diff --git a/.ipynb_checkpoints/Fitting_HEOM-checkpoint.ipynb b/.ipynb_checkpoints/Fitting_HEOM-checkpoint.ipynb deleted file mode 100644 index 8935534fad..0000000000 --- a/.ipynb_checkpoints/Fitting_HEOM-checkpoint.ipynb +++ /dev/null @@ -1,494 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "cb83932f", - "metadata": {}, - "outputs": [], - "source": [ - "from qutip import *\n", - "import numpy as np" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "3e389834", - "metadata": {}, - "outputs": [], - "source": [ - "# Defining the system Hamiltonian\n", - "eps = 0.0 # Energy of the 2-level system.\n", - "Del = 0.2 # Tunnelling term\n", - "Hsys = 0.5 * eps * sigmaz() + 0.5 * Del * sigmax()\n", - "# Initial state of the system.\n", - "rho0 = basis(2, 0) * basis(2, 0).dag()\n", - "tlist=np.linspace(0,10,1000)" - ] - }, - { - "cell_type": "markdown", - "id": "45b970e7-5064-479a-9450-48a533748716", - "metadata": {}, - "source": [ - "## Spectral density fitting" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "4d63e22e", - "metadata": {}, - "outputs": [], - "source": [ - "w = np.linspace(0, 20, 20000)\n", - "def ohmic_spectral_density(w, alpha, wc):\n", - " \"\"\" The Ohmic bath spectral density as a function of w\n", - " (and the bath parameters).\n", - " \"\"\"\n", - " return w * alpha * np.e**(-w / wc)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "3dac107b-86ff-4b6c-9662-a726080c617a", - "metadata": {}, - "outputs": [], - "source": [ - "alpha=0.05\n", - "T=0.5\n", - "wc=1" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "c9aa3205", - "metadata": {}, - "outputs": [], - "source": [ - "J=ohmic_spectral_density(w,alpha,wc)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "14741f8b", - "metadata": {}, - "outputs": [], - "source": [ - "obp=heom.FitBath(alpha,T,wc,sigmaz())" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "e3533b74", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Parameters [k=1]: lam=[0.09458066]; gamma=[1.77943935]; w0=[0.1], Obtain a normalized RMSE of 0.00016082566438015624\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Parameters [k=2]: lam=[0.05021707 0.03401139]; gamma=[1.43484572 1.24938702]; w0=[1.80511587 0.1 ], Obtain a normalized RMSE of 7.935919929349685e-05\n" - ] - }, - { - "data": { - "image/png": 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d+vXXX7VuBBw8eDAAYPr06ZgxY4Zm+YoVK+Dh4YHevXuXycvKygqLFy/GO++8AyEEWrZsqemGw1QdOnQITZs2hefff6t+eKpajAUFqS5XpqQAly8DBjz6TURGJpMB9epJnYVJc3Fx0byvykNhD95C07BhwzLr69evX7XE/nX//n3N+4qu5hhytccQdhUUvurvZ11F1rVr1/Dkk08iISHBoGNV5cnS2sAsijEAePPNN/Hmm2/qXKdrqIaBAweW29Q7cuRIg4aR+Oyzz/DZZ5/pXNenTx9NvzHmoLi4GD179kRJSQnkADwB7La0RJUuVNrYQAQF4cyff6L5nj2wZzFGRGagY8eOmvdxcXGV2rakpATx8fEAVIVQ6Zv3AZjkzekPY9iwYUhISIBMJsOoUaMwePBgtG3bFo0aNYJCoYBMJoNSqdT8u5hqZ7kmf88Y1ZybN29q/nIpAXANgIu/f6X3s2vXLowZMwbNTp+GP4DdDwwfRURkyjp06IAGDRoAAA4ePIiMjAyDt/3jjz+Q+++DBY899phR8nuwZe1uBaOgVLTe2C5evKjp4uPDDz/E8uXL8dRTT2k6flU/EKDuSsSUsRgjg5XuJdlOJkODUj3rG2LhwoVYtmwZbv57c+qO2NhqyY+ISGoymUzzZH1eXh6+//57g7ddtGiR5r2xBvhu37695n1sBf/3njhxwig5GOrBofdefPFFvXFS51kdWIyRwe7fvw+FQqGZb2prq/NR5YqEh4drze/MzYUyMfGh8yMiqg0mTJigeXpw5syZuKJ+4KkcGzZswI4dOwCoWteeeeYZo+TWpUsXTUe0a9eu1RuXkpKCPXv2GCUHQxUXF2ve5+Tk6I1bsmRJTaRjVCzGyGDPPvusasiMCRNwCsCPVbwfrm/fvlrzdgBu6XgalYjIFHl7e2v6vsrOzkavXr3K7XJh06ZNGDFiBABV1xVr1qyp0h+6hrCxsdG03B0/fhxfffVVmRilUokxY8ZoxteUSqsHHhDTN8bmd999V22d00rJbG7gp5ohk8nQ6O5dNAKAKvbL1rJlSwwbNgwdO3ZE3xMn0HbjRsgM+MuRiMhUvPXWW7h69Sq++uorJCYmokuXLhgyZAj69esHLy8vFBUV4eLFi1i3bp2m30tra2usXbsWnTp1MmpuM2bMwObNm5GcnIyJEyciNjYWL7/8stZwSIcPH0ZQUBCOHTsGAEYrDssTEBCADh064OzZs1i6dCnu37+PYcOGoUmTJrh58ybWrl2Ln3/+GY8++ij++uuvGs+vOrEYo8pTX1KsYg/QADQD6WLNGmDjRuAhBmknIqqNFi5cCF9fX/zf//0f0tLSsGbNGqxZs0ZnbNu2bbF06VKj3bj/oAYNGmD37t146qmncPfuXZ15jRw5Eo899pimGKuu3vgrQyaTYc2aNXjyySdx//59bNq0CZs2bdKK8fPzw+bNm3U+eWpKeJmSKq8aijGNrl1Vr7GxQGHhw++PiKgWeeONN3D16lUsWrQIffr0gaenJ2xsbGBvb48WLVpg8ODBWL9+Pc6cOVMjhZiav78/zp8/j0mTJqFVq1awtraGi4sLnnjiCaxbtw4rV67UGgGgMgOeV6dOnTrh1KlTeOONN+Dl5QUrKys0aNAAQUFBmD9/Po4dO4YmVXiQrLaRCVPtlKMOyczMhJOTEzIyMnT2yFyjiosBGxugpAS4dQt42L9GhAAaNQLu3QOOHlV1BktE1So/Px8JCQnw8fGRpIWDTNOrr76K5cuXw8PDAzdu3JA6HUlV9XfI0O9vtoxR5SQlqQoxKyugigOra5HJ/msdO3Lk4fdHREQPLS8vT3NjfFf1/9FkNCzGyCAFBQU4cuQIEo8dQxEAeHgAFtX046N+EID3jRER1YirV6/q7a2+pKQEY8eO1YzzqH7Sk4yHN/CTQa5evYqQf4smGYDGN2/iRlERrKysHnrfBZ074zCAqF27MOb6dXh5eT30PomISL9Zs2bh2LFjGDx4MIKDg9G4cWPk5eUhPj4e33//PU6ePAkACA0NLdM3JFU/FmNkkKSkJM17AaBIJquWQmzEiBH4+eefkQsAGRnw2rgRY95//6H3S0RE5btw4QKmT5+ud/2jjz6KDRs2SNKtRV3Dy5RkkDt37mjNu1bTgwRFRUWasdgAIMoMOu8jIqrtpkyZgk8//RRPPPEEfHx8YG9vD2tra7i7u6Nfv3746aefcPDgQTRs2FDqVOsEtoyRQTIzM2FhYQGlUgkAaPzvQLgP66mnnsL69es189EnT6KkpARyubxa9k9ERGW1adMGH374IT788EOpUyGwZYwMNGbMGBQVFeFu+/Y4D+DbyMhq2e9TTz0FQNW5XyCAsR4eyMvLq5Z9ExERmQK2jJHBLCws4HL3LlwAIDi4Wvbp4eGB3377DV3lcrj07QtkZwP16lXLvomIiEwBizEyXHExcPeu6n019nj8zDPPALm5gFwOJCcDt28DTZtW2/6JiIhqM16mJMPduaPqMV8uV/WaX53s7ID27VXvT5yo3n0TERHVYizGyHDq7i1cXauvw9cHdemieo2Nrf59ExER1VIsxshw6mLMWIOyBgaqXtkyRkREdQiLMapQcXEx4uLicPP8eRQA1TMmpS7qlrETJ1SXQ4mIiOoA3sBPFUpJSUHnzp01846//46EtDQ0qKa+xtQSnZ1xwMIC++/exVFfX5w8cwYKhaJaj0FERFTbsBijCt1VP0H5r+ziYjg7O1frMe7fvw9vX9//Bq79+28cP34cjz76aLUeh4iIqLbhZUqqUOlirGG9erCo5hv469evj44dO2ot279/f7Ueg4iIqDZiMUYVysjI0Cq+Gtevb5Tj9OjRQ2uexRgREdUFLMaoQi+88AKKioqQ2rQpzgP46dNPjXKcnj17ooGTEwYAWFivHr5YsMAoxyEiIqpNeM8YGcRCJkPDu3fREAAef9wox3j22Wdx9/ZtWDg6Ajk5QDU/IEBERFQbsWWMDHP/PlBYqHpvpK4tLC0tYWFnB7Rtq1pw6pRRjkNEVButWrUKMpkMMpkM165dkzodqkEsxsgw6pv4HR0Ba2vjHisgQPUaF2fc4xARGcn+/fs1hZUh06pVq6ROmSTEYowMk5qqeq3uMSl16dRJ9cqWMSIijZEjR0Imk8Hb21vqVKia8Z4xMoy6ZczFxfjHYssYEZmRsWPHYty4ceXGeHh4wNnZGSNHjqyZpKhWYTFGFfr7779hf/kyGgCwqYmWMX9/1WtCAopTU5FtaVntncwSEdWUxo0bo0OHDlKnQbUYL1NShR599FE0ff992AKw3bULf/75p1GPdyoxEdOdnPAUgPrNmuG9994z6vGIiIikxGKMyiWEwP379zXz+SUlsLe3N+ox9+3bh48zMvAHgOy8PPz1119GPR4RUW2g72nKGTNmQCaTYfXq1QCA69ev63wIgEyX2RRjixcvhre3N2xsbBAcHIxjx46VG79582b4+vrCxsYGfn5+2Llzp9b6LVu2oHfv3mjYsCFkMhlO6biZvGfPnmV+Gd544w2tmMTERISHh8POzg6NGzfGe++9h+Li4oc+35qSlZWFkpISrWXVPUB4aaXHo7xw4QLS0tKMekwiIiKpmEUxtnHjRkRGRmL69Ok4efIk/P39ERYWhjt37uiMP3z4MIYMGYLRo0cjLi4OERERiIiIwNmzZzUxOTk56N69Oz7//PNyj/3aa68hKSlJM82dO1ezrqSkBOHh4SgsLMThw4exevVqrFq1CtOmTaueE68B6enpZZbVN9JwSGqdOnWCjUKhtSw2NtaoxySi/9y9e1drKu8PyNKxRUVFemNTU1O1YgvVfRfqcO/ePa3YgoICvbFpaWkGxz7Y0m8qxo0bhzNnzqB///4AAHd3d5w5c6bMRCZMmIGgoCAxfvx4zXxJSYlwd3cXs2fP1hk/aNAgER4errUsODhYjBkzpkxsQkKCACDi4uLKrOvRo4eYMGGC3rx27twpLCwsRHJysmbZd999JxwdHUVBQUEFZ/WfjIwMAUBkZGQYvE11Ki4uFqn+/uJvQBxZsEAolUqjH3PcsGFiEiC2WFiI5OvXjX48InOWl5cnzp8/L/Ly8gyKB6A1nT17Vm+snZ2dVuyxY8f0xrq4uGjF7tu3T2+sl5eXVuz27dv1xrZr104rdtOmTXpju3Tponddddq3b58mn7Fjx4ozZ87onVJSUoQQQqxcuVKzTUJCQpl9jhgxQgAQXl5eNXIO9J/K/g6pGfr9bfItY4WFhYiNjUVoaKhmmYWFBUJDQxETE6Nzm5iYGK14AAgLC9MbX56ffvoJLi4u6NChA6ZMmYLc3Fyt4/j5+cHV1VXrOJmZmTh37pzefRYUFCAzM1NrkpJcLkfD+/fRCkDwo4/WyL0Ji1evxvwGDTBAqYSruo8zIiIT9N1338HPz0/v9O2330qdIknM5Iux1NRUlJSUaBU8AODq6ork5GSd2yQnJ1cqXp+XXnoJa9euxb59+zBlyhSsWbMGQ4cOrfA46nX6zJ49G05OTprJ09OzUnkZhbqfsZro2gIAZDJ2/kpERHUC+xl7CK+//rrmvZ+fH5o0aYJevXrh6tWraNGiRZX3O2XKFERGRmrmMzMzpS3IcnKAvDzV+5oqxgBV569797LzVyIyadOnT8eMGTOkToNqMZMvxlxcXCCXy5GSkqK1PCUlBW56BrR2c3OrVLyhgoODAQBXrlxBixYt4ObmVuapTvVxyzuWtbU1rI09/mNlqC8TKhSAkbu10MKWMSJJlH74qbyHdkoPaF1eB80XLlyAEEIz7+TkpDc2NjYWSqVSM+/o6Kg39s8//9R66ru82N9//13vOiKpmPxlSoVCgcDAQERHR2uWKZVKREdHIyQkROc2ISEhWvEAEBUVpTfeUOruL5o0aaI5zpkzZ7T+Y4uKioKjoyPatWv3UMeqUQ9eoqzJvmzUwyKdOgU88J8yERlXo0aNtCZLS/1/t5eOtbKy0hvr4uKiFaso9dT0gxo2bKgVW94fqA0aNDA41thPgxNVhcm3jAFAZGQkRowYgS5duiAoKAgLFy5ETk4ORo0aBQAYPnw4mjZtitmzZwMAJkyYgB49emDBggUIDw/Hhg0bcOLECSxbtkyzz7S0NCQmJuL27dsAgEuXLgFQtWi5ubnh6tWrWLduHfr27YuGDRsiPj4e77zzDh5//HF07NgRANC7d2+0a9cOw4YNw9y5c5GcnIyPPvoI48ePr10tX+W4ffs2xIULaADAtiYvUQJAmzaAjQ2QnY27x4/jfH4+evToUbM5EBERGZnJt4wBwIsvvoj58+dj2rRp6NSpE06dOoXdu3drbpZPTExEUlKSJr5bt25Yt24dli1bBn9/f/z888/Ytm2b1thhv/76KwICAhAeHg4AGDx4MAICArBkyRIAqha5P/74A71794avry8mTZqE559/Hr/99ptmH3K5HNu3b4dcLkdISAiGDh2K4cOH4+OPP66Jf5Zq8dZbb8Fj+HDYAbCNj9fqR83Ybt+5g8F2dmgOoHHXrujVqxdycnJq7PhERLUJe9k3X2bRMgYAb775Jt58802d6/bv319m2cCBAzFw4EC9+xs5ciRGjhypd72npycOHDhQYV5eXl5levc3JRkZGZr3+UpluZcrqpuTkxM2378P9QXKkpISxMXFoXv37jWWAxFRbWFjYwMA5XZqS6bJLFrGyHgeLMaA8m+4rW716tVDB3d3rWUVDXNFRGSu1Pcj37lzB1lZWRJnQ9WJxRiVq3SHszVZjAFAUOfOmvd2dnZlikMiorqiW7duAFQPqb3xxhs4cuQIrly5opnIdJnNZUoyjvj4eGS+9BIytmxB5jvvwPvJJ2v0+MPHj0fwb78hCEC7K1dg+e9fhkREdc2TTz6Jrl274siRI1i3bh3WrVuntf7BbkPItLBljMplbW2NRnl5aAmgs58fGjRoUKPHfywsDK+2aoWOACzLGUKKiMjcWVhY4Pfff8dHH30Ef39/2Nvb86Z+M8FijCqWlqZ6lap/Hnb+SkQmpmfPnhBCQAhhcO/7I0eO1Gzj7e2tM8bBwQGzZs3CqVOnkJWVBaVSqdmGTBeLMarY/fuq1xpuFdPw91e9shgjIiIzxGKMKqYuxtgyRkREVO1YjFH5hPjvMqVULWPqYuziRSA/X5ociIiIjITFGOmVl5eH5KtXkVdSAgFI1zLm7g64uCCvpATHNm7EkiVLkKYuEImIiEwcizHSKyoqCk1atYIdAGsAgY89JkkeAkBIYSEcAASPHImxY8fi+PHjkuRCRERU3ViMkV4PdrBaBNVwRFKQyWSQ1auHB49+8uRJSXIhIiKqbizGSK/Sve87OjpKlAnQuX17rXkWY0REZC5YjJFeUo5LWVrnxx8HAMgA+Pr6wsvLS7JciIiIqhOHQyK93n33XbxqY4PMSZOQ0b07bD//XLJcwkeNwqFZs+BfVAT7HTuA5s0ly4WIiKg6sWWM9FIoFGhcUoKWAAJ9fNCuXTvJcnH18MCjfn6wB9jfGBERmRUWY1Q+qfsYexA7fyV6KBwyh6hqjP27w2KMyid17/sPYjFGVCUWFqr/6qV6IprI1BUXFwMA5HK5UfbPYozKVxuLsdOnJU2DyNRYWVnBysoK2dnZUqdCZJIyMjJgbW0NS0vj3GrPYozKV5suU3bsqHpNTPwvLyKqkEwmg4ODAzIyMpCXlyd1OkQm5f79+8jKyoKzszNkMplRjsGnKUmv1NRU2N+7B2sAstrQMubkBKW3Ny5fu4aTX3yBkwUFGD58OPz8/KTOjKjWc3FxQV5eHhITE+Ho6AgHBwfI5XKjfbkQmSohBJRKJfLz85GdnY3c3FzUr18f9Y34PchijPRq1aoV0tPTYQXAaehQ7NizB0FBQZLmFJKRgWMA8OmnAAAvLy8WY0QGkMvl8PT0RGpqKrKyspCeni51SkS1moWFBezs7ODu7m70fjZZjJFOQghND/xFAFLT02FtbS1tUgDaNGuGY+r72ACc5v1jRAaTy+VwdXVF48aNUVRUBKVSKXVKRLWShYUFLC0tNQ+/GBuLMdIpJyenzH/UUg6HpNYxIEDrBn4WY0SVJ5PJoFAopE6DiP7FG/hJp9LjUgK1oxjzDw0FADQF8HRYGMLDw6VNiIiI6CGxZYx0cnV1xa3Tp5Ht748sANl790o6NqXaY889h7uOjnDJzATmzPmvuwsiIiITxZYx0kkul8Pd1hatAQQ6OKDHE08YrX+VyrCxtYVL586qGXb+SkREZoDFGOmXkaF6rQUtYlrYEz8REZkRFmOkn/q+sdpajPHmfSIiMgMsxkg/dctYLbhxX4u/v+r11CmAAx8TEZGJYzFG+tXWy5Tt2gFWVkB6umpoJCIiIhPGYox0KigoQJG6c9Xa1jKmUOB6y5b4FcCsKVPwwgsv4Pjx41JnRUREVCUsxkinuXPnQhEZCRsALr/8gtdee03qlLREpKSgP4Bp69fjf//7H44cOSJ1SkRERFXCYox0ys7OBgAUALhXUIC8vDxpEyqlY/PmWvPsiZ+IiEwVizHSSV2MqTk4OEiUiW7+jzyiNR8fHy9RJkRERA9H+l48qVYqXYzZ29tLlIluHUND4fzdd/AH0PH11xH02GNSp0RERFQlZtMytnjxYnh7e8PGxgbBwcE4duxYufGbN2+Gr68vbGxs4Ofnh507d2qt37JlC3r37o2GDRtCJpPhVKkORtPS0vDWW2+hTZs2sLW1RbNmzfD2228jQ/0E4r9kMlmZacOGDdVyzsa0YMECXHj0URwHsG/y5Fp3z9iTERFI8/TEfgBfv/wyhg4dKnVKREREVWIWxdjGjRsRGRmJ6dOn4+TJk/D390dYWBju3LmjM/7w4cMYMmQIRo8ejbi4OERERCAiIgJnz57VxOTk5KB79+74/PPPde7j9u3buH37NubPn4+zZ89i1apV2L17N0aPHl0mduXKlUhKStJMERER1XLexuTi4gJfpRJdAPQMDkbr1q2lTkmLhYUFZAEBqhn2xE9ERCZMJoTp95oZHByMRx55BN988w0AQKlUwtPTE2+99RY++OCDMvEvvvgicnJysH37ds2yrl27olOnTliyZIlW7LVr1+Dj44O4uDh0qmBQ6s2bN2Po0KHIycnRjOMok8mwdevWhyrAMjMz4eTkhIyMDDjWZDcT7dsD588D0dHAk0/W3HENNX068PHHwCuvAMuXS50NERGRFkO/v02+ZaywsBCxsbEIDQ3VLLOwsEBoaChiYmJ0bhMTE6MVDwBhYWF64w2l/scuPaD2+PHj4eLigqCgIKxYsQIV1b8FBQXIzMzUmiRRWzt9VXuwJ34iIiITZfI38KempqKkpASurq5ay11dXXHx4kWd2yQnJ+uMT05Ofqg8Zs2ahddff11r+ccff4wnn3wSdnZ2+P333zFu3DhkZ2fj7bff1ruv2bNnY+bMmVXOpdqoi8Da1umrmrql8uxZoKhI1Ss/ERGRiTH5Yqw2yMzMRHh4ONq1a4cZM2ZorZs6darmfUBAAHJycjBv3rxyi7EpU6YgMjJSa/+enp7Vnne5SkqArCzV+9raMubtrSoUMzOBixcBPz+pMyIiIqo0k79M6eLiArlcjpSUFK3lKSkpcHNz07mNm5tbpeLLk5WVhT59+sDBwQFbt26FVQWtM8HBwbh58yYKCgr0xlhbW8PR0VFrqmkl6en/zdTWYszCAvu8vPAFgJHjxqFz587466+/pM6KiIioUky+GFMoFAgMDER0dLRmmVKpRHR0NEJCQnRuExISohUPAFFRUXrj9cnMzETv3r2hUCjw66+/wsbGpsJtTp06hfr168Pa2rpSx6pJRUVFsHRxgR2AxgCat22LhIQEqdPS6Z2kJEwCsPrQIcTFxSEuLk7qlIiIiCrFLC5TRkZGYsSIEejSpQuCgoKwcOFC5OTkYNSoUQCA4cOHo2nTppg9ezYAYMKECejRowcWLFiA8PBwbNiwASdOnMCyZcs0+0xLS0NiYiJu374NALh06RIAVauam5ubphDLzc3F2rVrtW60b9SoEeRyOX777TekpKSga9eusLGxQVRUFD777DO8++67NfnPU2k5OTkAgLx/p7sJCVAoFJLmpE/HVq1wOjVVM8+e+ImIyOQIM7Fo0SLRrFkzoVAoRFBQkDhy5IhmXY8ePcSIESO04jdt2iRat24tFAqFaN++vdixY4fW+pUrVwoAZabp06cLIYTYt2+fzvUAREJCghBCiF27dolOnToJe3t7Ua9ePeHv7y+WLFkiSkpKKnVuGRkZAoDIyMio9L9LVSQmJpY5p/T09Bo5dmXNmzBBK8+uXbtKnRIREZEQwvDvb7PoZ8zc1XQ/YxcuXEC7du20lhUVFZXpsqM22LdnDyb36YOOADrOnInOTz6J7t27S50WERGRwd/fte/blSTXvHlznF+wANmTJiHLzw85n35aKwsxAHgiLAzHOnRQdW/RuTPAQoyIiEyMyd/AT9XP2toabZ2d8QiAJz098eyzz0qdUvnUnb+ePi1tHkRERFXAYox0U/cx5uAgbR6GUHf+yp74iYjIBLEYI92ys1Wv9vbS5mEIFmNERGTCWIyRbqbUMqa+THnlyn95ExERmQgWY6SbKbWMNWoENG2qeh8fDyEElEqltDkREREZiMUYlSGE+K8YM4WWMQDL6tfHWACPDh8OJycnHD9+XOqUiIiIDMJijMp4//33UW/tWrgCaDFvntZg57XVl0lJWALg8D//ICsriz3xExGRyWAxRmVkZ2cjt6QEdwD8k5qKtLQ0qVOqUMfWrbXmWYwREZGpYDFGZajHplSrV6+eRJkYrmPXrlrzLMaIiMhUsBijMkoXY3Z2dhJlYrjuzz6Ll+RyzAGw47vvsG7dOqlTIiIiMkjtHOOGJDVv3jy8d/gwcpKTkTN3Llo984zUKVWoxxNPoEdQEBATAzg5/fd0JRERUS3HljEqo3nz5uhaXIxeAPo9/TTatm0rdUqGYeevRERkgliMkW6m1OmrGosxIiIyQSzGqKyiIqCgQPXeFDp9VVMXY3FxgBCSpkJERGQoFmNUlrrDV8C0WsY6dAAsLIC7d4HkZKmzISIiMgiLMSpLXYxZWQEKhbS5VIadHaDub+z0ady5cwfFxcXS5kRERFQBFmNUlokNhaQmhMB7AHoDcBs4EK6urjh79qzUaREREZWLxRhpUSqVcA4KgjuAlpmZ8Pf3R0JCgtRpGUQmk+F/d+4gCkDKvwUlO38lIqLajsUYacnNzUVGdjaSAFwtLkZ8fDxkMpnUaRmsY5s2WvMsxoiIqLZjMUZacnNzyywzhR741UoPi3ThwgWJMiEiIjIMizHSUnooJMA0xqZU6/PCC5harx42A/h70yb8+uuvUqdERERULhZjpMXNzQ1/TpqEPQC2BAVh7dq1sLW1lTotg3Xr1g0fd++OFwC0SkuDXC6XOiUiIqJycWxK0mJra4vubm6qmTZtgJdfljahqujUCdizhz3xExGRSWDLGJWlHgrJlHrffxCHRSIiIhPCYozKUvczZqrFmL+/6jU+HigpkTYXIiKiCrAYo7JMcZDwB7VuDdjaArm5wNWrUmdDRERUrmq/Z+zu3bv4559/kJycjJycHFhZWcHZ2RnNmjVDy5YteUO1KTD1ljG5HPDzA44dQ+bhwzibmoqgoCBYWvIWSSIiqn0e+tspJycHv/zyC3bt2oUDBw7g1q1bemOtra0REBCA3r17Y8CAAejYsePDHp6MwUSHQ1IrLCzEoJQUxANIGDUKAHD+/Hm0bdtW2sSIiIh0qPJlyri4OLzyyitwc3PDsGHDsG7dOty8eRNCCL1Tfn4+YmJi8PHHHyMgIAAdO3bE0qVLdXY0StL45ptv4PH772gDIOCTT/Duu+9KnVKlKRQKHE9Px4ODOLEnfiIiqq0q3TIWFxeHqVOnYteuXQBUgzMDqv6pgoKCEBgYiMaNG6NBgwaoX78+8vLykJaWhvv37+Pvv//G8ePHER8fj6KiIpw9exbjxo3D1KlT8f777+Ott96CtbV19Z4hVUpqaipuFRSoZq5fR4tr1yTNp6o6tm2L20eOaObj4+Px4osvSpgRERGRbpUqxkaNGoU1a9ZAqVQCADp37oyXX34Zzz//PJo1a2bwfgoLC3Hw4EH89NNP2Lp1K1JTUzF58mR8++23+PHHH9G9e/fKnQVVm9I98JtS7/sP6hgSgt3/FmNyuRz379+XOCMiIiLdKnWZcvXq1bC0tMRrr72Gixcv4sSJE3jnnXcqVYgBqstIoaGhWLlyJVJSUvDjjz+iTZs2uHbtGvbu3VupfVH1MpdibNDLL+NHT0/EAchZvx7ffvut1CkRERHpVKlibNy4cbh8+TKWLl2K1q1bV0sC1tbWGDp0KM6dO4cNGzagVatW1bJfqpq3334bO52c8DOA1Z98gmHDhkmdUpUEBgZi2FNPoRMAa3b+SkREtZhMqG/6olorMzMTTk5OyMjIgKOjo/EPaG8P5OQAV64ALVoY/3jGsmQJMHYs0Lu3angkIiKiGmTo97fZdPq6ePFieHt7w8bGBsHBwTh27Fi58Zs3b4avry9sbGzg5+eHnTt3aq3fsmULevfujYYNG0Imk+GUjtaV/Px8jB8/Hg0bNoS9vT2ef/55pKSkaMUkJiYiPDwcdnZ2aNy4Md577z0UFxc/9PkajRCqzlIBwEQvUWp06aJ6PXFCdV5ERES1kFkUYxs3bkRkZCSmT5+OkydPwt/fH2FhYbhz547O+MOHD2PIkCEYPXo04uLiEBERgYiICJw9e1YTk5OTg+7du+Pzzz/Xe9x33nkHv/32GzZv3owDBw7g9u3beO655zTrS0pKEB4ejsLCQhw+fBirV6/GqlWrMG3atOo7+eqWn/9f4WJnJ20uD8vPD7CyAtLSgISEiuOJiIgkUG2XKW/fvo3Y2FhcvXoVSUlJKCoqgp2dHZo1a4bAwEAEBATAwsI4tV9wcDAeeeQRfPPNNwAApVIJT09PvPXWW/jggw/KxL/44ovIycnB9u3bNcu6du2KTp06YcmSJVqx165dg4+PD+Li4tBJPQA1gIyMDDRq1Ajr1q3DCy+8AAC4ePEi2rZti5iYGHTt2hW7du3CM888g9u3b8PV1RUAsGTJEkyePBl3796FQqHQeT4FBQUoUHcvAVUzp6enZ81cpkxNBRo1Ur0vLlb1Zm/KHnlE1TK2cSMwaJDU2RARUR1i6GXKahkfxsfHB4mJieXG2Nvbo1+/fhg5ciR69epVHYcFoOomIzY2FlOmTNEss7CwQGhoKGJiYnRuExMTg8jISK1lYWFh2LZtm8HHjY2NRVFREUJDQzXLfH190axZM00xFhMTAz8/P00hpj7O2LFjce7cOQQEBOjc9+zZszFz5kyDc6lW6kuU1tamX4gBQJcuyD9xAhd27MCZ/HwMHTrUaH8UEBERVUW1fCtdv3693J73hRDIysrCunXr0Lt3b3Tv3h2XLl2qjkMjNTUVJSUlWgUPALi6uiI5OVnnNsnJyZWK17cPhUIBZ2dnvfvRdxz1On2mTJmCjIwMzXTjxg2D83po6q4tTP0SJVStl+1//RX2ADr/+CNGjBiB69evS50WERGRlmppGWvfvj26dOmC9u3bw8PDAy4uLgBU910lJibi1KlTOHDgAP755x8AqpapwMBAbN++HT179qyOFMyKtbW1ZCMRdB4wAHkA6mVnw+7xx7Fo0SL4+/tLksvDcnR0RHJODkoeWBYfHw8fHx/JciIiIiqtWoqxM2fOGBQXHx+Pr7/+GqtXr0Zubi4iIiJw8eJFuLm5VfnYLi4ukMvlZZ5iTElJ0btfNze3SsXr20dhYSHS09O1Wsce3I+bm1uZpzrVx32YczamS9evIxcAioqAP/9Efn6+1ClVmUwmg39AAPbt369ZFh8fj/79+0uXFBERUSk1evNMx44d8cMPP2Dv3r2wt7dHVlYW5s2b91D7VCgUCAwMRHR0tGaZUqlEdHQ0QkJCdG4TEhKiFQ8AUVFReuN1CQwMhJWVldZ+Ll26hMTERM1+QkJCcObMGa2nOqOiouDo6Ih27doZfKyaolQqkVuq+DLVHvjVOj7Qqte8cWOOfUpERLWPkMgXX3whZDKZaN269UPva8OGDcLa2lqsWrVKnD9/Xrz++uvC2dlZJCcnCyGEGDZsmPjggw808X/99ZewtLQU8+fPFxcuXBDTp08XVlZW4syZM5qYe/fuibi4OLFjxw4BQGzYsEHExcWJpKQkTcwbb7whmjVrJvbu3StOnDghQkJCREhIiGZ9cXGx6NChg+jdu7c4deqU2L17t2jUqJGYMmVKpc4vIyNDABAZGRlV/ScySHZ2tgCgNV29etWoxzS2CxcuiMMDB4pMQIgJE6ROh4iI6hBDv78lK8aOHz8uZDKZsLW1rZb9LVq0SDRr1kwoFAoRFBQkjhw5olnXo0cPMWLECK34TZs2idatWwuFQiHat28vduzYobV+5cqVZQoTAGL69OmamLy8PDFu3DhRv359YWdnJwYMGKBVrAkhxLVr18TTTz8tbG1thYuLi5g0aZIoKiqq1LnVVDFWWFgotr/zjtgEiJUdOohvvvlGZGVlGfWYNWLNGiEAIbp1kzoTIiKqQwz9/pZsOKSPP/4YM2bMQP369XHv3j0pUjAZNToc0nffAePGAQMGAFu2GPdYNeXiRaBtW8DWFsjMBCyr5VZJIiKictVoP2P6DBs2DCdOnEDr1q3RtGlT1KtXD9nZ2Th+/Dji4uIgk8kQFhZmzBSossxlKKQHtW4NODgAWVnA+fNAx45SZ0RERKRh1GKsuLgYly5dwt9//621XAgBmUyG0NBQfP3118ZMgSrLjPoZ07CwAAIDgf37Vb3xsxgjIqJaxKhPU06aNAkff/wxevfuDVtbW6iviD7++OM4cuQI9uzZo+mTjGoJdTFmTi1jgPag4URERLWIUYuxLl264KOPPsKuXbtw7949bNq0CY8//jgOHjyIHj16YMWKFcY8PFWFOV6mBFASGIhLADbv3o1Zs2ZBolsliYiIyqiWYsyQLzZra2u88MIL2LdvHzZs2ACZTIbXXnsNe/furY4UqLqY4WXKW7duwWHUKPgCGJSQgGnTpiEpKUnqtIiIiABUUzEWEBCAP//80+D4QYMGYc6cORBC4LPPPquOFKga/Pbbb/DbsgVBAHquWIHx48dLnVK1aNKkCeSlnqCMj4+XKBsiIiJt1VKMxcfHo2fPnujfvz9iY2MN2kbdS33p4YJIOikpKTibkYHjAA5cuWLwZ1nbWVhYwM/PT2sZizEiIqotqqUYa9u2LYQQ2L59O4KCgtCjRw/8+OOPyMzM1LvNzp07ARh2iZNqRl5enta8ra2tRJlUP/Vg524Aeru6wtPTU9qEiIiI/lUtXVucPn0a8+bNw6efforc3FwcOnQIhw4dwquvvoqAgAAEBASgRYsWcHZ2RnZ2Ng4ePIjffvsNMpkMvr6+1ZECVYNc9c37/zKnYuyjjz7CzLAwNB4wALCyAoYMkTolIiIiAEC19sCfkpKCTz/9FN9//z0KCgpUB5DJdMaq+xr7/vvv8corr1RXCmappnrgv3jxIuKeegp5N28i98034Rkaiv79+xvteDUuJwdwdASUSuDGDcDDQ+qMiIjIjBn6/W2U4ZDS0tKwcuVKbN68GbGxsSgpKSkTY21tjSlTpmDatGnVfXizU6PDITVvDiQkAIcPA//e12dWAgKAU6eAn38Gnn9e6myIiMiMSTocUoMGDTBp0iRMmjQJWVlZOHfuHK5cuYKMjAwAgKenJ3r06AEnJydjHJ4ehrl2+qrWtauqGDtyhMUYERHVCkYfMdnBwQFdu3ZF165djX0oqg5m2umrRteuwJIlqmKMiIioFjBqD/xkYoQwy05ftaj/KIiNBYqKpM2FiIgILMboQfn5qoIMMMuWMSEEbtjYYEe9epiTl4cxgwdLnRIREVHlirEtW7YYKw8AwO3bt3GEl4+k82DXFmbYMnb58mU08/bGMzk5mAJg2ZYtuH37ttRpERFRHVepYuyFF15Ap06d8PPPP1drEjdu3MC4cePQokUL/P7779W6bzLcq+PHoxuAXjIZnh0wAHv27JE6pWrVsmVLODg4aC0zl1EGiIjIdFWqGGvRogXi4+Px4osvwsfHB//3f/+Hc+fOVenAOTk5WLt2Lfr27YsWLVpgyZIlKCkpQYsWLaq0P3p48efPIwbA3n9HU7h165bUKVUrCwsLBAQEaC1jMUZERFKr1NOU58+fx8KFCzF37lxcv34dc+bMwZw5c9CqVSt07doVjzzyCAICAtC4cWPUr18f9evXR15eHtLS0nD//n38/fffOH78OI4dO4Zjx44hPz9fMxzSc889h88++wytW7c2yolSxfLMuAd+tS5duuDEiRMIyM1FIIDH/x0miYiISCpV6vQ1Ozsb3377LRYvXowbN26odqSnp31d1Ie0trbGc889hwkTJiAoKKiyadQZNdXpa0sPD1x9oDVs27Zt5tUDP4CsrCzY2dlB3r49cOkSsH07EB4udVpERGSGDP3+rtLTlPb29nj//feRkJCAXbt2YdSoUfDy8oIQosLJ2toaPXr0wBdffIFbt27hp59+YiFWS8wdNQpLASx0d8dnn32G9u3bS51StXNwcIBcLge6dVMt+OsvaRMiIqI676E6fbWwsEBYWBjCwsIAALdu3cLhw4dx8+ZN3L17F2lpabCxsUGjRo3QqFEj+Pn5oUuXLrCysqqW5Kl6PRcYqHrTrBkwZYq0yRhb9+7AypXAoUNSZ0JERHVctfbA37RpUwwcOLA6d0k1KS9P9WqG3VqU0b276vX4caCgALC2ljYfIiKqs9jpK/1HXYyZ4Y37ZbRqBTRqpOro9uRJqbMhIqI6rNLF2M6dO9lRprmqS8WYTAY8+qjqPS9VEhGRhCp9mfKZZ56BTCaDi4sL/P394e/vj06dOqFTp07w9fVV3RxNpkndtYWZF2NKpRJHjhxBLIATAGJnzcLuIUPg4eEhdWpERFQHVemeMSEE7t69i+joaERHR2uWW1tbo127dpriTF2ole71nGqpOtQy1rdvX2RkZKhmsrIQe+IEizEiIpJEpYuxefPm4fTp0zh9+jQuXryIoqIizbr8/HzExcUhLi5Oaxtvb2+tFrROnTqhWbNmD589VZvr169j6Pffww6A7R9/wHbIEKxdu9YsWzotLCzQuXNn7Nu3T7Ms9vff0T8iQrqkiIiozqpSp69qRUVFOH/+vKY4U0/37t0re6BSncI6OTmhU6dOCAkJQc+ePdGrVy9YWPB5Al1qotPXU6dOaQ0VJJfLUVRUVKnOfE3Je++9h/nz52vm+/r5YUd8vIQZERGRuTH0+/uhurawsrLS3Df2oNu3b5cp0C5fvoySkhJNTHp6Og4cOIADBw5gzpw5cHFxwVtvvYXIyEjY1YWuFWqZPPUlyn/Z2tqabSEGAMHBwWjfvj26yOUIjI9HCFtqiYhIIg/VMlYZ+fn5OHv2LE6fPo1Tp07h9OnTiI+PR2Zm5n/JyGRo3bo1tm/fzgHDH1ATLWPR0dEIDQ3VzDdq1Ah37twxyrFqld27gaefBlq0AK5ckTobIiIyIzXSMlYZNjY26NKlC7p06aK1/O+//8bevXuxZs0axMTE4NKlSwgPD0dcXJxZDlRdW7Vu3RrfBgQgNy4Oec88A8Vjj0mdUs0ICVF1c3H1KpCUBDRpInVGRERUx0h+k1br1q3xxhtv4K+//sKGDRtgZWWFy5cv4/vvv5c6tTrF09MTY93dMQnARwMG4P3335c6pZrh5AT4+anec5xKIiKSgOTF2IMGDRqEiRMnQgiB//3vf1KnU/fUkX7GylAPjcTOX4mISAK1qhgDVJ3KAsC5c+cqve3ixYvh7e0NGxsbBAcH49ixY+XGb968Gb6+vrCxsYGfnx927typtV4IgWnTpqFJkyawtbVFaGgoLl++rFm/f/9+yGQyndPx48cBANeuXdO5/siRI5U+P6OrQ/2MaVFfkj14UNo8iIioTqp1xViDBg0AqJ62rIyNGzciMjIS06dPx8mTJ+Hv74+wsDC9N6EfPnwYQ4YMwejRoxEXF4eIiAhERETg7Nmzmpi5c+fi66+/xpIlS3D06FHUq1cPYWFhyM/PBwB069YNSUlJWtOrr74KHx+fMvfG/fHHH1pxgYGBlTq/GlFXi7EePQAAhXFxyL11S+JkiIiozhG1TFFRkThw4ID44osvKrVdUFCQGD9+vGa+pKREuLu7i9mzZ+uMHzRokAgPD9daFhwcLMaMGSOEEEKpVAo3Nzcxb948zfr09HRhbW0t1q9fr3OfhYWFolGjRuLjjz/WLEtISBAARFxcXKXO50EZGRkCgMjIyKjyPgzSurUQgBAHDhj3OLXI7t27xTvvvCO62dgIa0Asev11qVMiIiIzYej3d61rGbO0tMTjjz+Od955x+BtCgsLERsbq9U1g4WFBUJDQxETE6Nzm5iYGK14AAgLC9PEJyQkIDk5WSvGyckJwcHBevf566+/4t69exg1alSZdf369UPjxo3RvXt3/Prrr+WeT0FBATIzM7WmGlEHW8bWr1+PL7/8Eofz81EA4AgvVRIRUQ2rdcVYVaSmpqKkpASurq5ay11dXZGcnKxzm+Tk5HLj1a+V2efy5csRFhamNcahvb09FixYgM2bN2PHjh3o3r07IiIiyi3IZs+eDScnJ83k6empN7a6LFmyBH2Tk/E8gKEzZ2LlypVGP2Zt0LVrV635I//8I1EmRERUV9VYP2Pm7ubNm9izZw82bdqktdzFxQWRkZGa+UceeQS3b9/GvHnz0K9fP537mjJlitY2mZmZRi/Izpw5g13qcUZ37ICDp6fOFj5zExwcrDV/tbAQaVevogE7HSYiohpiFi1jLi4ukMvlSElJ0VqekpICNzc3ndu4ubmVG69+NXSfK1euRMOGDfUWWA8KDg7GlXJ6e7e2toajo6PWZGy56m4t/lVXhqTy8/NDv379MGPGDOz28EAagAYPPMRBRERkbGZRjCkUCgQGBiI6OlqzTKlUIjo6GiEhITq3CQkJ0YoHgKioKE28j48P3NzctGIyMzNx9OjRMvsUQmDlypUYPnw4rKysKsz31KlTaFLLenrPy8nRmq8rox9YWlril19+wfTp0xH2zDOoDwD79kmdFhER1SFmc5kyMjISI0aMQJcuXRAUFISFCxciJydHc6lt+PDhaNq0KWbPng0AmDBhAnr06IEFCxYgPDwcGzZswIkTJ7Bs2TIAqnEyJ06ciE8++QStWrWCj48Ppk6dCnd3d0RERGgde+/evUhISMCrr75aJq/Vq1dDoVAgICAAALBlyxasWLECP/zwgxH/NSpv2PPPo/PmzcgDkPfuu3j88celTqnmPfEEsGQJsH+/1JkQEVEdYjbF2Isvvoi7d+9i2rRpSE5ORqdOnbB7927NDfiJiYmwsPivIbBbt25Yt24dPvroI3z44Ydo1aoVtm3bhg4dOmhi3n//feTk5OD1119Heno6unfvjt27d8PGxkbr2MuXL0e3bt3g6+urM7dZs2bh+vXrsLS0hK+vLzZu3IgXXnjBCP8KVRf++OMIB1TjNM6dq3qta/7tbwzx8UBaGvBvn3dERETGJBNCCKmToPIZOur7Q/nnH6BFC8DODih1ybJOadcOuHAB2LoVKNUCSkREVBmGfn+bxT1jVA3qYB9jOj3xhOqV940REVENYTFGKupirI48RamP6NEDVwDs++03qVMhIqI6gsUYqdTxlrHz589j4MCBcH/rLbQC8FJCAoSezn2JiIiqE4sxUqnjxZilpSV+/vlnJP87sHwygH/Wr5c2KSIiqhNYjBEAYNDMmRgEYMStW3jjjTdw7do1qVOqUa1atULjxo21lv35v/9JlA0REdUlLMYIALDlyBFsBvBjaiqWLl2K9PR0qVOqUTKZDI899phm3hVA7tmzAB82JiIiI2MxRigqKkKJUqm1rK70wP+gMWPGYPny5fg7Ph5JCgXGZWQAFy9KnRYREZk5s+n0laouT32/2APqYjH21FNP/TfTowcQFQX8/jvQtq10SRERkdljyxjB0tISnz39NKYCmNS2LcaNGwdnZ2ep05KWujCLipI2DyIiMntsGSPY2dlhSkgIsGsX8NhjwOLFUqckPXUxtn8/UFgIKBSSpkNEROaLLWOkUse7tiijY0egUSPV0FBHjkidDRERmTEWY6TCYkybhQUQGqp6z0uVRERkRCzGSIXFmJacnBz83qQJPgAQ/fPPUqdDRERmjPeMkUpuruqVxRgmT56ML7/8EkVFRQCAjIsX0SstDWjQQOLMiIjIHLFljFTYMqbRqFEjTSEGANGAqosLIiIiI2AxRjh8+DBePnwYowGM37IF8+bNkzolST355JNa85cB3Ni0SZpkiIjI7LEYI1y5cgXrbt/GCgDf7tuH9XV8gGx/f3/Ur18fcrkcIe3b4/8AyPfvB0pKJM6MiIjMEe8ZI+Tn52vN29jYSJRJ7SCXyxEVFYXWrVvDwcZG1cXF/fvAsWNASIjU6RERkZlhyxixGNMhMDAQDg4OgJUVEBamWrhzp7RJERGRWWIxRggMDMSUhg0xEcAb/frhmWeekTql2iU8XPW6Y4e0eRARkVmSCSGE1ElQ+TIzM+Hk5ISMjAw4Ojoa5yDNmwMJCUBMDNC1q3GOYaru3AHc3AAhgFu3AHd3qTMiIiITYOj3N1vGSEV9qZKXKMtq3Bh45BHVe16qJCKiasZijFRYjJUvPBwlAEp4qZKIiKoZizFSKShQvbIY05KcnIzVq1dj8KFDaAQgevfu//6tiIiIqgG7tiDVvVBsGdPpueeeQ0xMjGZ+V34+eu/f/98TlkRERA+JLWMEFBcDSqXqPYsxLX369NGa3wUAW7dKkgsREZknFmOEr774AmMATAAwedYsHDx4UOqUao3SxdglADe2bPmveCUiInpILMYIu/bswTIAXwOY+8UXOH78uNQp1RpdunRBixYtMGDAACz79lsk2tvD8+5d4OhRqVMjIiIzwXvGCPl5eVrz7IH/PxYWFrh8+TJkMplqwZ9/AuvXqy5VcmgkIiKqBmwZIxZjFdAUYgAQEaF63bpV9eADERHRQ2LLGGFwWBiCTp9Gvo0N8l54Aa1bt5Y6pdrr6acBa2vgyhXg/HmgfXupMyIiIhPHYowwceBAYO5cVU/za9ZInU7t5uAAhIaqxqncupXFGBERPTRepqT/+hiztpY2D1MxYIDqdds2SdMgIiLzwGKM2OFrJaX36IH1MhnOxsYC169LnQ4REZk4FmPEYsxAP//8M3r37o1GbdviJSGwAgA2b5Y6LSIiMnFmVYwtXrwY3t7esLGxQXBwMI4dO1Zu/ObNm+Hr6wsbGxv4+flh586dWuuFEJg2bRqaNGkCW1tbhIaG4vLly1ox3t7ekMlkWtOcOXO0YuLj4/HYY4/BxsYGnp6emDt3bvWccHVhMWaQs2fPIioqCsXFxQCAbQDE+vWS5kRERKbPbIqxjRs3IjIyEtOnT8fJkyfh7++PsLAw3LlzR2f84cOHMWTIEIwePRpxcXGIiIhAREQEzp49q4mZO3cuvv76ayxZsgRHjx5FvXr1EBYWhnx18fKvjz/+GElJSZrprbfe0qzLzMxE79694eXlhdjYWMybNw8zZszAsmXLjPMPURUsxgwSoe7W4l8JAM6cPKl6spKIiKiqhJkICgoS48eP18yXlJQId3d3MXv2bJ3xgwYNEuHh4VrLgoODxZgxY4QQQiiVSuHm5ibmzZunWZ+eni6sra3F+vXrNcu8vLzEl19+qTevb7/9VtSvX18UFBRolk2ePFm0adPG4HPLyMgQAERGRobB2xgqPz9fjHviCREJiA9bthQff/yxSE9Pr/bjmAOlUim8vLwEAGFjYyOeb9xYnAGE+OQTqVMjIqJayNDvb7NoGSssLERsbCxCQ0M1yywsLBAaGoqYmBid28TExGjFA0BYWJgmPiEhAcnJyVoxTk5OCA4OLrPPOXPmoGHDhggICMC8efM0l7HUx3n88cehUCi0jnPp0iXcv39fZ24FBQXIzMzUmowlOzsb3+7bhy8AfHblCqZNm4bc3FyjHc+UyWQyTJ06FWvWrEFKSgp+njMHHQBg40apUyMiIhNmFv2MpaamoqSkBK6urlrLXV1dcfHiRZ3bJCcn64xPTk7WrFcv0xcDAG+//TY6d+6MBg0a4PDhw5gyZQqSkpLwxRdfaPbj4+NTZh/qdfXr1y+T2+zZszFz5swKz7s6lL7kCrAH/vKMHj36v5mICGDMGODMGVUHsO3aSZYXERGZLrNoGZNSZGQkevbsiY4dO+KNN97AggULsGjRIhQUFFR5n1OmTEFGRoZmunHjRjVmrE1XMWZra2u045mV+vWBPn1U79k6RkREVWQWxZiLiwvkcjlSUlK0lqekpMDNzU3nNm5ubuXGq18rs08ACA4ORnFxMa5du1bucR48RmnW1tZwdHTUmoylXr16GBsYiJEABrdqhf79+2tdUqUKvPii6nXDBo5VSUREVWIWxZhCoUBgYCCio6M1y5RKJaKjoxESEqJzm5CQEK14AIiKitLE+/j4wM3NTSsmMzMTR48e1btPADh16hQsLCzQuHFjzXEOHjyIoqIireO0adNG5yXKmubm5oZvn3gCKwGs798f27Ztg4WFWfxY1Ix+/VRPof79N3DypNTZEBGRCTKbb93IyEh8//33WL16NS5cuICxY8ciJycHo0aNAgAMHz4cU6ZM0cRPmDABu3fvxoIFC3Dx4kXMmDEDJ06cwJtvvglAdbP2xIkT8cknn+DXX3/FmTNnMHz4cLi7u2u6OIiJicHChQtx+vRp/PPPP/jpp5/wzjvvYOjQoZpC66WXXoJCocDo0aNx7tw5bNy4EV999RUiIyNr9h+oPOzaouocHID+/ZELAD/+KHU2RERkimro6c4asWjRItGsWTOhUChEUFCQOHLkiGZdjx49xIgRI7TiN23aJFq3bi0UCoVo37692LFjh9Z6pVIppk6dKlxdXYW1tbXo1auXuHTpkmZ9bGysCA4OFk5OTsLGxka0bdtWfPbZZyI/P19rP6dPnxbdu3cX1tbWomnTpmLOnDmVOi9jdm0hhBDitdeEYBcNlXb37l2xZMkS0bNjR9EUEEUNGwrxQBcmRERUtxn6/S0Tgje61HaZmZlwcnJCRkaGce4fGz4cWLMGmD8fmDSp+vdvhm7evAlvb2+UlJRolu0A0HfbNqB/f8nyIiKi2sPQ72+zuUxJD0F9mdLaWto8TIiHhwc6d+6stWwVAKxeLUU6RERkwliMEe8ZqyL1/YhqRwAU/vYbcO+eNAkREZFJYjFWxx0+fBiTz5zBdABzoqKwkf1lGWzw4MFwcHDAgAED8Ouvv+Jqp05QFBcDHDyciIgqwSx64Keqi42Nxdx/+0TDpk144u5dvKjuO4vKVb9+fSQlJaFevXqqBf/8A0ycqLpU+e9TuURERBVhy1gdV7oHfg6FVDmaQgwAXnoJsLQETpxQDZFERERkABZjdVxeXp7WPIuxh9CokaoTWABYulTaXIiIyGSwGKvj/Pz8MNTBAS8AeKZbN3Tp0kXqlEzbG2+oXtesAXJypM2FiIhMAvsZMwFG72fMywtITASOHQMeeaT691+XKJVAq1aq+8eWLwdeeUXqjIiISCLsZ4wMx64tqs2NW7fwkZcXegMQS5ZInQ4REZkAFmPEYqwapKWlYcCAAfD29san+/YhCsDh48eBU6ekTo2IiGo5FmPEYqwaODs748yZM1AqlZpliwHeyE9ERBViMVbXCQEUFqresxirMgsLC4wdO1Zr2VYA99esATIzpUmKiIhMAouxuq6g4L/3LMYeyqhRo2BjYwNbW1uMHzcO55o3R/2cHGDlSqlTIyKiWozFWB33w7Jl+ATAfADfrFiB8+fPS52SyWrQoAH+97//ITExEd8sXozm772nWvH110BJibTJERFRrcWuLUyAMbu26BoYiKMnT2rmf/jhB4wePbpaj1Fn5eYCHh7A/fvA1q1ARITUGRERUQ1i1xZkkHz2wG88dnbAmDGq9wsXSpoKERHVXizG6jiOTWlk48erxqs8cACIi5M6GyIiqoVYjNVxvYODEQGgj7U1evbsCTc3N6lTMi8eHsDAgRAAlGwdIyIiHViM1XFfT5yIrQB2ubtj3759ePTRR6VOyezs694dPQCs+ukn4MYNqdMhIqJahsVYXccOX43mxIkTeOKJJ/Dk+PH4E8AnJSUomjtX6rSIiKiWYTFW16mLMWtrafMwQ/fu3cP+/fs18wkAVi9dCty5I1lORERU+7AYq+vYMmY0vXv3RkhIiNayX4qKgK++kigjIiKqjViM1XUsxoxGJpNh5syZAAA3Nzf8MH48tgHAN98A6ekSZkZERLUJi7G6jpcpjSo0NBTff/89Ll++jNFffw15+/aqsSq//Vbq1IiIqJZgMVaHZWZmYva2bfgSwJKkJKxatQqF6kHDqVrIZDK8+uqrsLe3BywsgClTVCsWLOAA4kREBIDDIZkEYw2HdPXqVbRs2VJrWW5uLmxtbavtGFRKcTHQoQNw6RIwYwYwfbrUGRERkZFwOCSqUOne9wH2wG90lpbArFmq9wsWAKmp0uZDRESSYzFWh5UuxqytrSGTySTKpg55/nmgUyckZ2Xh2MSJUmdDREQSYzFWh9nb2+OZVq0QCqB7kybo2rWr1CnVCSVCYHFICHwBvPDTT8i+fFnqlIiISEIsxuqwNm3a4LfnnkMUgD8HD9bqoJSMIy0tDV27dsWb332HDAA3AMx84QWp0yIiIgmxGKvr1E9PKhTS5lFH1K9fH05OTlrLvoyPx+n//U+ijIiISGosxuq6ggLVK/sZqxEymQyLFy+G4oHidwyAFosXA3ywmYioTmIxVtexGKtxbdq0wZQpU+Dh4YHfV63CYoUC9vv2ATt2SJ0aERFJgMVYXcdiTBIffvghzpw5g6dGjADUT1ROmvTfZWMiIqozWIzVdepijPeM1SiFQgFnZ2fVzP/9H9C4MfD336pxK4mIqE4xq2Js8eLF8Pb2ho2NDYKDg3Hs2LFy4zdv3gxfX1/Y2NjAz88PO3fu1FovhMC0adPQpEkT2NraIjQ0FJcf6Ibg2rVrGD16NHx8fGBra4sWLVpg+vTpWkMKXbt2DTKZrMx05MiR6j35Kjh+/DgWXbyI7wGsjYvDoUOHpE6pbnJ0BD79VPV++nTg5k1p8yEiohplNsXYxo0bERkZienTp+PkyZPw9/dHWFgY7ty5ozP+8OHDGDJkCEaPHo24uDhEREQgIiICZ8+e1cTMnTsXX3/9NZYsWYKjR4+iXr16CAsL03SWevHiRSiVSixduhTnzp3Dl19+iSVLluDDDz8sc7w//vgDSUlJmikwMNA4/xCVsHv3brx95gxeBzBs5UosWLBA6pTqrldeAUJCgOxsZI8bh71790qdERER1RRhJoKCgsT48eM18yUlJcLd3V3Mnj1bZ/ygQYNEeHi41rLg4GAxZswYIYQQSqVSuLm5iXnz5mnWp6enC2tra7F+/Xq9ecydO1f4+Pho5hMSEgQAERcXZ/C55Ofni4yMDM1048YNAUBkZGQYvA9DfPjhhwKAZhoyZEi17p8qKT5exMvlog0grK2sxKlTp6TOiIiIHkJGRoZB399m0TJWWFiI2NhYhIaGapZZWFggNDQUMTExOreJiYnRigeAsLAwTXxCQgKSk5O1YpycnBAcHKx3nwCQkZGBBg0alFner18/NG7cGN27d8evv/5a7vnMnj0bTk5OmsnT07Pc+KrKy8vTmue4lNJaeeIEgmUyXAJQUFSEARERSOXYlUREZs8sirHU1FSUlJTA1dVVa7mrqyuSk5N1bpOcnFxuvPq1Mvu8cuUKFi1ahDFjxmiW2dvbY8GCBdi8eTN27NiB7t27IyIiotyCbMqUKcjIyNBMN27c0Bv7MFq0aIEnHBzQFUCn5s3h7e1tlOOQYU6fPo284mLNfMK1a5gwYYKEGRERUU2wlDoBc3Hr1i306dMHAwcOxGuvvaZZ7uLigsjISM38I488gtu3b2PevHno16+fzn1ZW1vDuga6mhg/fjzGL10KnDkDLF0KlGoppJo1d+5cHDlyBEePHgUAdAWwoH9/aZMiIiKjM4uWMRcXF8jlcqSkpGgtT0lJgZubm85t3Nzcyo1Xvxqyz9u3b+OJJ55At27dsGzZsgrzDQ4OxpUrVyqMqxHsZ6zWUCgU2Lp1K5o2bYqhrVtjHwC3SZOA9HSpUyMiIiMyi2JMoVAgMDAQ0dHRmmVKpRLR0dEICQnRuU1ISIhWPABERUVp4n18fODm5qYVk5mZiaNHj2rt89atW+jZsycCAwOxcuVKWFhU/E966tQpNGnSpFLnaDQsxmqVJk2a4Pjx4/gxNhY2LVuqurl4+22p0yIiIiMym8uUkZGRGDFiBLp06YKgoCAsXLgQOTk5GDVqFABg+PDhaNq0KWbPng0AmDBhAnr06IEFCxYgPDwcGzZswIkTJzQtWzKZDBMnTsQnn3yCVq1awcfHB1OnToW7uzsiIiIA/FeIeXl5Yf78+bh7964mH3Xr2erVq6FQKBAQEAAA2LJlC1asWIEffvihpv5pysdirNbRFOo//gh07w6sWQM8+ywwcKC0iRERkVGYTTH24osv4u7du5g2bRqSk5PRqVMn7N69W3MDfmJiolarVbdu3bBu3Tp89NFH+PDDD9GqVSts27YNHTp00MS8//77yMnJweuvv4709HR0794du3fv1jx1GBUVhStXruDKlSvw8PDQykc8MOjzrFmzcP36dVhaWsLX1xcbN27ECy+8YMx/DsOpO6hlD/y1T0gI8MEHwGefAa++CnTuDNG8OS5dugRfX1+psyMiomoiEw9WDVQrZWZmwsnJCRkZGXB0dKzendvbAzk5wNWrQPPm1btvenhFRcATTwB//QXRqRPe79kTi777Dlu2bEHfvn2lzo6IiMph6Pe32bSMUeVt3rwZ2Xl5sAVgs28fgmxs4O7uLnVa9CArK2DDBohOnfDRqVOYf+oUACAiIgKbN29Gfz5tSURk8sziBn6qmmnTpuEVpRJDAAx49VUcPnxY6pRIFw8PbB07Fp89sKioqAjDhw9HOp+0JCIyeSzG6rC83FytefbAX3v1nzEDw/38NPMymQyrVq2Cs7OzdEkREVG1YDFWh6kHPFeztbWVKBOqiFwux8qTJ/GqlxcAYKG9PQbUgsHmiYjo4bEYq8M6+/mhC4AOUA2NVO0PB1C1srC0xNL4eGzz8sLbWVlAv35AdrbUaRER0UPi05QmwGhPU964ATRrpurWQt3fGNV+168DQUHAnTtAWBjw669aXZNkZWXBwcFBwgSJiAgw/PubLWN1GTt8NU1eXsAvvwB2dsCePcDIkYBSCUA1uoO3tzdWrFgB/p1FRGQaWIzVZepijB2+mp6uXYH//Q+wtATWrwcmTEDavXt47rnnkJaWhtGjR2PQoEG4d++e1JkSEVEFWIzVZere99kyZpr69AFWrwYAlHzzDV4OCkJCQoJm9c8//4y1a9dKlR0RERmIxVhdxsuUpu+ll4BvvoESQMt//tFa9fjjj+PNN9+UJi8iIjIYi7G6jMWYeRg/HlaLFmERgC0AGtrYwMnJCWvWrIFcLpc6OyIiqgCLsTrq/v37WLNjBzYD2F5QgD/++EPqlOhhvPkm8N13GAAgPj8fW7p1Q7Nyhra6c+dOzeVGRETlYjFWRyUkJGD4vHkYBODZhASEh4dLnRI9rDfeAH74Ae4WFnhy1y6gf3+d/ZBdvXoVXl5eePXVV5GUlCRBokRE9CAWY3VUXl6e1jyHQjITo0cDW7YAtrbAzp3AE08AKSlaIZMnT0Z+fj6WL1+OVq1aYd68eRIlS0REAIuxOqv0UEgsxsxI//7A3r2Aiwtw4gTQpQtw/DgA4NChQ/jf//6nCc3JyUFRUZFUmRIREViM1Vk2Njbo1KwZfAF429rC09NT6pSoOnXtChw+DLRpA9y8CTz2GLBiBa5evYp69eppwurXr88nLomIJMZirI569NFHETdlCi4ASAgLw4kTJ6ROiapbq1bAsWOqlrKCAmD0aIz46y9cPn0ao0ePhkwmQ2RkpN4hOnJzc3Ho0CH25E9EZGQsxuoydvpq/hwdVfeQzZoFyGTA99+jSXg4fhg7FufOncPbb7+td9O1a9fiscceQ+fOnfHNN9/g/v37NZg4EVHdwWKsLmM/Y3WDhQXw0UfA778D7u7ApUtA165o+8svcLSz07mJEAILFy4EoBrv8q233sI777xTg0kTEdUdLMbqMhZjdUtoKBAfDzz3HFBcDEyZAgQHAydPlgn9/fffceHCBa1lo0aNqqlMiYjqFBZjdRmLsbqnYUPg55+BFSsAZ2dVIfbII0BkpFafZPn5+fDx8dHMt2zZEo8//rjOXQohMGPGDOzduxeF6kvfRERkMBZjdZm6GFMopM2DapZMBowaBVy4AAweDCiVwJdfAq1bA8uXAyUl6N+/Py5fvow9e/Zg0KBBGDt2LGQymc7dnTx5EjNnzkSvXr3g4uKCgQMHsigjIqoEFmN1VHx8PLZduIDdAPYnJ+Py5ctSp0Q1zc0NWL8e2LULaNECSEoCXn0V6NQJ2L0bcgsL9O7dGxs3bkRkZKTe3WzcuFHzPisrC5cvX4aCBT4RkcFYjNVRP/74IwZs346nATyxbh0+++wzqVMiqfTpA5w/r2odq18fOHsWePpp4NFHVYVaOV1bCCGwadMmrWXlDa3122+/4f3338e2bds4FBMR0b9YjNVRHA6JtCgUwMSJwNWrqvvHbGyAmBigb18gKAjYuhUoKSmzWUFBAUaNGoUuXbpolpVXjG3YsAHz5s3DgAED4O7ujsmTJxvjbIiITAqLsTqq9HBItra2EmVCtUr9+sCCBUBCAjBpEmBnpxpS6bnnVJcy584F7t3ThNvY2GD69Ok4fvw4kpKSsHLlSgQHB+vctRAC+/bt01rWtm1bvals27YNu3btQlJSEjueJSKzxmKsjnJxcUFLe3t4AHCxt4eTk5PUKVFt4uYGzJ8PXLsGfPgh0KABcP06MHky4OGhegBg/37Vzf+aTdwwcuRIyOVynbv8+++/y1ya7Nq1q94UJk+ejL59+8Ld3R2urq7Yu3dvdZwZEVGtIxP8k7PWy8zMhJOTEzIyMvQOXVMl/foBv/0GfP+96sZtIn3y8oANG4BFi4C4uP+WN2sGDBsGDB0K+PqWu4ubN29i2bJlOHz4MI4dOwa5XI579+7BwqLs34Q5OTlwcHDQahE7deoU/P39de574sSJsLe3h4+PD3x8fBAcHKw1BicRkRQM/f5mMWYCjFaMhYWpemX/8UfVFypRRYRQ3Uu2ahWwcSOQmfnfunbtgIgIYMAAIDBQ1YWGHiUlJbh58ya8vLx0rj9y5AhCQkK0luXk5MBOx4gBBQUFsLOzg/KBVrpz586hXbt2OtIXiI6Ohru7Ozw8PKr394mIqBRDv795mbIuY6evVFkyGdCtG7BsGZCcrCrI+vYFLC1VT2R+9pmqE9lmzYDXXwc2bQJSU8vsRi6X6y3EAKC4uBjdunXTtG55eXnpLMQA4MqVK1qFGAB4e3vrjM3IyMBTTz2F9u3bw8nJCQ4ODrhx44bO2JKSEpw/fx6pqall9k9EVJ0spU6AJMROX+lh2NoCgwappvR0YOdO1VOXu3YBN2+qLn9//70qNiAA6NUL6N4d6NoVcHUtd9fdu3fHX3/9BaVSiX/++QfJycl6Yy9evKg137hxY72F261bt7Tms7Oz0ahRI52xd+/eRfv27QEAFhYWaNSoEc6dO4eGDRuWiS0sLMS+ffvQoEED1K9fX/Oqr6NcIqIHsRiry9S9pLNljB6WszPw0kuqKT8f2LsX+OMP1XTmjOo+s7g41UMBAODtrSrKQkKAzp0BPz9Ax0MkFhYWaNmyJVq2bKn30N7e3pg4cSISEhLwzz//