAjypz5WcruskiuLVFWCe55Ft2xRFETqHNeI7EX0SBEEmYI0hoGsOP7Wkb3XdPZZlkW3bL3XYHw7oYvGk5t/fX5rP58mhxnk2mw19fn6SJEl3954CgP/iV3290ntrmzAMabPZ3FwBZlkWLRYL0jQNAV2N+jZ/Lub7Pn18fNDHx8fVJEPfAtiu6Nv8OZZlWaTreuZvLNvTAV1MFMWkB71arW4Ox55OJ/r6+iJJkrCIAqAAPtDpUyUnSdLN+oL+6gz6m8/EvxdQnb5mhdkG9VpAhyxdM9gy16f5c1EU0ff3N202m8rXF7wc0LFM0yTf9+l4PNJsNruatWMXUcTfAwBZfZ8k7Hkebbfbq0EDmy3hV9lDNfizNPuUFbYsi5bLJa1Wq6urWK+VRahWX7PCoijSz88PGYZBlmXxT5eq1IAuxg6t3svarddrGo/HpGkaeuAAnL5WcjFRFG/+Xa/MJ4Hn9DVTQn/lybIsMk3zatmyLItWqxWGXmvEdyJu1QldpOs6ua5bqHP0ShxUSUDHKpq12+129PHxcbXXBDBEfR36KmqIf3PT+t6JKMI0zatDslA+PogZarl7dQFp5QFdjM3axenHvODu6+sr8+ECDBG/6qtI765vhlqxN4kN6IZY5mJ9yky2Xd+nlhTh+z5tNhtaLBb8U4XVFtCx4vQjG9yx6W0slgBI91q7fpbmLb7vk67rpOs6/xRpmpacwQn16NNZmteEYVho/jbKXj2GMhIRRRE5jpN7/FwZu380EtCx4uAuCAK6XC50uVxyK3aAoRnK0JfjOLTZbGiz2eRWapiGUR+2zPW5E+G6bjJ/+1YCgZ3XBdUZyqkkmqbR19dXbkeijJHJxgM6AMg3lF5rPDl9Pp/nTlTXdZ222y0mqddgKMOt7P10rSHNa3ShfPz73Ne6zvf9yo+TQ0AH0EJ93lCY57ouXS6X3GGImKZplS/5h+FkhTVNo+PxSPv9PndEKAiC3OtQvqHMn2PrcNM0U8+VBQEdQAvxWYM+N65F9bWib5OhZIXprzxd6yh5nod9D2sylDIniiL9/v7Sfr/PDejKqN8Q0AG0ENtrvbWP45DkDcdCefhV1X1uXO/Jm8sJ1RhKVpj+6rBrnYhWB3S+75Pv+8mKDv4RPx8/bk1Mhfbq+w3YlCFVckWhjqgWW+aGPl+Rz5BDNdCJ+C9FUWg2m9FsNuOfKu7ypN/f38tyubyoqnohostkMkk9T0RPPSaTyeV4PKZ+FrRP/Llvt1v+KSiBIAjJPfHz88M/3Uvz+fyiqmpumToej5fJZJK8J/P5nH8JvMgwjOT9nc1m/NO9tN1uL5PJ5LJcLlPX4/qNfaDMlW+1WiXv72g04p8eLFmWL0R0UVWVf+qmpzJ0QRAky2/j5cZlpag3m81LOyUDdN1Qe62+79Nut8tMRrdtm97f32mz2aSuQ7mGlhX2PI/G4/HV7XKgekMrc/R3tNzb2xuJong11nl2esnDAZ3nefTx8XFz+S37IT1qNBplKnSAIeGHvp69ubvm2n2PodbqRVGU2nPt2jyfPhIEIVP2ypjPBPcNZUEEK67Pzudz6XXbQwFdEAS5qzPoRmX8iOVySWEY4maCQWMruSE1rJZl0eVyyWRLUB9UbyhbR7B0XU/KG3+fDeHvbxq/NdNQAjrHcWgymdBsNru6FRNfBxZVOKCLoog0Tctdyi3L8tVAj2UYBhmGwV9OYCIqwDCHIaBZKHNpZSQo4LYhdiLor7Pged7VE3D8FzYgLhzQOY6TG8xNJhPyfT81LJSXRhyNRuS6Lrmue3XXd8/zno5MAfqAH/pC44psSR2GmhW+RlEUnONasSEOt94TRRGNx2P+cmEPBXS85XJJnudl5vjkBWVspaxpGvm+nwnqzufz1UmCAEPA9loFQRhkMMNn6of4HtRtKGdpPgLlrlrICmfxdd+jCgV0vu9nsnOyLF8d/83r4fHXRFHMDRIR0MGQDb2SsyyLPj4+SBTFpGPIdxihXHwngq+r+y6KIjJNM9OYDvH+qxPbiRhamYv5vp9KgOWNbj6icEDHe/QDyHt93g2z2Wxe/qMAumrowxBxXcOuAMurO6A8bP0+xPfacRxar9ekaVru6BKUD52I/yzEGY/HqcQYH/s82pktFNDx/wk9ceNfa5zy5ink/X/QLviMqjH0Xqtt2zQajcgwjEH+/U0Yeicidj6fyXVd/jJUYOhzNl3XTRY+3OpEPPreVBLQ8XMPbs0FunYd2o2duA/l4DPhQ2xcdV2nMAwzDSvOs63O0If5TdMkWZZJlmW0RzUZepnTNI1kWabRaES2bfNPP61QQPcoSZJoNpuRqqo0m80yDdU9tyJWgL5ie60IYKAOYRgO8lQSliRJFAQBBUGQ2q7kVtICXjP0rLCiKBQEAYVhWGo5KxTQPTqOS3/zEnzfJ8dxHv6F8zKCAH039F4r1I8tc/yuA0P3TLsH94VhiK2Zrng0VuIVCujy/pOygi5+ZRHhA4aBGvrkdKgfOhFQN3Qirnt1yL9QQJd3o/NzXJ4RcIeQ098iCTRmMDQY+kqL97fM6/BBeYY+9BWLoohc10V5qwHKXBo7Z1hRFJrP5/xLCisc0AmCkLq22+0KHfd1S95kQBy5AkPE91qHPtzjum5q1WFZIwLwX/xZmkPuSLuuS9PplD4+Ph6e8w2PwUjEf4VhSO/v7zSdTpO67pW4qlBAR38bfvLW6zXpuv7wIoYwDEnXddpsNqnrgiDk/j8AfTf0Zfw8XddJVdWkcsOq6vKxDeuQztLMw2aKkKWrDt+JGHqGjj1IIY6jXrkPHwro+Cwd/W0ELEkSWZZ180aIoog8zyPLskhRlEwwR38Zu1f+GICuwlymNNM0yfd9UhQFGZOKYOjrvxRFoe12S/P5POlEICtcPrbMDb0TQUzwJgjCS5m5WOGAThRF8n0/N6g7n8/0/f2dHNmjaVrqIUkS/fv3jz4/P+n7+zszb47+tmlAdg6GCL3W29CwVgNDX2mappFt28l0B5S78qHMpem6TqvVioIgKGWaTeGAjv4+gLzzV1nn85l2u13qcW+4xDAMnOEKg8X2Wm9twj1UqBuqwZ5Kgk4E1AEjEVmmaZZW5z8U0NHff77f73Mzdc+Yz+fkum4p0SlAF6GSu87zvNzpGfAatswN8SxNaAbmClfr4YCO/j6IMAxpNps9HdgZhkH7/T53pSt0R1k9iyFDQJcvCIJS5pVAFhrWfPEWEo8u9IP7+G3KUNeV76mAjv7m1DmOQ2EY0nK5LHRUUXwU2PF4JNd1UZH0AAK616Fxzed5XtIAPNtxhHzoROSzbZum0ylpmoY5dCVjy1yReGFILMu6u7C0iKcDupgoimRZFvm+T5fLhfb7PW2329Rjv9/T5XIh/+8oMAQBAP+BXut17DQMLJgqF1a45ovbpsPhQP/3//5f/ml4ATqu17muS9/f33fXKNzzckDHUxQls8oVHx5APvRar7Msi1arFf38/CDoKBHO0rwuLnOr1Yr+z//5P/zT8AJkha8LgoDm8/nLWbrSAzoAKA6ZkttM08TpMSVjG1acpZkmiiKZpkmmaWIeXYmiKEIn4gZJksi2bVIU5aVyh4AOoEHYlwnqhk5EMezekPAatp4bjUbY1aIiCOgAGoJea3FsgwCvwdDXffG5mlAOlLniXqnrWhXQBUFAruuSaZqpOXimaZJt2y/9oQBtww99odeaz3EcWiwW/GV4An8qCbLCWUEQYBFOybAgopj4iNRntSKgC4KANE2jj48Pmk6ntF6vUydNrNdrWiwWNB6PSRRFsm37pXFmgDZAJVcM9qosD1vmcJZmPt/3c4+nhOfhVJJiFEV5aai/8YDOdV36+PhIfeC3nM9nWiwWJEnSoNPiQRCQbdukaRrpup7sCQjdgWGIYrAoojwoc/eZponFIiXiR9bQec3n+/7dY1LvaTSg832fptMpf7mQ8/lM0+l0kDvJ27ZNHx8ftFgsaLfb0Wazoa+vL1IU5aV0LdQLvdZiXNel0WjEX4YnYBHOfaIoDjpZUDY2K4ytmarVaECX1/OWZZkMw6D5fE7z+ZxWq1Xyb1VVMzvGr9frQQUxtm1fnU90Pp/p8/MTQ1QdwDasgiBg6OsOvD/lQCeiGEVRaDKZ8JfhCcgKF6NpGh2PRzIMg3+quEtDfn5+LkSUPGRZvhyPR/5luZbLZep7R6MR/5Je2u/3qb/71uPn54f/9lLF/w88hy3Dk8mEfxo4qqqmyvd8PudfAnew9YcgCPzTwJnP5yhzJRAEIXkPt9st/zTkkGX5qTLXWIaO3w3Z87zCvXDLsmg2myVfn06nQSyS4FdeybJM8/k8tyfJvxbaBb3WxxStG+A6DLc+Bvfl68IwTC0wQbkr5tn6rrGAjvXMkNPQCkYURanhktlsliyM8DwvE9QNJcjtKqxwfcyj9QNkYUNhqBu2ZnpcFEWZhFdRjQV0bCN2Pp8fOmolCILUIbZD2HmanyfIzz/MWxzybKGAauEsTWgCssJQN3RcHxOPVD672rWxgE7TtNQCh/V6TZIkkWma5Hke+b5Pvu9TGIbJvx3HSfarY/dq4YObPuIDOr5C7ntA2ydsw4pVX1AHdCIehwDkdehEPEYUxZf2QGwsoBNFMTPP63w+03q9ps/PTxqPxzQej+n9/T3599fXV2a/OlmWB7Gqk81e5u2RlFf5IEPXThj6grph64jHoZP8GpxK8jhN03Lb96IaC+jobwuOV5boyrJMrusO4sZjA9m8vzfvWtEh7Eexva6q/o8+w+R0qBvK3Ouwcftj2E6EIAgodwW9Ml+40YCO/jYNXa1Wmf3l7pnNZuT7PgoJ45XI/ln//v2jt7e3mw9d18m2bbJtm1zXTTUuQ8T2WpGhe87Qy9CjkBV+HQK6x2C49TmvxDSNB3T0N6E/DENaLpc3hwPibTqOxyM5jpOblRqCa1kx/gy4VyL9oiaTSbLx83a7TR6/v790uVzocrmQ53lJQGea5qBvbqz6giawGf5XGgyAopAVrl8rAjpi5tT5vk+XyyUVHOz3e7pcLsk2HXUEKm3GB27X1PE+WZaVBGuapiUPBCr5UMlB3dgyNxqNaqkXAJAVrl9rAjoeGxyg4fvPHAQW0v/dhGEIqBvKHNQtCILUak2Uu+LY9+rR2Ke1AR2k8R9skTlE/PdUoY7/o0/Qa30OskrPw15gUDd+agk859GRrlYFdMg6Xcc3aOzGypSzT11d87OuzeeDLLbX+szpKEOG9+p5yNBB3dBxbUbjAV0YhuQ4DimKgg/+Bn7PvsPhQK7rEv0FVfzzdb2XCMKLQyUHdWPP0sTWEa/Bvp7FoRPRjMYCOtd1Sdd1en9/p6+vLzocDk8fdzEEiqJk9uybTqdkmmbuUSF1nZ6BDF1xqOTKg8a1GCzCKc8rO/gPSRRFqfYI5a4+tQZ0YRiSZVkkiiJNp1PabDb8SwrNDRsq13VpMpmkrq3X60xFM5vNagsYbNtGUFcQGtfy8GUe8iErDHXDqurmVB7QRVFEruuSoij0/v5O39/fqIxf4HkeLZdLGo1G/FMkCAItl8vM/LoqHQ6H2rKBXcb3WtG4vg5ZuvuQFS5XPM0FrkPHtTmVBXRBECTDgdPptPDeaXCfZVkUhiHt93vabrf08/ND2+02dy5dHXa73SDO030FW8nd2jwbikOAch9OJSnXdDrFvOE7kBVuTqkBXRRF5DgOSZJEHx8fucOBUJ54IYmu643eOLIsI0t3BzIl5UOZuw1bR1QDAd1tOJWkOaUEdL7vk2ma9O/fP/r6+spM0H8E5tB1j23buHHvwF5g5UNgfBs6EeWbTCZ4L2/g22+8V/V6OqCL58ZJkkTj8ZjW6zX/kqtkWablcknH4zF3Lhh0CzIl97G9VlRy5cBk69sw9FUuVVUz+31CGlvmMLWkfg8HdPFK1XhuXNFs3Gg0otlsRsfjkYIgSH4GKuXuw+T02/ihrzo2fB4CBCm3YXJ6uVDe7kNWuFkPBXTxvnFFV6oKgkCGYdB2u002EEYA1z+apmH7khvQsJYPmf3b2A2FsXUE1AV1XbMKB3RBEOTuG3fNarWiMAzJdV1E6j13Pp9psVhgpesVGPoqnyRJFARBZs4O/Aca1vL5vp88IIvtRBDquqe98r4VDugURaGfn5/CPWPbtslxHKwI6rnRaESCIBBh6PUqNK7l+3//7//Rx8cHjcfjWvdd7AoMfZVvt9vReDym8XiMui4HW+ZGoxGmljSgcEBHf0OuQRBc3diWdTqdaLFY0Pv7O+m6jsmkPeW6bpKZw7BOVhAEOEuzAv/zP/+TdCRQt2QhK1wtBCtZKHPNeyigo7+CHG9su91uyTCMpGK9ZrPZ0OfnJ0mSRLZt38za4UbpHtM0aT6fY8g1Byq56vi+j3KXI4qi1IbC6ESUR1VV2m636LzmwEhE8x4O6FiappHruhRFEf38/NwN7opk7VAQukcURbJtG5VcDlRy1VEUhWzbRqDMwdYR1VBVlXzfR3nLwXci8B4146WAjqXrOrmuS2EY0mq1yhwiz4uzduz+XNA9mEtyG+YyQd1Q5qphmiZ/Cf6w7QCmljSntIAuJooimaZJnufR7+9voeAOuuvW8PnQRVGU2qcRjWt5kA2+DgFd+QRBwAbqN2Akoh1KD+hYbHB3PB5puVziTMGeYXtmlmWRrutY1v+HfR8w9FWuOKDzPO/q9I2hYu9JNK7lUBQlNb87nmoE/4FORDtUGtCxJEkiy7IoCAI6Ho80n8/vrpSF9oszdK7r0vf3N202G2wj8Qe91upEUURhGNLn5ydtNhuyLIt/ySCxq6pxKkk1XNel6XSKjB0Di7/aobaAjsWudt3v9zSbzRDcdVQ8pKhpGqmqSoZhkOu6/MsGCZVcdYIgIEmSkkVYGIL9D5S5arAdsjgbvNvtkKXjOhGEzmujGgnoWIqiJBsQ//z8oGLuoLhx9X2fXNdFVuAPu+AHjWs14noDQ67/gaxwNTzPywRvy+USdR1X5pAVblbjAR1L13UEdB3EV3SAXdPrIooi6bqO9/cPMnTVOJ1OybC+67q03+8xzP8HZa49WhXQQTfwW5VgEUQWJglD3di9wARBQOe4ZOv1muivE4Hs538hK9weCOjgYXxGDluXZKHXCnVDmSsXX88R6roMbM3ULgjo4GVsJRefGDH0rB16rfUKgmDw8+iQFS4XPxJBCOgy+KklyAo3q7SAznVdkiSJRFEcfGM+NGzj4fs+nU6nQW9dEoZhsuoLu6bXQ9d1+vz8zG2EhwKdiPrYtk1vb2+Dn0eHMtcupQV0YRjS6XSi8/mMbSsGxDCMVKUW/3vINzcyJdXjA7d42CdvmGwosKq6PnH5+/7+zpTFIcEwf7uUFtCxkJYeDsdxUisMdV2n4/FItm2nXjck6LVWj933iojoeDzS8XgcbKPCNqw4laR6juPQaDSi0Wg06HscnYh2qSSgg+HI2y5i6PMo0GutB9txlCRp0OUOWeF6SZJEYRgOOnnBT60acmDbFqUFdPyHC8Mw5CGuPOzWEYTGtVJDbkx5yArXY8idBh6ywu1TWkDHiqKIHMch27aTh6ZpuY+3t7fkoSgKKumOuTV/ZIjBHtuwopKrFuqK/0KGrnpYxZmGMtc+lQR0h8OBvr6+aLFYJI/dbpf74L9v6FsPdE3eatYwDJMhsKF9nmyAi0xJtfiALgxDMk1zcI0Lu6oaRy9VYzQaXe28DrHjSgjoavFoB6KSgO5RqqomB7ubpsk/DS222Wwyn5nnecmK56EFdKjk6sM3pIqi0Hq9vtrw9hWGW6t37Xg5y7Lo379/g3vf2U4EodxVphUBnaqqdLlcCj983ycfB7t31nq9Tm1Vo+t6sgKMD/b6Dqu+6sMGbmwD82gl2HXoRFTvWrsU13uHwyGTMe4ztswhK9wepQV0/PApDAvbuLIrwIbUwLCV3Gg0QiVXMfb9lSSJJpMJCYIwuC1zENA1x7IsEgSBZrPZoDoSWMnfTqUFdCx+KAT6b2jDXHlQydVHVdXM/E3P8yiKItJ1PXW9z8K/Dd3p71SSIQUVdbpWv9m2nSwCHBJ0ItqpkoCO3bYBhmFIww3XoJKrh6qq5Ps+gheUudrEU4JQz2W3ZsL8ufaoJKAjZm4BDAMaV0xOr8vQ5mXeglXV9TifzzSdThE0c2UOW7m0S2UB3XQ6JV3Xk2EQGB7P80jX9VSg01fspHxBENC4VuheAxJFEfm+P4h6Bxm6esXD27wgCAaTvUOZa6/KAjr629Li8/MzWdZtWRYCvJ7ib+woiujz85M2m80g5pegkqvPrfojiiKSJInG4zFZlsU/3Sv80BfKXT34DqrruvTx8UHv7++DCOowEtFepQV0giDwl1IOhwN9f38nAZ6maWTbdubmgO7J255EFEXabrdkGEbvG1ZCJVcr27avTukIgiDJlPb9c2DLHE4laQ77OVwrl32CrZnaq7SA7tHKc7fb0WKxoPF4TG9vb6Rp2uA2oe0DVVWTkyF4mqaR67qDuOmRoasWO2/ncDjQdDrNbTw1TaP5fE6r1ar3HQl0ItrBcRwyDINUVe39vc/eh5ha0j6lBXR8g/7z80Pz+ZxUVaXRaJR6Ls9ut6PPz08EdR3DZ+aGKIqi1NyavlfqTcgbZr2235xt24Mol+hENINv60RRJNd1yff93n8ObPvc97+1i0oL6PjecBRFyZBqGIb0+/tL2+2WlsslGYZxNcgbwhyEPuErtyHC0FczTqfTYKdsYP5cc4Zc5yEr3G6lBXSKopBhGMnX/ER4URRJ0zSyLCvZzycO8ubzOU0mE5rNZoPaFLQPipyG4Hle7vBYX6CSa85QAzp+64gi9yG8ZjQa0XK55C8PCubPtVtpAR39BXGyLBMVPNsuDvJs2ybP88hxnEH3frpIUZQkC5vHdV36/Pyk6XSaCfL7AkNfzbm2g7/neWTb9tVy2XUoc/ULgiAzEsXyfb/XC/34vwvlrn1KDehEUSTf95Ogrs9ZGfjvymZd1wvd3HnzoPoAu6Y351qZchyHFotFb+fSIaCrV5EsqK7ryUK/PsLUkvYrNaCjv6AuCAL6+fnpbWUK/6EoSrKh7ul0ys2G6LpO8/mc5vP5zd5tV7GVHHZNb4945WEfyxxh6Kt2Re7ruMytViv+qV7Agoj2Kz2gi+m6XugmgG5jg7i84S9RFMm2bbJt+24Pt4uQKakfu3L+WkZUURRyXbeXc3LRiWgn0zTJdd1eJjL4RTjX7jtoVmUBHQxPXkDXd1gQ0QzP82g+n1/duqTP0Imon6ZpFEVRctrR0GD+XDcgoAN4UhRFGPpqiKIovc363oNORDNs26bv7+9eZuDuYcucLMuDvO+6AAEdPIydiF70xg7DkCzLIsuycufadRHbU8eu6e0UD4H1pcwRlwlHJ6I+8fseHy13TRRFvcviISvcDXcDOsdxyHXdq6vJqub7Pvm+39j/D1lsg6IoSrLa9VZw53kefX9/0/f3d28qO3a4D8Fc+wRBQNPplNbrdW8WR7Bn1aITUS+2U8APQbIsy6LPz8/edCL4+XMI6NrrbkD39fVF0+mUJEki27ZrCayiKEr2pBuPxzQejwc5P6sr4vlMt4YiTNOk1WpFq9Xq5uu6wnVdHPfVcmwH41Zno0uQKWlO0cUn8WfUl44r/3egE9FedwO62Pl8psViQZIkkWma5HleqcFdGIbJqrR///7R19dXqsEsejNB/bS/zaFvNZqiKJJpmmSa5s3XdQXfQ0fjWr97q1glSaLtdkur1ao3m1ojoGvOo21QXwIfrKrujrfL5XLhL7J0XafNZsNfTsQfsKIoqYaa/5pyGsH4a3ZieR5VVTPfC83RNI12ux1NJpNM720obNumxWKRfH3nNoIXse93XB9IkkSn04mWy2VvhlTvEUUxGXLd7/e9CRrayPf9ZJPg+XxORJSUwe12ezWgDoKAoii6+nzXsGXOMAwcGFCDt7c3omfalcsdv7+/F1mWL0TUyEOW5ct+v+d/LWiQqqoXIrrM53P+qcEwDCMpo6qq8k9Dyebzeeb9jr8eSjnc7/fJ3ywIAv80lGy5XKbK2M/PT/L17+8v//JeYsscEV1WqxX/EqhA/H4/6u6Qa3zyw2q1SjbzrIthGOT7Pnqh0DrYNb09hpK95xcjQbX4KUW6rtNoNBrUth18Ng51XbvdDehipmlSEAQ0n8+TVY1VEASBZrMZHY9Hcl13MDfOUJim2fmtSzzPS21dgEquWXzDm8fzvEzj1DWYP9c83/cHNc2E7UQIgoD5czUoUp9dUzigI+YYpzAM6efnhwzDKC1rN5lMaLlcUhiGyQpX6I74qLd7gdp6vabv729SFOWlgtskPiOExrUZ8QHh9zp9vu/T5+cnTafTTp8sgYCueZIkFWqbfN8nTdM634nAxun1i4PoZ2KrhwK6mCiKpOs6ua5LYRjSfr+n+XxOqqomlewto9GIVFWl2WxG2+2WLpcLeZ5HlmXdrZyhfYIgoM1mQ6fT6W4Ftlwuif5WTXd1Kxq2h16kvEM1ig47sh2Hrpa5MAyxTU6H+L5Pu92OptPp3TqxrfjOOcpcvYp0HHhPBXS8+Bge/28T4MvlQpfLhfb7PW232+QRXw/DkHzfJ8dxUEh6gG0w72XdLMui4/F4c5VYmwVBkGpYiwYVUL6i772u60ld1NXhMjY7h05E+5mmSaPRiEajUSfrOcrp/HT17xiSUgK6axRFIU3Tkgf0H18J5JEkqbPlge9td/Xv6ANd10kQhEKfQVwXdRWGW5v1aLYknn4ShuHD39sW/Py5oh0oaE6lAR0Mw5BudD5gReNav7iBjFfgd3leXFEI6JrV1aDsFWyZG1Id32UI6OBloihWuvK5rYa0fUGbsI3rEBpaz/Mwf65FFEUZRIDDzqFDmesGBHRQiriCKxLg+L5PoigWWhXbNqjkus227cywedux8/5kWU49B/U7HA50OBwyq937hJ8rjLquGxDQQSniG75IzzUMQzqfz3Q6nTo1SR0rDbstDENaLBadOyYMm1i3U5GAznVdent769znxv9tXfv9h6pQQOd5Hr29vSUFs2s9XKieZVmFJ6ibpkmz2YxGo1GhALAtMH+u2/hGqguCIMAm1i11b0U/MYuo7p1X3jaO4yT/xqrq7igU0LENWby3TrzJcJFCDf3EDq+KovjQgdSO41AYhoVf3wZsQID5c+1RdNhe0zSaTCadCuz4DHaX7pe+4zt4eUzTJEEQaDKZ8E+1luu6GInoqEIBnWVZmV2Lz+czLRYL+vfvX3IsGAxLl7JrZWAb16H97W2l6zq9v78XWukqSRJ5ntfZzw6diHaIF4AV6UiYpklRFGUC8zbj76Wu3i9DVCigE0WRPM+7OiF3vV7Tx8cHKYpCrusiawe9g/lz7RTXNX2dBsJ2lFHm2iEOcNj6oE/4TgPKXXcUCujorxAHQUDz+Zx/KnE4HGg6nZIkScjaQSFRFHWinPABAyq5dogbn9Pp1MuOJPs3IVPSDn2/99mADlnhbikc0MVs26bj8Ujz+fzq3mPn8zmVtXMcp5eVLbwm3kX94+Oj9UMSbEA3Go0Gsf9ZF7BBTtGOQRRFnZlHhwxd+8THel0bscrTlY4rYWumTns4oKO/uSi2bVMYhjSfzzPz61iHw4G+vr6SuXZdqUjhOUEQFA7e4+1L4n+3FSYJtxebPSha7nRdp/F4TIqiFP6eJvi+n9wf6ES0R7x/5iMB2r9//+jj46P1W+bwm1gjK9wtTwV0sXilaxiG9PPzc3clz3q9pvF4TJIkZYawoB90Xc9Mqr1G07Rk+xJd1/mnW4PPHiKga49nMnRxYBSGYWsDuiiKyDTN5GuUuW6Ls3l8XdI2fLuMctctLwV0LF3XyfM8+v39peVyeTMdfTqdkrl2fAGC7vJ9n06n00MLY+LtS9qcfdhsNqmvUcm1B1tuHilz2+2WgiBobbmzbRtZ4R7xPI8Mwyjc2W1CFEWpug5Z4e4pLaCLiaJIlmVREAS03+/JMIyrc+3YwK5o7xra73w+9+bz5IMEVHLtIklSUr8ULXOiKJKmaa3+HPm/BQFdt8XJCzbr2jZ8cgVlrntKD+hY7DYmq9Xq6pDs6XQiTdMyjSe007XPiZ0H15e5kmhY28+2bVJVtbefDToRUAe+Xu/r/dRnlQZ0LNM0yfM8Oh6PtFwuMwsp+pTV6bvD4cBfIuIqhEc/S8/zOhEEYpJw+1iWRb7vPzWc1dbFOOz9gzLXPmEYJtNF+goBXffUFtDFJEkiy7IoDEPabrdkGEYS3D0aBEC7sA0P39u75/Pzk8bjcevLACq5ftE0rXUrDz3Pw/mtLacoCn19fT312TyyE0BTkBXuptoDOpamaeS6LoVhSPv9vtXzC6Baj86DqoPruqnGXhAEZEt6hF3E0yZ8gPlM0ADVYje0fiRLFwQBfXx8tH7eOMpcNzUa0LEURcGO1B3Df15sj+7RbUh836fJZPLw91XFdV2aTqep4WVUcv0SZ0n4ctwkfs9DdCLaia3rHgno4rJ2Pp/JcRz+6dZAmeum1gR00D38TS9JEi2XSzIM4+Fsq6Io5HleaxrXvEoaAV17xZn+RyiKQrPZrFUZOn4eIMpcO7EB3SNzfyVJShYIPlpHViUMQ9I0LRVgotx1EwI6KJVlWeS6bmsCs2eZppnZSxGVXHtNp1PSHlwpL0kSOY7Tqs+Vn7fUpt8N/osdSXi0IxEvEGzLZ+t5Hu12u2TeJrLC3YWADiCH9He8XQyVXPudTqfW78T/qLY0+pCmaVoy7/fRgK5t+Awjylx3vV0ulwt/kccPA1RF0zQUpg54e3sjIqICRecpQRA0HjxFUUSapiVz6CaTSe+ChS6xbZsWiwURES2Xy8zCgbhMdv1z0jSNdrtd8nVV9xjcx5a57XabaZvi51VVzQRFXSKKYmpVdd79BfXxfZ/G4/Fz5epSABHV8pjP5/x/DS0Uf15VmM/nFyK6CIJw+f395Z+uxe/v70WWZZTNFonLBRFdttst//RFEISk3Dzq9/f3MpvNLvP5vLEyF1NVNfk7VVXln4YasZ9FXpm7XC6X5XJ5+fn54S8X8vPzc9nv9/zlWu33+1Q9R0SN/05Dt91un77/MeQKrRL3SJrcaNqyrMzmyXzvHNolzug+U248z6Pv729aLBYPf2/Z2LmnKHPtZ1nWUyvzgyCgz89P+vj4eDwLUyJ+9A1TS9rjmfsfAR2UzrKsTEVRlOM4NJ/PabVaPVWgX2VZFq3Xa/5yI78LFPfKptamaZJhGDSZTBprzOJJ8uzh6Chz/fXKqTpl8TwvVd4IZa7zENBB6eJsxzNBnaIoZNt2I0v6wzCk7+9v/jKpqspfgpZhG6JHAzr62/akyW1zHMdJzZ0jNK69pigKqara2PYlQRDk/r8oc92GRRHwsHuLIuLn6cZr2sqyrExQN5/Pa7sHIN+9CephGNL7+/vV59uOvWforxPR5FAcpBeodLFM3aLreiY7R0S03+8by1LDf8SLIp5qd/hJdQD3xJNnr2EXFDw7YbhJo9EoNUn42oRoqM+9RREXZmFEF7HljbAIpxWKLIroqtVqlSlzzywogvL9/Pw8XQdgyBVKxw5bPTs/xPd90ho6OB2bu3aT53m03W75y62Xt48Zylw3xHMfu7ZVjmmatFwuU9dQ5trh2TaTMIcOqvDqfCb6C+h2ux19f383euYh5s91RxlTNnRdp7e3t1o7Egjouss0Tdrtdrnz0YqKg8K6j6CzLCt1Gg7KXPchoIPSPXtwNeuVVYuPiqKITNMkXdczvy8quWGJ563V0bgGQUC2bWeCR3QiuiPekPeZ7XJicVDIl4M6YJucfkFAB6VjK4Zn9miiv58hCEItq8Bc16X1ek2bzYbCMEytNkQlNyxxWXu23BYVhiF9fHzQYrHAnocdxma4nu14xp/3+XzOdCjL5vt+6v9gg1Ashug+BHRQOkmSaL/f036/fzoYE0WRoigiz/Myc9rKxvZS/+d//if1HBrXYXEch/b7fS0ZumtQ5rqDrTueXZUcz/3c7/eV1nWu69J4PKb393dSFIU0TUsyjMgK9wMCOqiEoiid6fGZpkmyLJMsy/S///u/yXVUcu1RNPsRBAFpL05Sr6PcSpKUyu6wENB1B/tZFS2jeTRNq7zcscHn4XDASEQPIaAD+AsEfN9PBQKo5Nqj6Pwky7Jot9s1upCmKNd1SRCE1DV0ItrpWrDF1hFFy2hTdF0nwzD4y0So63oDAR085NlhhVcEQUCKopAkSS9lXu5xHCcZgiBUcp0UN6r8qQvPCMOQXNetbF6ToiiZifBVz92D51w7QUTTNBqNRvzl1nJdNzeoQ13XDwjooPU8z6PD4UCn06m0zEsURWTbdhIARFGU+tmCIKCS6yA2IH9lCIz+GrnpdErv7++VBXV8QIcy1z2O42Qyrc+SJIkkSaq144yscH8goKtIHCDouk6iKCaTUB8+yoPhui69vb3lPiRJIk3TSNf1lxuyttF1nWRZptFo9PQiC55pmrRYLJIG1Pd9ZOd6gG2cXh0CO51ORH/BfRl83yfTNFP3pyiKyc8XBOHq0B60l67rFARBKaMHp9Op1I5rHr5zgrquPxDQVSAeIvz6+qLNZkPn8zmZhLpYLEiSpKcam1u9ttPpRLvdjjabTaWVwSOiKCJRFF/+fRRFoSAIKAzD0gK6+L2Mgzj+vUUl103sKsFXOzb7/Z6WyyUFQVDK6kPbtmm9XmfKcFwGUea6S5Kkq8Oyj4iHb8sob/TXFomiePP0HpS7/kBAV7IgCOjj4yPp3ec5nU5PZdL4oCNPHfu2FRUEAZ3P50a3gLgmfo8mkwkRKrneYOeg8Z/po+I5bmU1rnGjymZIsAgHWKZpkqqqL43ksDzPo/P5TOfzOdOJjaHc9QcCupLxwZSqqvTz85PZouB0Oj2Uog/DMBMkjkYjMgyDlsslbbdbulwutezb9qjD4ZBJ85fh0YCY5TgOHY/H5DNgfz8MfXWXruulDZGWzXVdWq1WScY6iqLUHDo0rGDbNvm+X0q2j