wLWcQu/mzZta8y4uLnq7dblz547mvVKpxJ07d/Q+6JKUlIQ+ffpoLUtPT9cZn5mZiVmzZsHBwQGOjo5wcHDA0KFDYc3fQ6I6i8VYXcbLlGQMNjaqS5d9+6rmU1JUxdm+far7zc6dUz2lee2a6qEANS8voGNH1eTnB7RpA7RsCdjbl3u4wMBABAYGGpRabm4uGjRogLS0NABA06ZN9cY+WIwBQMOGDWFpqfu/zPv372vNy+VyvfeH3L17F/PVRem/hgwZojM2NTUVzZo10xRtDg4O2L9/v8595+fnY8GCBbCzs9NMzz//vM5WQiEEsrKyYGNjAysrK7bgEUmMxVgdFR0dDXH/PmwA2CQkoHVmJm9mJuNwdQWGDFFNgOqm/+PHVYXZ0aPA6dPAjRuqrjOuX1c94fugJk1URVmrVqrJ2xvw9FR1seHuDlhZGZzKgAEDMGDAAOTl5eH27dtlOj9+kLpgU2vcuLHBsc7OznoLnMwHH3qAqnDT189fZmYm8vLykJeXh5SUFADQO9RURkYGPvroI61lffr00VmMZWVlabXa2djY4PLly/Dw8CgTW1JSgj59+sDa2ho2NjawtrbGvHnz4O7urjOPxYsXw9LSEgqFAlZWVggPD0f9+vV1xp4+fRpyuRxWVlawsrJC06ZN2UJIdZJZPU25ePFizJs3D8nJyfD398eiRYsQFBSkN37z5s2YOnUqrl27hlatWuHzzz9HX/Vf81D99Th9+nR8//33SE9Px6OPPorvvvsOrVq10sSkpaXhrbfewm+//QYLCws8//zz+Oqrr2D/wF/z8fHxGD9+PI4fP45GjRrhrbfewvvvv2/weRnjacomTZpo3YcTFRWF0NDQatk3UaXdv6+6nHn6NBAfrxqS6fJlrQ5mdZLJVH2iqYuzJk2Axo2BRo1U04PvGzQAdHSjUZ7CwkKkpqYiJSUFRUVFev8/+f333zFixAikpaWhsLAQLVu21Dve68GDB9GjRw/NvLOzc5mWNbXTp0+jU6dOD5yuDCUlJToLvYSEBDRv3lxrWXZ2ts4uPu7evVumuExJSdFZcObm5pbZx9WrV8scC1D9n1m6q5KzZ89q7r0rzc7OTqsgPnLkiN5Og728vJCenq4p3LZu3aq3n7p+/frh7t27sLS0hFwux+eff653vx988AFSUlI0sWPGjEFAQIDO2OXLl2vtt0+fPno7Lt6zZw9SU1NhYWEBCwsLPPLIIzr/zQAgLi4O9+/f18S2aNFCb6vtjRs3kJ2drYl1cXHRW+xmZ2ejqKgIFhYWkMvlUCgUHDe2hhn8/S3MxIYNG4RCoRArVqwQ586dE6+99ppwdnYWKSkpOuP/+usvIZfLxdy5c8X58+fFRx99JKysrMSZM2c0MXPmzBFOTk5i27Zt4vTp06Jfv37Cx8dH5OXlaWL69Okj/P39xZEjR8Sff/4pWrZsKYYMGaJZn5GRIVxdXcXLL78szp49K9avXy9sbW3F0qVLDT63jIwMAUBkZGRU4V9GN2dnZwFAM/3555/Vtm+iapOWJsSxY0L89JMQM2YIMXSoEI8/LoSPjxBWVkKoOtswbLKwEMLFRYgWLYTo3FmIJ54QIiJCiBEjhJgwQYhp04RYsECIH34QYsMGIX79VYg//hDi8GEhTp0S4vJlIW7dEuL+fSEKCoRQKsukq1QqRU5Ojrhz547eUzpz5owYPny4iIiIEL169RLPPvus3tiDBw9q/Z7Wq1ev3P0+GAtAlJSU6IxNTEwsE5uenq7nI0grE3vr1i2dsQUFBWViL126pDdnS0tLrdiTJ0/qjXVyctKKPXTokN5Yd3d3rdg9e/bojW3ZsqVW7JYtW/TGdurUSSt27dq1emNDQkK0YpctW6Y3NjQ0VCv2yy+/1Bvbv39/rdhPP/1Ub+yQIUO0Yj/88EO9saNHjxYAhIWFhZDL5eLdd9/VG/vee+8JJycn4ezsLBo0aCAiIyP1xs6ePVt4enqKZs2aCW9vb/HOO+/ojV2yZIlo37696NChg+jYsWO5sevXrxchISGiW7duonv37uXmsGPHDtGnTx/x9NNPi759+4r33ntPb2x1M/T722wuU37xxRd47bXXMGrUKADAkiVLsGPHDqxYsQIffPBBmfivvvoKffr0wXvvvQcAmDVrFqKiovDNN99gyZIlEEJg4cKF+Oijj9C/f38AqsG1XV1dsW3bNgwePBgXLlzA7t27cfz4cc3YfIsWLULfvn0xf/58uLu746effkJhYSFWrFgBhUKB9u3b49SpU/jiiy/w+uuv19C/Tlkcm5JMQv36qq4yHnmk7DqlErh7V/Xk5o0bqiklRbXszh3Vq/p9eroqPjVVZ1cbVSKXq4aLsrNTPZGsUECmUMDu3wl6pg4KBVZbW6ta8iwtVfuZPFn1Kpf/t0wuR6fiYhx9+21kFhYiq6gIhUIAS5eWiYNcDtu7d9E/KAi5BQXIKShAiVIJi507Va2HpaaC27fLnI7N0aOq+0dLxebraJ20Pn8eSErSjrWwQJGOy75W//yjelioVGueEALFxcXasYmJ/93DWiq+SP3A0b8sb94E1E/SlootVt8Pq/6okpKAv//+b8ED8SWlhoazvHMHuHJF+yT+jS/OzdXeb2oq8M8/OmOVpf4tLNLSVPdJliaTQVlqvxbp6apL9jqUZGdrx2Zk6I1VZmVpx2Zl6Y/99/K5uhsXZTk55KakICMjQzOfk5ysN/b+tWta3cfcvXZNb2zKpUs4d+6cZr6lu7ve2FtnzyImJkYzX8/CQm9sYlwcdu/erZnPvHtXd2yzZuX2j2hUNVIaGllBQYGQy+Vi69atWsuHDx8u+vXrp3MbT0/PMn99TJs2TXTs2FEIIcTVq1cFABEXF6cV8/jjj4u3335bCCHE8uXLhbOzs9b6oqIiIZfLNX9dDRs2TPTv318rZu/evQKASEtL05lbfn6+yMjI0Ew3btyo1pYxpVIpfHx8hBsgnAFhY22t1SJIZHYKC4W4fVuIM2eEOHRIiB07hFi3TohvvxVi9mwhPvhAiLFjhXjpJSHCw4Xo2VOIoCAhOnQQonlzIVxdhXBwULWuVaY1rpZORYC4Doi/AREPiOOAUOqJzQTEl4CYDYgZgPgAEHl6YrMA0QMQ3QDxCCD8AZGkJ7YQEJalWtEulpOzVanYE+XENigVu7+c2GalYneUE9u2VOzmcmK7lIpdWU5sj1Kx35QT27dU7OflxA4sFTutnNiRpWInlRM7rlTsG+XEvlcqdng5sTNKxT5fTuzcUrF9yoldXCr2MX2xBQXV/l9PnWoZS01NRUlJSZlH2l1dXcv0QaSWnJysM159H5X6taKY0vdYWFpaokGDBloxPj4+ZfahXqfrWv/s2bMxc+ZM/Sf8kGQyGf755x9VdwS5uapBoZs0MdrxiCRnZaX6GX/Yn3MhgKIi1e/Ng1NhoWFTQYH2fFERUFKifyouLn+9rqn0V4yybJllKQSaVRCjnhyEwMQKYtSTvVKJ/fr+3Up/JACKhIAQAsUAigDYAKqWCR3xh4uLUahUoghAIYBWlpZ6Y78uKECuECgBUAygpZXVf/cLloofk5+PNHWsEPBWKFStjTpy75mfj+ZKpWa/buXEts7PR5EQKBECSgDOVlaq1kwd/y71CwrQWKmEEkAJABtdsf9SFhRojQlrYWmp9yGW0rHy8mILC1U/P/+SlRMrSsfK5Xr7qxRFRaqfYwNilaVjLSz0Pu1fZr/lxRYXq37XDIiVilkUY+ZmypQpiIyM1MxnZmbC09Oz+g+Unl79+yQyZzLZf5ccnZ2lzsYsyKAqzCp6JrZLJfb5ciViP6xE7LeViP2pErFbKxG7C6pLierJwsJCb+H2/f37+DovTxPr6Oio9+f205s38e79+xBCQKlUqjpD1vMQwbv//IOXk5I0sU2aNFE96azD6IsX8WRCgibWw8MDeOChlAcNPHsW7c6dg1KphBBC9b332GM6Y8NOn0b9Y8e0Y8PDdcZ2i4vDvOhoiH+Lfw8PD1WfiLWIWRRjLi4ukMvlmke/1VJSUuDm5qZzGzc3t3Lj1a8pKSmqH7QHYtRPN7m5uZXpi6i4uBhpaWla+9F1nAePUZq1tTUf7yYiIp3UT1JWpH79+nqftCzNw8NDZ9cmujRv3lzvk6Gl+fr6wtfX16DYDh06oEOHDgbF+vv7w9/f36DYgIAAvU/I1hZmMTalQqFAYGAgoqOjNcuUSiWio6PLDDasFhISohUPqLp3UMf7+PjAzc1NKyYzMxNHjx7VxISEhCA9PR2xsbGamL1790KpVGoeow4JCcHBgwdR9EATaVRUFNq0aWPwLwkRERGZsWq/W00iGzZsENbW1mLVqlXi/Pnz4vXXXxfOzs4iOTlZCKG6kf6DDz7QxP/111/C0tJSzJ8/X1y4cEFMnz5dZ9cWzs7O4pdffhHx8fGif//+Oru2CAgIEEePHhWHDh0SrVq10uraIj09Xbi6uophw4aJs2fPig0bNgg7OzvJu7YgIiIi4zL0+9tsijEhhFi0aJFo1qyZUCgUIigoSBw5ckSzrkePHmLEiBFa8Zs2bRKtW7cWCoVCtG/fXuzYsUNrvVKpFFOnThWurq7C2tpa9OrVq0yfOffu3RNDhgwR9vb2wtHRUYwaNUpkZWVpxZw+fVp0795dWFtbi6ZNm4o5c+ZU6rxYjBEREZkeQ7+/zaoHfnNljB74iYiIyLgM/f42i3vGiIiIiEwVizEiIiIiCbEYIyIiIpIQizEiIiIiCbEYIyIiIpIQizEiIiIiCbEYIyIiIpIQizEiIiIiCbEYIyIiIpKQpdQJUMXUgyRkZmZKnAkREREZSv29XdFgRyzGTEBWVhYAwNPTU+JMiIiIqLKysrLg5OSkdz3HpjQBSqUSt2/fhoODA2QyWbXtNzMzE56enrhx44ZZjnlp7ucHmP85mvv5AeZ/jjw/02fu52jM8xNCICsrC+7u7rCw0H9nGFvGTICFhQU8PDyMtn9HR0ez/AVTM/fzA8z/HM39/ADzP0een+kz93M01vmV1yKmxhv4iYiIiCTEYoyIiIhIQizG6jBra2tMnz4d1tbWUqdiFOZ+foD5n6O5nx9g/ufI8zN95n6OteH8eAM/ERERkYTYMkZEREQkIRZjRERERBJiMUZEREQkIRZjRERERBJiMWbmFi9eDG9vb9jY2CA4OBjHjh0rN37z5s3w9fWFjY0N/Pz8sHPnzhrKtHJmz56NRx55BA4ODmjcuDEiIiJw6dKlcrdZtWoVZDKZ1mRjY1NDGVfejBkzyuTr6+tb7jam8vkBgLe3d5nzk8lkGD9+vM54U/j8Dh48iGeffRbu7u6QyWTYtm2b1nohBKZNm4YmTZrA1tYWoaGhuHz5coX7rezvsbGUd35FRUWYPHky/Pz8UK9ePbi7u2P48OG4fft2ufusys+5sVT0+Y0cObJMrn369Klwv7Xl8wMqPkddv5MymQzz5s3Tu8/a9Bka8t2Qn5+P8ePHo2HDhrC3t8fzzz+PlJSUcvdb1d9dQ7EYM2MbN25EZGQkpk+fjpMnT8Lf3x9hYWG4c+eOzvjDhw9jyJAhGD16NOLi4hAREYGIiAicPXu2hjOv2IEDBzB+/HgcOXIEUVFRKCoqQu/evZGTk1Pudo6OjkhKStJM169fr6GMq6Z9+/Za+R46dEhvrCl9fgBw/PhxrXOLiooCAAwcOFDvNrX988vJyYG/vz8WL16sc/3cuXPx9ddfY8mSJTh69Cjq1auHsLAw5Ofn691nZX+Pjam888vNzcXJkycxdepUnDx5Elu2bMGlS5fQr1+/CvdbmZ9zY6ro8wOAPn36aOW6fv36cvdZmz4/oOJzfPDckpKSsGLFCshkMjz//PPl7re2fIaGfDe88847+O2337B582YcOHAAt2/fxnPPPVfufqvyu1spgsxWUFCQGD9+vGa+pKREuLu7i9mzZ+uMHzRokAgPD9daFhwcLMaMGWPUPKvDnTt3BABx4MABvTErV64UTk5ONZfUQ5o+fbrw9/c3ON6UPz8hhJgwYYJo0aKFUCqVOteb2ucHQGzdulUzr1QqhZubm5g3b55mWXp6urC2thbr16/Xu5/K/h7XlNLnp8uxY8cEAHH9+nW9MZX9Oa8pus5vxIgRon///pXaT239/IQw7DPs37+/ePLJJ8uNqa2foRBlvxvS09OFlZWV2Lx5sybmwoULAoCIiYnRuY+q/u5WBlvGzFRhYSFiY2MRGhqqWWZhYYHQ0FDExMTo3CYmJkYrHgDCwsL0xtcmGRkZAIAGDRqUG5ednQ0vLy94enqif//+OHfuXE2kV2WXL1+Gu7s7mjdvjpdffhmJiYl6Y0358yssLMTatWvxyiuvQCaT6Y0ztc/vQQkJCUhOTtb6jJycnBAcHKz3M6rK73FtkpGRAZlMBmdn53LjKvNzLrX9+/ejcePGaNOmDcaOHYt79+7pjTX1zy8lJQU7duzA6NGjK4ytrZ9h6e+G2NhYFBUVaX0mvr6+aNasmd7PpCq/u5XFYsxMpaamoqSkBK6urlrLXV1dkZycrHOb5OTkSsXXFkqlEhMnTsSjjz6KDh066I1r06YNVqxYgV9++QVr166FUqlEt27dcPPmzRrM1nDBwcFYtWoVdu/eje+++w4JCQl47LHHkJWVpTPeVD8/ANi2bRvS09MxcuRIvTGm9vmVpv4cKvMZVeX3uLbIz8/H5MmTMWTIkHIHX67sz7mU+vTpgx9//BHR0dH4/PPPceDAATz99NMoKSnRGW/Knx8ArF69Gg4ODhVewqutn6Gu74bk5GQoFIoyfyBU9N2ojjF0m8qyrJa9EElo/PjxOHv2bIX3KISEhCAkJEQz361bN7Rt2xZLly7FrFmzjJ1mpT399NOa9x07dkRwcDC8vLywadMmg/5SNSXLly/H008/DXd3d70xpvb51WVFRUUYNGgQhBD47rvvyo01pZ/zwYMHa977+fmhY8eOaNGiBfbv349evXpJmJlxrFixAi+//HKFD8rU1s/Q0O+G2oAtY2bKxcUFcrm8zBMiKSkpcHNz07mNm5tbpeJrgzfffBPbt2/Hvn374OHhUaltraysEBAQgCtXrhgpu+rl7OyM1q1b683XFD8/ALh+/Tr++OMPvPrqq5XaztQ+P/XnUJnPqCq/x1JTF2LXr19HVFRUua1iulT0c16bNG/eHC4uLnpzNcXPT+3PP//EpUuXKv17CdSOz1Dfd4ObmxsKCwuRnp6uFV/Rd6M6xtBtKovFmJlSKBQIDAxEdHS0ZplSqUR0dLRW68KDQkJCtOIBICoqSm+8lIQQePPNN7F161bs3bsXPj4+ld5HSUkJzpw5gyZNmhghw+qXnZ2Nq1ev6s3XlD6/B61cuRKNGzdGeHh4pbYztc/Px8cHbm5uWp9RZmYmjh49qvczqsrvsZTUhdjly5fxxx9/oGHDhpXeR0U/57XJzZs3ce/ePb25mtrn96Dly5cjMDAQ/v7+ld5Wys+wou+GwMBAWFlZaX0mly5dQmJiot7PpCq/u1VJnMzUhg0bhLW1tVi1apU4f/68eP3114Wzs7NITk4WQggxbNgw8cEHH2ji//rrL2FpaSnmz58vLly4IKZPny6srKzEmTNnpDoFvcaOHSucnJzE/v37RVJSkmbKzc3VxJQ+v5kzZ4o9e/aIq1evitjYWDF48GBhY2Mjzp07J8UpVGjSpEli//79IiEhQfz1118iNDRUuLi4iDt37gghTPvzUyspKRHNmjUTkydPLrPOFD+/rKwsERcXJ+Li4gQA8cUXX4i4uDjN04Rz5swRzs7O4pdffhHx8fGif//+wsfHR+Tl5Wn28eSTT4pFixZp5iv6Pa4t51dYWCj69esnPDw8xKlTp7R+LwsKCvSeX0U/57Xl/LKyssS7774rYmJiREJCgvjjjz9E586dRatWrUR+fr7e86tNn58QFf+MCiFERkaGsLOzE999953OfdTmz9CQ74Y33nhDNGvWTOzdu1ecOHFChISEiJCQEK39tGnTRmzZskUzb8jv7sNgMWbmFi1aJJo1ayYUCoUICgoSR44c0azr0aOHGDFihFb8pk2bROvWrYVCoRDt27cXO3bsqOGMDQNA57Ry5UpNTOnzmzhxoubfwtXVVfTt21ecPHmy5pM30IsvviiaNGkiFAqFaNq0qXjxxRfFlStXNOtN+fNT27NnjwAgLl26VGadKX5++/bt0/lzqT4PpVIppk6dKlxdXYW1tbXo1atXmXP38vIS06dP11pW3u9xTSrv/BISEvT+Xu7bt0+zj9LnV9HPeU0q7/xyc3NF7969RaNGjYSVlZXw8vISr732WpmiqjZ/fkJU/DMqhBBLly4Vtra2Ij09Xec+avNnaMh3Q15enhg3bpyoX7++sLOzEwMGDBBJSUll9vPgNob87j4M2b8HJSIiIiIJ8J4xIiIiIgmxGCMiIiKSEIsxIiIiIgmxGCMiIiKSEIsxIiIiIgmxGCMiIiKSEIsxIiIiIgmxGCMiIiKSEIsxIiIiIgmxGCMiIiKSEIsxIiIiIgmxGCMiIiKSEIsxIiIiIgmxGCMiIiKSEIsxIqIaUFRUhPbt20Mmk6Fjx44oKSkxaDs/Pz/IZDJ4eXkZOUMikgqLMSKiGjB//nycP38eAPD1119DLpcbtF1gYCAAIDExETdv3jRafkQkHRZjRERGlpycjE8++QQAEB4ejp49exq8bfv27TXvY2Njqzs1IqoFWIwRERnZZ599htzcXADAtGnTKrWth4eH5v3Vq1erNS8iqh1YjBERGdG9e/ewbNkyAED37t0RFBRUqe1dXFw075OSkqo1NyKqHViMEREZ0apVq1BQUAAAeOWVVx5qX0VFRdWREhHVMizGiIiMaNOmTQAAuVyOAQMGlFl//PhxDB48GEOHDoUQosz6nJwczXs7OzvjJUpEkrGUOgEiInOVmZmpuek+ICAAzs7OZWJ2796NjRs3onXr1pDJZGXWJyYmat43a9bMaLkSkXTYMkZEZCTnzp3T9CcWEBCgM+avv/4CALRu3Vrn+lOnTmneq7u5ICLzwmKMiMhIrly5onnfokWLMuvz8/Px559/AgCaNm2qcx8HDhwAANjb2+st6IjItLEYIyIykoyMDM17XZcot2/frunyol69emXWnz59Gv/88w8A4Nlnn4WlJe8sITJHLMaIiGpAdnZ2mWXffPON5j4xXesXLVqkeT9q1CjjJUdEkmIxRkRkJJ6enpr3Bw8e1Fq3adMmHDhwAN27dwegeqryQX/++SdWrVoFAOjatSueeuop4yZLRJKRCV3PUhMR0UNLT0+Hm5sbCgoKIJPJMH36dPTt2xdHjhzB5MmTUVJSgoMHDyIkJARCCMyYMQN9+/bFoUOHMG3aNGRnZ8PW1hYnTpxAu3btpD4dIjISFmNEREY0c+ZMzJgxQ+e6ZcuW4bXXXkPv3r0RFRVVZr2DgwO2bt2KXr16GTlLIpISizEiIiP74Ycf8N133+HixYuQyWR45JFH8OGHH2ouPd65cwdvv/029uzZg7y8PHh6eiI8PBzvv/8+3N3dJc6eiIyNxRgRERGRhHgDPxEREZGEWIwRERERSYjFGBEREZGEWIwRERERSYjFGBEREZGEWIwRERERSYjFGBEREZGEWIwRERERSYjFGBEREZGEWIwRERERSYjFGBEREZGEWIwRERERSYjFGBEREZGEWIwRERERSej/ARyo+sD5osDHAAAAAElFTkSuQmCC", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "obp.get_fit(J,w,N=False,plots=True,final_rmse=1e-4)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "0b9dbb68-63a8-45fe-b8cc-eaca06211e57", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Parameters [k=4]: lam=[-0.0678983 0.00926223 0.12182157 0.00016335]; gamma=[4.30107026 1.0030766 2.29685523 0.30763992]; w0=[3.97689247 0.1 0.1 0.1 ], Obtain a normalized RMSE of 2.308571144699614e-06\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "obp.get_fit(J,w,N=4,plots=True)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "4b07bd43-970c-414f-9cb2-159fa0397375", - "metadata": {}, - "outputs": [], - "source": [ - "obp.matsubara_coefficients_from_spectral_fit(Nk=15);" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "cb51b1d5-bd14-4b65-a1a6-5eea464664a8", - "metadata": {}, - "outputs": [], - "source": [ - "Ltot = liouvillian(Hsys) + obp.terminator\n", - "options = {'nsteps':15000, 'store_states':True, 'rtol':1e-12, 'atol':1e-12, 'method':\"bdf\"}" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "c8349e53-001f-4ee5-80ed-fc03bd08e132", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "10.0%. Run time: 1.18s. Est. time left: 00:00:00:10\n", - "20.0%. Run time: 2.37s. Est. time left: 00:00:00:09\n", - "30.0%. Run time: 3.68s. Est. time left: 00:00:00:08\n", - "40.0%. Run time: 4.89s. Est. time left: 00:00:00:07\n", - "50.1%. Run time: 6.04s. Est. time left: 00:00:00:06\n", - "60.1%. Run time: 7.20s. Est. time left: 00:00:00:04\n", - "70.1%. Run time: 8.47s. Est. time left: 00:00:00:03\n", - "80.1%. Run time: 9.67s. Est. time left: 00:00:00:02\n", - "90.1%. Run time: 10.96s. Est. time left: 00:00:00:01\n", - "100.0%. Run time: 12.24s. Est. time left: 00:00:00:00\n", - "Total run time: 12.24s\n" - ] - } - ], - "source": [ - "HEOM_spectral_fit = heom.HEOMSolver(Ltot, obp.Bath_spec, max_depth=4, options=options,)\n", - "result_spectral=HEOM_spectral_fit.run(rho0,tlist)" - ] - }, - { - "cell_type": "markdown", - "id": "a68fa018-26b0-4a38-9298-f4f54dccc7c1", - "metadata": {}, - "source": [ - "## Correlation Function Fitting" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "e1878268-b61c-4209-b86b-e1996a918ce4", - "metadata": {}, - "outputs": [], - "source": [ - "from mpmath import mp\n" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "75f32f68-9729-462f-b168-02b730dd970f", - "metadata": {}, - "outputs": [], - "source": [ - "def ohmic_correlation(t, alpha, wc, beta, s=1):\n", - " \"\"\" The Ohmic bath correlation function as a function of t\n", - " (and the bath parameters).\n", - " \"\"\"\n", - " corr = (\n", - " (1 / np.pi) * alpha * wc**(1 - s) * beta**(-(s + 1)) * mp.gamma(s + 1)\n", - " )\n", - " z1_u = (1 + beta * wc - 1.0j * wc * t) / (beta * wc)\n", - " z2_u = (1 + 1.0j * wc * t) / (beta * wc)\n", - " # Note: the arguments to zeta should be in as high precision as possible.