5j7IZ4TzCcFMH+uXxDQlSgIgtSu74IgkOd5pOs6+b6fWQ31SEDH34jL5TJZhWdZVusbg0f+1ns8z6O3tzf69+/fSz+XDXzZYBkrDbstDpjKahTLIooimaaZ3Kumaabm6aETAXn4uv8RiqJQFEVXO79tbzfgMQjoSsQPLTqOkzQqoihmVrQ9krXih4/4n1W3R7Mgr86jY7HvBf+eX+O6bmZC+jWo5LrNNE26XC6l3iO2bSeLj/h78Rm+79Nms0m+Rpnrvkfq86IURaHxeFxq/clCuesXBHQl4it6fvjVNM1UIMSf4XgL/7MtyyLHccj3/UJBStmKZBPYyuJ0OmX+hmeZpkmGYdBkMik818SyLFqv17mv53vAqOSAF5f3R6ZKuK5L2pVTK/iOCMpct+m6Tu/v77n1y7PCMEzaiEfq+DAMC78e5a5fENBVJJ5sz4q3L3kGv1Hq9/c3fX190Xg8pn///pEkSWRZVuEbuQl8I/YsSZLIdV3yPK/Q+xkvzqACw3Cj0ah1cxChebqu02q1ovl8XjjzN51OabfbZTp2lDMFAQ1rt8X17mKxKC1TJ0nSw6tebdum9/f3q69nfzfMn+sfBHQFBX9HQ/m+f/WGZYOua4EGX3Ff+1msIpmt0+lE39/fyRYfVYuiKHk/bj3YxSB8I1a2+HfiKYpCqqrSbDbL7UGzQTD/+QDETNMk27YznYIwDHPvubjB5MuUz+15iPlz3cd+xmV1XOmvzlwul7mdgjx59R+L/d1Q5voHAd0N/t9qo7e3N/r4+KDxeEzj8Zje39/p7e2NRFEsFJDdUuT7rzUWy+Uykwk8nU6FMwivOBwOyftx68EOKz8yXPWoKIpIkiQaj8e5vVPf96/OQ2HfX77xBbjF8zx6f3+nj4+PzL3s+36y8py/zkKZ6z42OOI/31fEW+ewwjAkXdcz14n5PfIWdjmOk0o6oNy10yujbAjobuB70rzz+ZyprB9VpJekaVrS21dVlVarFfm+T5Zlked5maBut9uVWqk8azQakaqqycMwjEx2oyyiKJKmaSQIQm5ldgsb0D36vVC/ImXoWtasbOz/wQd01/D3Jspc97HBET89pmye59Fms6Hv7+9MWbJtmwzDyJSpIAjo6+srdQ0BXTu9Um8hoHtRXjboEUUaJ+nvbL/L5UL+3/FBrLwUP3+jV+Fyudx8hGFIPjP8Gk8Sr4rneRRxZ7LeEv2d5xqvNpRludDnAc0q0gmybZs+Pj5ysxhlsiyLJpMJybL8dNl+9vugPURRzOw1WhW2zeGzOaIokuu6mYCO/xp1XT8hoLvBsiyaz+c0mUxIVVWSZTmVbVoul6kbhd1n7lrmjg20ilYAcTDE37yxOiuTvoiiiDRNo8VikVxDw9ofcaP3/f199b4pgyiK5Hne071qLMLpj7rqD13XaTabkSzLhTo3nudlNqWv63eFeiGgu0EURbJtmzzPI9/3Uwsj4g19WWzFnHc6QhRFqXR80R7SeDym6XRK//79y83GUc7P4r+GNMdxMtvGoJLrD7b8F83Y1oVthFHm+oNvD6rkOA4FBc8Yziv/KHftV+Sz5SGgKxHfW+KDL/7G4l8fRRG5rnuztz+dTjM/h3LG3fmfDWl57yEquf5gy/+1bHlT2GATZa4/JEmi5XJJ8/mcf6oxfBIhhnLXfgjoGsYHUYvFIgm0XNdNDe9RzsbDiqLQdDrNzP0xDCP1uq+vr9T3uq6bWrzxynyeqnielwlwm8K/X/S32ARZzf5g70U+E9s0NnPftvsU/isvELrHsqzcrZGawnf0CfPneg0BXYn4kyCIiD4+PkjTNJpOp6nrqqqmGp0gCFLzHNi5dnmp/PV6nRxFxP/svOxT00zTpOl0WstijXvyMjZoWPtFFMXUxql5DVsToihKyh/mz0HV8upb1HX9hYCuZHlZKL6nJwhC5nV8xc4Ge4qiZLJ0MTYIFASBfn5+Wn3DtqH3mte4t/k9g+ewC5aqXBhRVBRFZFlWkh1GmYMmoNz1FwK6kum6Ttvt9uqxKqqqUhiGmQBOFEXabrdkGEbuiQau69JqtUqtpI0JgkCGYZDv+5nl6W0RB6i73S43oKpLFEWZFV+ESq6X4s90NBo1/vkqikL//v2j9XqdXGv6d4L+yytjbW0j4HVvl8vlwl+EcsSrYqMoIvFv41t+nt0z+DR63k1bFcdxkg0qHyk6lmXR9/c3ERHNZrNGh4Xf3t5SX6uqmnlPoV00TUsy3Y+UO9/3SVGURucM+b5P4/GYv0zH4zHTsYP2YOuJR8pc2yiKkswjnUwmuVNOoD3ium673T7ctiNDVyHl79gW27bJsqxSgjn6+8DZR52eHbpiG66mgyc+e4oea39pmtZoMEdX5rRi/lx/eZ5Hmqblfu5NwKrq4UBAB7Vgg6amVx3yw9mo5KAqURQlJ5Gw0Inor/jM1K+vr8xepE1Dues3BHRQC0mSWnOaBdtjFQShtMwpAO9aNhqdiP5i65Nrn39dwjBMpiogK9x/COjgKXmLM+6Jt1/ht3apGztsjIYVqnStQUe56y/2s21qvlp8ohE7GoEy138I6OApz/T0TNOk5XJ5tZGrC7vKFpVcN/Bb/zwiPreX3yqoDnllHRu79htbp2w2m6fnHT/LNE0aj8c0Ho9Tq6ox3Np/COigVmUuDnkEew4vO1kZlVz/eZ5Hu92ukY2t8+aLohPRb6IopqaX1JmlC8MwFcSxUO76DwEd9J7v+/Tx8ZH0WuN96DCnZBjYz7julYer1SozxQANa/+xp/vUuTCCX/AVw9GGw4CADnqPPzM3hoZ1GNiAbrPZ1NrAmqaZOboP5a7/dF3PBPJ1uJYNxEjEMCCgg15zXTf3ZAhCwzoYkiSlFvHUPezKwvy5YRBFkYIgoPl8ngnoqxIEQXKsHA91XXe80uFEQAe1c12XFEWpZZL6tR4roZIbFDZDUffRc2wAiUzJcEiSRLZt1xbAs+WM7cBga6ZuuZaAKAIBHdTO9306HA6VT1IPwzB3U1f6y5Rg/txwsFmSugM69v9DQAdViTuvgiCkOqsoc8OBgA5qx1Y21+a3lYHNzqmqmprTguzcsEiSRIZhEL24BUoRruuSpmkUhiGFYZgMgyFTAlWKM4GO46SG7VDXDQcCOqgdW8GcTqfKhl7ZgM40zdT8kioDSWgnx3FIluWnNsUuKgxDmk6ntNvtyHVdDLdCbRzHof1+T6ZppjotKHfDgYAOasdmS6jCSerxUJdhGDjuC5KJ6q9MOr6H7ShomoZNrHtAVVX+0sPqGOaXJIkURUl1ZLEIZ1gQ0EEj2IavqoAuDEPa7/fkui7mMUHlfN9PMiNxp4FtXBHQDZNt2/Tx8VHbaldkhYcLAR00QtO0pOd7Op0qyZqIophk4thKDg0rVIGdOmBZFkVRlKxYwyKc4Yo7k9/f35V1Xlmo64YLAR00hm0Aq67okKGDqrGrDE3TRHYOiLj6puwsXRiGqbotiqLkuDl+tSv0HwI6aIwkSbRarYiYFVpV8H0/WRCBOSVQBc/zkjJm2zZJkpQK6NCJGC721IjD4VDafLogCEhRlFTQhk7EsCGgg0aZpknH47GUBi+KIvI8j6IoSl3nV7sCBEFAoije3Hj6EXEjPZlMkuFWdj4dGtfhEkUxVb+Vsao/iiLSNI3O53Oqg4pOxLAhoIPGlTG3KK7gPj8/MxUm5pQAL4oiOp/P9Pn5Wcpwv2matFwuk7KHTAmwHMdJsnRldCLiYI5uLDBDuRseBHTwkLKGC8oUB3Px3BFWGIbJ9dFohO1KgIgoVQ5M08xkdR8lSRJZlpVkS7DSEFiiKJLjOER/i8BeqUcdx0nNk4vn5bHD/qPRqJSOMnQLAjp4yKsNXxVM00wFc+ix9hd72scrRFEkWZaJ/hpY27b5l7wEGTrgmaZJk8mEv/yQKIpSZZXtRGC4tV+eqTcQ0EFrhGFIoig+lDFxHCd1XutsNsOckh4rM8PKBv7f39+lbZ3DL8JBpgRinufRdrt9uhw7jpOUrclkkgru0HkFBHTQGvG5l+v1mjRNuxvUhWGYqtBkWc5kWthgD5UcsEzTTGX8+LLzLGTn4JZXykQctMmynJorHARBsuchofM6WAjo4ClVbP2haVpyzubhcCBJkm7ONeHnjLiuezU7N5lMKvmdobtEUUztC7Zer+9m6YIgIF3X6e3tjd7e3nLLJ7LCUBXXdWm73SartNnrsVeHdaG7ENDBU54dMrjH87wka3I+n0njzsNk+b5PsiyTYRjJnkz887FXesXQX7Zt02q1SjoS11a8xnOXPj4+kqxv3sTzMAxTmRKUO7jH9/27oxExSZJyyxTqOiAEdNA2iqKklvjfCuo8z6MgCDKZOfb5GDIlcI1pmhSGIV0ul9x9CuNV1IvFIrk2Go3I87xMueOzwtBNefVNFRRFofF4fHc04hZ2JT8hoBs0BHTQOqZpku/7qaAur6G9hc2U5GVSAIrI2xJHVdXcjDBh/lxvFM2YvSoe4j+fz/Tx8UGWZZFt28njWsaYxZY5bM00bAjooJUURaEwDGk+n9NoNMpkQu5Bdg7KYNt2as+v5XJJvu/nlkf2dAhCuYMCfN9Phvvpb7X1YrFIHuPxOPX6POhEQAwBHbSWKIpk2zaFYViop8piJwmjkoNnSZJEsizTbDajIAhuHq7OZ0qQFYZ74o7rarUiwzBIVVWSZZlUVSVVVWk+n/PfkoJORL882s7xENBB70RRlBoiQyUHz7Isi4IgIMdx7gZoOB0CnmWaJrmuS77vUxAE5Ps++b5/dysdthMhCALK3cAhoIPewcT0frm3lUhbYOgL6oYyBywEdNA7mD/XL10I6HzmdAhCuYOaICsMLAR00CtRFOF0CKgdssJQN4/ZWJ0Q0AECOugbtseKczShLhj6grrxnYi8ldcwLAjooFfQsELd+NMhkCmBOmBqCfAQ0EGvoJKDurFlDllhqEMQBKnhVnRegRDQQZ+wc0oEQUAlB7VgA7pHTzQBeAa7zyY6ERBDQAe9gRVfUDds7ApNQCcC8iCgg97AcCvUDcOtUDfM2YRrENBBLwRBkFRy2DEd6oJMCdQNnQi4BgEd9AI7pwTBHNSB3/MQ5Q7qgHOq4RoEdNALGG6FuiFTAnXjz6lGVhhYCOjgIW08hgnDrdAEx3GSf6NhhTqwnYjRaESKoqSeh2FDQAcPYSfjtgWGW6FuYRimMiUod1AHjETALQjo4CltOmYGlRzUDcOt0AR2ziaywsBDQAdPaUuqH8Ot0AQ2K4yGFerAdyLaUgdDeyCgg07DcCvUDcOt0AR0IuAeBHTQaRhuhbrxmRIMt0LVsEUOFIGADjoLw63QBGRKoG7oREARCOigs9CwQt2CIMBwK9QOJ5JAEQjooLNQyUHd2E4EMiVQBwy3Do8gCPylQhDQQSd5npcMt2KDTagLOhFQN3QihufZ9gwBHXQSFkNA3dg5m4RyBzVhAzrLslLPAbAQ0EEnIVMCdUOmBOqGLXLgEQjooHM8z6Pz+UyE4VaoEToRUDe2zE0mk1ad0APtg4AOOgfDrVA3DLdCE7BxOjwCAR10ShRFtF6vk6+RKYE6YLgV6sZukYN9NqEIBHTQKWzDiuHWYYiiiL9UO+x5OCxsmWuqjuGzcxhu7b8gCPhLD0FAB53CV3LQf69Wcq9yXTeZs0kod4PAlrmmAil0Iobn1c4rAjroDH6XflRyUAe2YZ1MJhhuhcqxnYjRaESapvEvAchAQAed4ThO8m9ZlhsbCoHhCMOQdrtd8jWyc1AHrKiGZyCgg06IogiVHNSO7UQIgoByB5ULwzB11BfKHBSFgA46gd17jlDJQU0wZxPqxpY5VVUxxA+FIaCDTmArOcMwGpuoDMPBL4bAsUtQByyGgGchoIPW4+cxoZKDOmCLHKib53nJBtYY4odHIaCDp9Q5DMDOY8KKL6gD34lAdg7qgCF+eAUCOnhKnQEdhiCgbmwnglDuoAb8Ygh0IuBRCOig1fh5TGhYoQ783nOYswlVY1fxY4gfnoGADlqNreSwqSvUAZ0IaAKbFUZ2Dp6BgA5aix+CQMMKdeAXQ2AuE1SNXQxBqOvgSQjooLBXz5l7FBpWqBu/GAINK9SBzc5hWyZ4FgI6KKzuQ9LZgM627dRzAFXgF0Ng6Auqhk4ElAUBHbQSvx8TsnNQB2xgDXVjO6uyLGNbJngaAjpoJTZTYpomGlaoHL8YAtk5qFoURbRer5OvUebgFQjooHV838emrlA7/gxNbBsBVWM7rhiJgFchoIPW4Ye9sFUJVI3vRGAeE9SBPxkCIxHwCgR00CphGKaGINCwQh3YeUw4QxPq4LpuaqsSjETAqxDQQauwDauqqpggDBSGIX+pVHx2Dg0r1IEdbsUQP5QBAR20Bj9BGFuVANUQ0PHZOQR0UDXf9+lwOCRfIyMMZUBAB63B91iRnYOq5WXnMI8JqsZ3IhDQQRkQ0EErhGGYCuiQnYM68KsMkZ2DquV1IgDKgIAOWsG27WQPMGTnoA78WcHIzkEd+M4qsnNQFgR00Dh+ZStf4QFUgR/2QqYEqsZn57AtE5QJAR00DitboW58JwJ7gEEd+M4q/zUAET1dFyGgg0bxDSsqOKgDn51DuYOqITsHRT27hQ0COmgUO3/EMAxk56ByfCfCsiw0rFA5vtPAfw3wKgR00BjXdZMeqyAIqRWHAFVhG9LRaIS5c1A5Pjs3n8/RiYDSIaCDRkRRlGpIbdt+et4A9FsURcm/nx2KiIVhSJ7nJV+j3EGeIAj4Sy9BJwLqgIAOGsFuU4IKDm5hd9R/NfiyLCu1PQ62jIA8bCfiVY7jpLJzruu+XI4B8iCgg9r5vk/f39/J167rpp4HqILv+6l95zDED1ULwzCVnZtMJpgnDJVBQAe1iqIolRWZzWaDquCqPpcUruPL3avDtwD36LqeZIQxTxiqhoAOamWaJp1OJyIikmV5cCu9fN/nL0ENbNtOyt1oNBpUuUMnohm2baemCziOM5iFEFEUodw1AAEd1MZxnNSQ1xDnkqCSq18QBKnMiOd5gyp37CIQqEcQBLRYLJKvDcMY1HzNIAhQ1zUAAR3UIggC+vr6Sr6ez+cY8oLKxUP88bDXEMtdmRP84b4wDFPTSGRZxlAr1AIBHVQuCIJUBaeq6qCGvKA5pmkmw15DHOKHekVRlJk3N8SRCGgGAroeCcOwdb3xuLcaV3CyLGMICGphmmYyxC8IAsodPKVonRpFEWmalpk3N7SMMDQHAV0PxBXJ+/t7bZNui0zuz+ut+r4/6N5q2RuWQj7TNJPjveJyV9e9Af1S9J61LCsVzC2Xy0HNm2MVDYKhXAjoOsz3fbJtmxRFSTauPJ/PhYKtqsXDrHEFh2DuP9hFIVC+uBPBntXquu6gsyRtqA/6ju1A0N8iiCFvll40CIZyIaDroDAMSRRFGo/HtFgsku0Yqla01+X7fm4wN+RGFaoXdyLYoHm1WpGu66nXDRFWHFYnL5jDZunQBAR0HeR5XjKMWSe213WtB+a6Lo3H48wwK4I5qJLrupn5S6vVarBDXjwEdOWLV1CzwZwsywjm/iAzXD8EdB1kmiYZhkGCIPBPEd0ItsrE36zxUNd0Ok2uIZiDqsWN6nQ6TXVyEMxBleJ5y3wwx9eLAHVCQNdBoiiS67oURRFtt1v+6cJDo69gK644aGOHuhDMZaGyL1dcvthGlRDMQcn47GbeatY4mBv6HOEY/55BPRDQdZymaVczdVU6n8+k6zppmkbj8Tg1jw/BHFQpDEMyTTNT7gjBXK54wRQ853Q6JZ1kz/NIkiQEc3cgoGvG2+VyufAXoRlBEFAURRT9nYMXB0SKotysLDRNS1Xa8/m8kg1UbdtOHWdzzWQyQTCXIwxDWq/XNJ/P+afgBrbMCYJwdf6oLMuZBRCSJD21Xcm9e65L3t7eaLvdpjb3htv4OnUymVAYhqlAjhDMXaVpGmmaVkk71GdxG/tsG46AriUkScpkG1iz2ezq8TF85fNsYbinaEAHMFSyLD/cuD8aPD4apI7HYzIM46HvGTrXdW/Wx7HZbPbQZzcUruuSJElXOxGPlnnWo+W/SxDQ9YDv+zQej/nLKaqqXp2DVVdA57ouVnBB7YIguJqVAwAoShCEp0ePng1CrwW1eVzXTUZxnmnDEdC1QBiG9P7+zl9OmUwmV48uqiugA4DhuNaBhOpEUVTLLgV1C8OwU/Pqmu5EPtuGI6BrCc/zkhs5rkjZ1LJlWVd7B/xQ6LOFAQAAALoJAV0PIKADAAAYNmxb0kOPjNkDAABA9yGgAwAAAOg4BHQ9gIwcAADAsCGg6wF+sURf9+gBAACAfFgU0ROu6yanS/C75QMAAEC/IaADAAAA6DgMuQIAAAB0HAI6AAAAgI5DQAcAAADQcQjoAAAAADoOiyKgNPFKW/4gZlEUSdM0siwr9XrICoKAPM8j3/cpCAKSJIkURSFFUcg0zcwWNQBFRFFEjuMk92Z8T2qaRoqi8C8HeEoUReS6Lvm+T5Ikka7r2Ce1Rgjo4GW+75Ou63Q+n/mnUmRZJt/3EZTkiKKIdF2n3W7HP5UQBIE8z0MFCQ9xXZcsy7p6f85mM7JtG/clvMRxHLJtO1PORqMReZ6HjkMOz/PI87xMAiTefuzh9+wC8ILj8XgRBOFCRKnHaDTKvT6fz/kfMXi/v78XWZYz71XeQxCEy36/538EQK7tdpspQ3kPWZb5bwUo5Pf396KqaqZM8Y/lcsl/66AZhpF5j/iHqqqX399f/luvwhw6eElez98wDAqCgMIwJFmWU8+5rpv6GohM06TD4cBfJkEQ+Et0Pp/Jtm3+MkAu0zT5S7kOhwPKFTwsiiLSNO3myELs6+uLPM/jLw+S4zi0Xq/5yxm73e6hERkMucLToiiif//+pa4ZhpEK2nzfp/F4nHrNfr9/PJXcU57n0efnZ+rabDYjy7JIkiQKw5BM08xUmL+/vxgig5tc16XpdJq6NhqNSNd1EkWRgiCgzWaTPCcIAkVRlHo9wC2maWYCE1mWSdd1iqKIvr+/U88JgpDM4Ryq+EQnPhEymUxIURQKwzDznv78/BQ7AYpP2QEUxQ/nGIbBv+Ry+U+HIfXYbrf8SwaLH2rNG5L+/f29jEYjvIfwEL5sybKcGb7hh31+fn5SzwNcczweM3W7qqqp1/BtBF2p44ZkNptl3pPVapV6zXK5TD0/m81Sz1+DDB08LYoikiSJ6G/oNW/IJi+Ldzwek+/jxas72UwBu2pWkqTke+N/s9e65u3tLfn3rd4rP6yx3W4fSsXDsOTdd3mZcT5DPJ/Pc+9jAF5eBjivbufrrslkMtih17jNZLNzq9UqMzUiCAL6+PhIvlZVlXzfT70mDwI6eEkcePFBSBRF5Ps+2badmh+WN6wTBAFZlpUZVnzEcrns5LYobGV37W/IS9HzAV0QBMm2FLEwDOl0OiVf09/7zzbquq7n/p9dEpe1IAhS14tUgJIkkW3bmUao6/ipDrIsZ94f+isj7+/vyddFGw4A27ZpsVgkX89mM3IcJ/UaynndkMsYe1+ORiNyHCd3KJW/fwsHwXzKDuBVk8kkk1KOH5PJJPXa7Xabuxr20YcgCKmf2yXH4zEzFMbi30/+b+WHzR59HI/H1M/rkrzhi0cf16YKdNnPz0/qb7w1zMW+jh8yG4rtdnuZz+eXyWRyUVX1oqpqZppD3iN+7RBXcLLDqbdWY/JD/3wbcPkrr/P5PHk/b62ajZ+fTCaX5XLZufpru93e3Kkgb9eDa+WLf98Q0EGp+IaEf/BzAfhg5dlHHxvlvBub/1vn83nm+UceXX7fXv3b6W97nT7OR+Tfm1tz4/j3ZGhuBQ9FH3nzE4fiVnCS1x6w88VWq9XLHfq+dEKOx+NltVrl1vl8HbVarfI7HKlXwaDFkT5fUARBuKiqmpm4mYefzMk/RqNR6vVxD2M+n1+Wy2VmEu1kMrlst9vLdrtNFXRZlu/2dOq23+8vk8nkagWlqmomoL3mWjBHRMnfHE9KFgThslqtcjN1s9ksEzTH713bGqDtdpvqoceP2Wx2mc/nmUqNfX9ms1nm/Yr/zrxGxTCMVpWdsvFlgX/vWPx7MyT36qv4sVwuM69t633UFvv9PrcujN+vvPvy0YcgCFezV12Rt+iNf7Buvm+pV8JgrVarbOHIedxTZJPJW9kC9vfghxbZYO/WEFJT+Eb02uOeaxUh/3fv9/sLMY01n5WJX8sHyW187y4FMyVsRtEwjMtkMkkCM/7vZxta/mf3Hf/3Xgvofn9/M+9x14awXvHz85N0HAzDyARtxA13sZ2Gtt5HbXAt88a+l4ZhJMmC2WyWqT8FQbj8/PxcttttJuCJg+k+uLY5P/tg78mb00xSPxkGi8/iXHs8Yr/fX35+fjKZk1spcvb34OdatD2gu3dTFnkPr1WEVGB4lG3E+WCY/TltfO8uOUHItcc1bIMgcycf8D+77/hK/1onig/2h/De3MO+F/yIAttpaOt91KTf39+rbcm9+osvi2yZ5TtrfQnmYvv9PhPQsg++LYxtt9vU9+GkCCD6WymoqmrmZAf6WyGnqiqtVqvU9byVhaz4PDp+RdNut0utxmSxG53mrf5pM9d1776Hy+WSfyoRbwPAbzhJf9tJ3Dtlg10lzC+D7wLLskhVVVJVlX+KBEEgVVVpNpvxTyXYcsb//UPb4oVfdX7rPoX/4usqfgV431ZDlykIAtI0LVWHxyaTyd36i28T2HuWL899oygKua5Lx+ORDMPgn6bNZpN7D2ualm4n+YgPoAi2N6Wq6tUMQIxPmef1sPi5AXlzU+71WLqKz6iw722RuV5875YfNmOf62Nmgd/klP/72R4+n73rI/5euvY385kPGniTwA+58uWo7aMETfn5+bk6slB0jhubaeLrd75+K1Intlle+8fKuy+vfQ/bdiBDB09h9zLb7Xb0+fl5tQcWRVFmP7Q8bO9YVdWbvTJ+L7susywrc0SOYRi03+/J9/3MZrB52PdOluVMJmE0GqW+7pt7fz/rVrnqC/5vPBwOmQwI5WRF8rLLQ8JmQUaj0c1yBP8RBAGZppkZWZBlmfb7fSbLeQ27z9q90ZkidWIbxRvHj8djEkUxkxGO5W3ufe217HUEdPAUURQzqeHpdJpb6PjCKQhC7hAY+733bui+8DwvE8wdj0dyXfehSot97/Iq0L43TOzfn1e2+ACn7/LKDn8fEteI0gDfJx4b0OXVQX3qSJYhHmZlgzlBEGg+nxfujNLfz2F/Rt573wdhGCZ/5/l8zkwNeVQYhqmN+xHQwdMcxyFBEFLXxuMxaZpGtm2TbdukKEomYMkLOKIoShXMawW9b5mmvL9TURQyTZNs2ybHccj3/eRxTTx/ThCEu5VhHxslNjC59p4OiSiKNJlMUtfW63Uqi27bdiarkhcMDwlbB+XdR3nzmIaMz8wZhkFBEJBt2w91Dtj7V5blzPf25f7lO9an0yl3ZCuvrs97D9j3TRCEgU+YgJcV3e4kflzbgJOd88PPn2CxqxW7Lt525NFHvJw/xs4vubaSjH3fbq0y7iL2feRX98aGOPeJn3fEfv7XViLyc8aGhH2/rpUjrHL9L36eV7wFSbwFzPxvf9F465G8ej/Glsdrc+7i56/NB+0Kfj65IAip+XHXtjHJuzfZ980wDMyhg9eYpplZ/XqNLMvkum6m90UFhgz7KO99KOJ8Pqd6Zux7l5edIq5n+Oz/21bsezGUslOEpmm5q4J3u13uSsTZbJbJIAzJveFW+K8oilLns9JfvbTb7Wi329F6vabFYkGLxYI+Pz9pPB7Tv3//SFGUzLxNenC6TdfrLz4jdz6fk5EtTdPo/f09kzm/Ni+Y3xUCAR28zDRNOh6PudtNUME5FZqmJdtS3Br2sW2bVFWl+XzOP9U5kiTRdrul+XxOk8kk2bLj1mM2m9FyuUwdgh2/d8vl8up7x77v117TVXEDIQjC1YCObQS63iA8wrbtzFzXPKqq5h6sPiTsVIRrHSP4D37uZVGHwyEzbM3On7u1ECWebtP1+1fTtNx7Mg6G8+Tdm+z7GE+1ebv8J5UJUIowDMn3/WQ1j6IovQsguiiKIvI8jxRFuRpUd5VlWeS67s0OA/29LgzDq1niPguCgDzPI9/3KYoiCsOQNE0j5W+vyFvv21AEQUCWZSVzgPOEYZgEe67rXg0++i6+j8IwzM248SRJIkmSkvLGiqIoueY4ztWy6Louua578zVdEv8914I4+tu/Ly6TPLYsxu8JAjoAAACAhuQFxnlB3D0I6AAAAAA6DnPoAAAAADoOAR0AAABAxyGgAwAAAOg4BHQAAAAAHYeADgAAAKDjENABAAAAdBwCOgAAAICOQ0AHAAAA0HEI6AAAAAA6DgEdAAAAQMchoAMAAADoOAR0AAAAAB2HgA4AAACg4xDQAQAAAHQcAjoAAACAjkNABwAAANBxCOgAAAAAOg4BHQAAAEDHIaADAAAA6DgEdAAAAAAdh4AOAAAAoOMQ0AEADEAQBCSKIr29vZFlWfzTANBxCOgAAAbANE06n89Ef8EdAPQLAjoAgJ4Lw5AOh0PytaIoqecBoPsQ0AEA9JzneamvTdNMfQ0A3fd2uVwu/EUAAOgPRVGSDJ0gCBRFEf8SAOg4ZOgAAHosCAIMtwIMAAI6AIAes2079TUCOoB+QkAHANBDURSRaZq02WxS18MwTH0NAP2AOXQAAD3hOA45jkOiKFIYhsk2Jbzf318SRZG/DAAdhoAOAKDjfN8n0zTpdDrxT+WSZZlc18XwK0CPYMgVAKDDbNum8XhcOJgjIjocDqRpGjYYBugRBHQAAB1lmiYtFovUNUEQaLVa0Xw+T13nnc9nBHUAPYKADgCggyzLovV6nbpmGAaFYUimaeZuHrxcLmk0GiVfn89n0nU99RoA6CYEdAAAHeS6burryWRCrusmix341ayTyYQsyyLf90kQhOT66XQi3/dTrwWA7kFABwDQMZ7nZVawOo6T+poP6CzLIiIiSZIy2Tv+ewGgexDQAQB0DJ9Rk2WZJElKXWPPbxUEgTRNS77mh1lxFBhA9yGgAwDoGH4PubztR9igjw3m6C9Lx8LCCIDuQ0AHANBx/PBqEASpIVk+oONfzwd4ANA9COgAADqOHzJlh1spJ6DjM3II6AC6DwEdAEDH8HPgDodDaoiV/bcgCJkhWX4RBB/wAUD3IKADAOgYRVFS+8nR34kR9Jet2+12yXU+mHNdN3WqhCAImVWvANA9COgAADooDuBiu92OXNfNZN/YBRRRFCXbl8Qsy8ossgCA7nm7XC4X/iIAALSfaZqZ0yJ4s9mMHMehMAxJ13U6HA7Jc7IsZ+bTAUA3IaADAOioKIpI07RUkMYTBIEkScq8RpZl8n0f2TmAnkBABwDQYWEYkqIomZMjrhEEgWzbzgy9AkC3IaADAOi4IAjo4+ODv0xERKqqkqZpJEkSKYqSWSQBAP2AgA4AoAfy5tPN5/PM4gkA6CescgUA6AF+bzpBEDCsCjAgCOgAAHqAX9ygaVrmGgD0FwI6AIAe4M9n5TN2ANBvCOgAAHqAP78VAR3AsCCgAwDouCiKaLPZJF9PJhMMtwIMDAI6AICO4097wNmsAMODgA4AoEdkWcZwK8AAYR86AIAeCMOQwjAkTdP4pwBgABDQAQAAAHQchlwBAAAAOg4BHQAAAEDHIaADAAAA6DgEdAAAAAAdh4AOAAAAoOMQ0AEAAAB0HAI6AAAAgI5DQAcAAADQcQjoAAAAADoOAR0AAABAxyGgAwAAAOg4BHQAAAAAHYeADgAAAKDj/n//lyu/F/sDZgAAAABJRU5ErkJggg==" } }, "cell_type": "markdown", "id": "bcbc55a7", "metadata": {}, "source": [ "![image.png](attachment:image.png)" ] }, { "cell_type": "code", "execution_count": 18, "id": "158402a4", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#phi_list = np.linspace(, 2*np.pi, 101)\n", "\n", "I_num = np.full_like(phi_list, np.nan, dtype=float)\n", "dphi = phi_list[1] - phi_list[0]\n", "\n", "for i in range(1, len(phi_list)-1):\n", " if np.isfinite(E_num[i-1]) and np.isfinite(E_num[i+1]):\n", " I_num[i] = (E_num[i+1] - E_num[i-1]) / (2*dphi)\n", "\n", "\n", "phi_list_n = np.linspace(-np.pi, np.pi, 101)\n", "I_analytic = -(Delta / 2.0) * np.sin(phi_list_n / 2.0)\n", "\n", "mask = np.isfinite(I_num)\n", "phi_mask = phi_list[mask]\n", "phin_mask = phi_list_n[mask]\n", "I_num_norm = I_num[mask] / np.nanmax(np.abs(I_num[mask]))\n", "I_an_norm = I_analytic[mask] / np.max(np.abs(I_analytic[mask]))\n", "\n", "plt.figure(figsize=(5,4))\n", "plt.plot(phi_mask, -I_num_norm, 'o-', label='I_num')\n", "plt.plot(phin_mask, -I_an_norm, '-', label='I_analytic')\n", "plt.xlabel(r'$\\phi$')\n", "plt.ylabel('I')\n", "##plt.title('Forma de I(φ) ~ dE/dφ: numérico vs analítico')\n", "##plt.grid(True)\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 21, "id": "5f9050a7", "metadata": {}, "outputs": [], "source": [ "# ---------- Normal chain (spinless) para T ----------\n", "lat_n = kwant.lattice.chain(norbs=2)\n", "def make_normal_barrier_1d(Vb, L=1, mu=0.0, t=1.0):\n", " \"\"\"\n", " Inifite Chain with a barrier Vb of one site in the central region\n", " \"\"\"\n", " syst = kwant.Builder()\n", " # Región de scattering: L sitios, barrera en el centro\n", " for x in range(L):\n", " onsite = -mu\n", " if x == L // 2:\n", " onsite += Vb\n", " syst[lat_n(x)] = onsite\n", "\n", " syst[lat_n.neighbors()] = -t\n", "\n", " # Lead izquierdo\n", " sym_left = kwant.TranslationalSymmetry([-1])\n", " leadL = kwant.Builder(sym_left)\n", " leadL[lat_n(0)] = -mu\n", " leadL[lat_n.neighbors()] = -t\n", "\n", " # Lead derecho\n", " sym_right = kwant.TranslationalSymmetry([+1])\n", " leadR = kwant.Builder(sym_right)\n", " leadR[lat_n(0)] = -mu\n", " leadR[lat_n.neighbors()] = -t\n", "\n", " syst.attach_lead(leadL)\n", " syst.attach_lead(leadR)\n", "\n", " return syst.finalized()\n", "\n", "\n", "def transm(Vb, mu=0.0, t=1.0, L=1, E=0.0):\n", " \"\"\"\n", " Transmission with a barrier Vb.\n", " \"\"\"\n", " systN = make_normal_barrier_1d(Vb, L=L, mu=mu, t=t)\n", " sm = kwant.smatrix(systN, energy=E)\n", " T = sm.transmission(1, 0) # lead 0 -> lead 1\n", " return T\n" ] }, { "cell_type": "code", "execution_count": 22, "id": "d9c3a098", "metadata": {}, "outputs": [], "source": [ "# ---------- BdG: SNS 1D corta con barrera Vb en la parte N ----------\n", "\n", "\n", "lat1d = kwant.lattice.chain(norbs=2)\n", "\n", "def make_sns_1d(phi,\n", " LS=4, # longitud SC izquierda\n", " LW=1, # longitud N (1 sitio)\n", " RS=4, # longitud SC derecha\n", " mu=0.0, Delta=0.1, t=1.0,\n", " Vb=0.0):\n", " \"\"\"\n", " SNS 1D finita (sin leads):\n", " - SC izquierda: Δ e^{-i φ/2}\n", " - N central: -mu τ_z + Vb τ_z\n", " - SC derecha: Δ e^{+i φ/2}\n", " \"\"\"\n", " syst = kwant.Builder()\n", " Ltot = LS + LW + RS\n", " for x in range(Ltot):\n", " # S1: x < LS\n", " if x < LS:\n", " Δ = Delta * np.exp(-0.5j * phi)\n", " onsite = -mu * tau_z + (Δ.real * tau_x - Δ.imag * tau_y)\n", " # N (weak link, 1D, con barrera Vb)\n", " elif LS <= x < LS + LW:\n", " onsite = -mu * tau_z + Vb * tau_z\n", " # S2: x >= LS+LW\n", " else:\n", " Δ = Delta * np.exp(+0.5j * phi)\n", " onsite = -mu * tau_z + (Δ.real * tau_x - Δ.imag * tau_y)\n", " syst[lat1d(x)] = onsite\n", " # hoppings 1D\n", " syst[lat1d.neighbors()] = -t * tau_z\n", "\n", " return syst.finalized()\n" ] }, { "cell_type": "markdown", "id": "f7c3f6f4", "metadata": {}, "source": [ "### Generalization when a weak barrier is included" ] }, { "cell_type": "markdown", "id": "0f7bb8c6", "metadata": {}, "source": [ "Consider a short, single-channel S–N–S junction with normal-state\n", "transmission probability $T$ (and reflection $R = 1 - T$). In the\n", "superconducting leads we assume a real, energy-independent gap $\\Delta$ and\n", "phases $\\pm \\phi/2$ on the left and right superconductors.\n", "\n", "\n", "For subgap energies $|E| < \\Delta$, quasiparticles cannot propagate in the\n", "bulk of the superconductors and are instead Andreev reflected at each\n", "S/N interface. The Andreev reflection amplitude can be written as\n", "$\n", "r_A(E) = e^{-i\\arccos(E/\\Delta)}\\,,\n", "$\n", "so that an electron converts into a hole (and vice versa) with a phase shift\n", "$-\\arccos(E/\\Delta)$.\n", "\n", "\n", "\n", "A bound state corresponds to a closed electron–hole orbit which picks up a\n", "total phase that is an integer multiple of $2\\pi$. For a short junction\n", "(the normal region length $L$ much smaller than the coherence length),\n", "we can neglect the energy dependence of the normal-region scattering\n", "matrix and characterize it by a single transmission $T$. The closed\n", "electron–hole loop acquires:\n", "\n", "\n", "\n", "1. Two Andreev reflection phases, one at each interface:\n", " \\[\n", " 2 \\arccos(E/\\Delta),\n", " \\]\n", "2. The superconducting phase difference $\\phi$ between the two leads,\n", "3. A normal-scattering phase that depends on $T$." ] }, { "cell_type": "code", "execution_count": 23, "id": "e33bc024", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T = 0.39024390243902457\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Parámetros físicos\n", "Delta = 0.1\n", "t = 1.0\n", "mu = 0.0\n", "LS, LW, RS = 100, 1, 100 # junta corta\n", "Vb = 2.5 # fuerza de la barrera (ajusta a gusto)\n", "E_F = 0.0 # Fermi ~ 0 en este modelo (mu=0)\n", "\n", "# 1) Transparencia normal T para este Vb\n", "T_normal = transm(Vb, mu=mu, t=t, L=1, E=E_F)\n", "print(\"T =\", T_normal)\n", "\n", "# 2) ABS numérico vs φ en el estado superconducting\n", "phi_list = np.linspace(0, 2*np.pi, 101)\n", "E_num = np.full_like(phi_list, np.nan, dtype=float)\n", "\n", "#k_eigs = 12 # nº de autovalores alrededor de 0\n", "\n", "for i, phi in enumerate(phi_list):\n", " syst_f = make_sns_1d(phi, LS=LS, LW=LW, RS=RS,\n", " mu=mu, Delta=Delta, t=t,\n", " Vb=Vb)\n", "\n", " H = syst_f.hamiltonian_submatrix(sparse=True)\n", " evals, evecs = sla.eigsh(H, k=k_eigs, sigma=0.0)\n", " evals = np.real(evals)\n", "\n", " # nivel más cercano a 0 en |E|\n", " evals_sorted = sorted(evals, key=lambda E: abs(E))\n", " E_closest = evals_sorted[0]\n", " E_num[i] = abs(E_closest)\n", "\n", "# 3) Analytical expression\n", "E_analytic_abs = Delta * np.sqrt(1.0 - T_normal * np.sin(phi_list / 2.0)**2)\n", "\n", "# ------------ Plot comparación ------------\n", "plt.figure(figsize=(5,4))\n", "plt.plot(phi_list, E_num, 'o', label='|E_num(φ)|')\n", "plt.plot(phi_list, E_analytic_abs, '-', label=r'$E(\\phi) = \\Delta\\sqrt{1 - T\\sin^2(\\phi/2)}$')\n", "plt.xlabel(r'$\\phi$')\n", "plt.ylabel(r'$E(\\phi)$')\n", "##plt.title(f'SNS 1D corta con barrera Vb={Vb:.2f}, T≈{T_normal:.3f}')\n", "##plt.grid(True)\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "b56ea560", "metadata": {}, "source": [ "### Symmetry Checking" ] }, { "cell_type": "markdown", "id": "50489ef8", "metadata": {}, "source": [ "Remember that when we defined `~kwant.builder.Builder` for the left lead above,\n", "we not only declared an electron-hole conservation law, but also that the Hamiltonian\n", "has the particle-hole symmetry :math:`\\mathcal{P} = \\sigma_y` which anticommutes\n", "with the Hamiltonian, using the argument ``particle_hole``.\n", "In Kwant, whenever one or more of the fundamental discrete symmetries\n", "(time-reversal, particle-hole and chiral) are present in a lead Hamiltonian,\n", "they can be declared in `~kwant.builder.Builder`. Kwant then automatically uses\n", "them to construct scattering states that obey the specified symmetries. In this\n", "example, we have a discrete symmetry declared in addition to a conservation law.\n", "For any two conservation law blocks that are transformed to each other by the\n", "discrete symmetry, Kwant then automatically computes the scattering states of one\n", "block by applying the symmetry operator to the scattering states of the other.\n", "\n", "Now, :math:`\\mathcal{P}` relates electrons and holes\n", "at *opposite* energies. However, a scattering problem is always solved at a\n", "fixed energy, so generally :math:`\\mathcal{P}` does not give a relation between\n", "the electron and hole blocks. The exception is of course at zero energy, in which\n", "case particle-hole symmetry transforms between the electron and hole blocks, resulting\n", "in a symmetric scattering matrix. We can check the symmetry explicitly with" ] }, { "cell_type": "code", "execution_count": 24, "id": "1d6b1f62", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "s_ee: \n", " [[-0.121+0.114j -0. -0.j ]\n", " [ 0. +0.j 0.481+0.008j]]\n", "s_hh: \n", " [[-0.121-0.114j -0. +0.j ]\n", " [ 0. -0.j 0.481-0.008j]]\n", "s_hh: \n", "\\ no order [[ 0.481-0.008j 0. -0.j ]\n", " [-0. +0.j -0.121-0.114j]]\n", "s_ee - s_hh^*: \n", " [[-0.+0.j -0.+0.j]\n", " [-0.+0.j -0.-0.j]] \n", "\n", "s_he: \n", " [[-0.+0.j -0.-0.877j]\n", " [ 0.-0.986j 0.-0.j ]]\n", "s_eh: \n", " [[-0.-0.j -0.-0.877j]\n", " [ 0.-0.986j 0.+0.j ]]\n", "s_he + s_eh^*: \n", " [[-0.+0.j -0.+0.j]\n", " [ 0.-0.j 0.-0.j]]\n" ] } ], "source": [ "#### Cheking the symmetries \n", "\n", "def check_PHS(syst):\n", " # Scattering matrix\n", " s = kwant.smatrix(syst, energy=0)\n", " # Electron to electron block\n", " s_ee = s.submatrix((0,0), (0,0))\n", " # Hole to hole block\n", " s_hh = s.submatrix((0,1), (0,1))\n", " print('s_ee: \\n', np.round(s_ee, 3))\n", " print('s_hh: \\n', np.round(s_hh[::-1, ::-1], 3))\n", " print('s_hh: \\n\\ no order', np.round(s_hh, 3))\n", " print('s_ee - s_hh^*: \\n',\n", " np.round(s_ee - s_hh[::-1, ::-1].conj(), 3), '\\n')\n", " # Electron to hole block\n", " s_he = s.submatrix((0,1), (0,0))\n", " # Hole to electron block\n", " s_eh = s.submatrix((0,0), (0,1))\n", " print('s_he: \\n', np.round(s_he, 3))\n", " print('s_eh: \\n', np.round(s_eh[::-1, ::-1], 3))\n", " print('s_he + s_eh^*: \\n',\n", " np.round(s_he + s_eh[::-1, ::-1].conj(), 3))\n", " \n", " \n", "check_PHS(syst)" ] }, { "cell_type": "markdown", "id": "f03498d1", "metadata": {}, "source": [ "Note that $\\mathcal{P}$ flips the sign of momentum, and for the parameters\n", "we consider here, there are two electron and two hole modes active at zero energy.\n", "We thus reorder the matrix elements of the scattering matrix blocks above,\n", "to ensure that the same matrix elements in the electron and hole blocks relate\n", "scattering states and their particle hole partners." ] }, { "cell_type": "markdown", "id": "0b4af405", "metadata": {}, "source": [ "Please send corrections to jalil@udel.edu" ] }, { "cell_type": "code", "execution_count": null, "id": "a0ee56a2", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python (qtransport)", "language": "python", "name": "qtransport" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.13" } }, "nbformat": 4, "nbformat_minor": 5 }