\n", - " # See http://mpmath.org/doc/current/basics.html#providing-correct-input\n", - " return np.array([\n", - " complex(corr * (mp.zeta(s + 1, u1) + mp.zeta(s + 1, u2)))\n", - " for u1, u2 in zip(z1_u, z2_u)\n", - " ], dtype=np.complex128)" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "ba2d7d9a-cebf-4468-a7c7-2479953a73b5", - "metadata": {}, - "outputs": [], - "source": [ - "C=ohmic_correlation(tlist,alpha,wc,1/T)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "af7df643-faab-4a60-aaa2-ec423badf3a4", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.0007850170272317621 0.0007459931927438035\n", - "Parameters: \n", - " [kr=1]: lam=[0.02645534]; gamma=[-1.28893512]; w0=[1.73069104e-12] with normalized RMSE 0.0007850170272317621 \n", - " [ki=1]: lam=[-0.11677207]; gamma=[-1.72572335]; w0=[0.39591075] with normalized 0.0007459931927438035\n" - ] - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.00038252526658879524 0.0003543130260187791\n", - "Parameters: \n", - " [kr=2]: lam=[0.0140705 0.0115834]; gamma=[-1.18030216 -0.64307704]; w0=[1.42584122e+00 3.79867762e-19] with normalized RMSE 0.00038252526658879524 \n", - " [ki=2]: lam=[-0.11677207 -0.01399813]; gamma=[-1.23993592 -1.43569016]; w0=[0.14401047 1.80508414] with normalized 0.0003543130260187791\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "obp.fit_correlation(tlist,C,final_rmse=5e-4)" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "53bf7d10-ccf0-43a9-bb3f-3283af0226cb", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "happened\n", - "3.376089578305972e-06 5.419385902718789e-05\n", - "Parameters: \n", - " [kr=4]: lam=[ 0.04446402 0.13064632 -0.1245144 -0.02721077]; gamma=[-2.80451837 -0.39768115 -0.38991104 -4.64012132]; w0=[4.16801101e-01 9.98355639e-05 4.25497734e-02 2.67295373e+00] with normalized RMSE 3.376089578305972e-06 \n", - " [ki=3]: lam=[-0.11677207 0.0054071 -0.11677207]; gamma=[-0.79497337 -4.15641417 -2.08872708]; w0=[0.02253055 4.81914662 0.47960412] with normalized 5.419385902718789e-05\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "obp.fit_correlation(tlist,C,Ni=3,Nr=4)" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "1d68e5dd-2283-485f-ae1f-f35989cf8880", - "metadata": {}, - "outputs": [], - "source": [ - "obp.matsubara_coefficients();" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "ee42d781-9da8-48ce-86e6-79b9c3522864", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "10.0%. Run time: 0.08s. Est. time left: 00:00:00:00\n", - "20.0%. Run time: 0.12s. Est. time left: 00:00:00:00\n", - "30.0%. Run time: 0.17s. Est. time left: 00:00:00:00\n", - "40.0%. Run time: 0.22s. Est. time left: 00:00:00:00\n", - "50.1%. Run time: 0.27s. Est. time left: 00:00:00:00\n", - "60.1%. Run time: 0.32s. Est. time left: 00:00:00:00\n", - "70.1%. Run time: 0.37s. Est. time left: 00:00:00:00\n", - "80.1%. Run time: 0.42s. Est. time left: 00:00:00:00\n", - "90.1%. Run time: 0.47s. Est. time left: 00:00:00:00\n", - "100.0%. Run time: 0.52s. Est. time left: 00:00:00:00\n", - "Total run time: 0.52s\n" - ] - } - ], - "source": [ - "HEOM_corr_fit = heom.HEOMSolver(Ltot, obp.Bath_corr, max_depth=4, options=options,)\n", - "result_corr=HEOM_corr_fit.run(rho0,tlist)" - ] - }, - { - "cell_type": "markdown", - "id": "5f8af268-5059-46a7-9d24-9a07a8a05d7b", - "metadata": {}, - "source": [ - "# Comparison between fits" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "2f29bd39-5a12-48f5-a78f-50a621b650eb", - "metadata": {}, - "outputs": [], - "source": [ - "def projection(result,i,j):\n", - " return [result.states[k][i,j] for k in range(len(result.states))]" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "930b28d4-90dd-4c8d-9568-20b33dde6fa7", - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "id": "fea8022a-02f5-4043-871f-da8048a598b7", - "metadata": {}, - "outputs": [ - { - "data": { - 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(tlist,projection(result_corr,0,0))\n", - "plt.plot(tlist,projection(result_spectral,0,0))\n", - "plt.xlabel('t')\n", - "plt.ylabel(r'$\\rho_{11}$')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "id": "86ef45f2-c782-4075-becb-2617381ff831", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "w=np.linspace(-10,10,1000)\n", - "plt.plot(w,obp.corr_spectrum_approx(w))\n", - "plt.plot(w,obp.spec_spectrum_approx(w))\n", - "plt.ylabel(r'$J( \\omega )$')\n", - "plt.xlabel(r'$\\omega$')\n", - "plt.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "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": "3.12.0" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/.ipynb_checkpoints/OhmicBath-checkpoint.ipynb b/.ipynb_checkpoints/OhmicBath-checkpoint.ipynb deleted file mode 100644 index fb5a119c20..0000000000 --- a/.ipynb_checkpoints/OhmicBath-checkpoint.ipynb +++ /dev/null @@ -1,295 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "2bb296b7-6f64-4660-a79a-30309e63153f", - "metadata": {}, - "outputs": [], - "source": [ - "from qutip import *\n", - "import numpy as np" - ] - }, - { - "cell_type": "markdown", - "id": "c4ed1d4b-69ee-495d-bdd4-e85d129bcea5", - "metadata": {}, - "source": [ - "Setting parameters" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "b52eb1f2-6579-4f8a-9329-8543d301090c", - "metadata": {}, - "outputs": [], - "source": [ - "# Defining the system Hamiltonian\n", - "eps = 0.0 # Energy of the 2-level system.\n", - "Del = 0.2 # Tunnelling term\n", - "Hsys = 0.5 * eps * sigmaz() + 0.5 * Del * sigmax()\n", - "# Initial state of the system.\n", - "rho0 = basis(2, 0) * basis(2, 0).dag()\n", - "tlist=np.linspace(0,10,100)\n", - "# defining Ohmic bath properties\n", - "alpha=0.05\n", - "T=1\n", - "wc=1\n", - "s=1\n" - ] - }, - { - "cell_type": "markdown", - "id": "7cad3ae4-1f51-4950-9d7f-b8c7ac6f0f77", - "metadata": {}, - "source": [ - "Obtaining an Ohmic Bath via Correlation functions\n", - "\n", - "If no Nk option is specified than the Ohmic bath is obtained by fitting the ohmic correlation function" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "f3f59052-a687-4a00-8a0a-ece534e77433", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "9.285525683845158e-05 0.00010330946735496302\n", - "Parameters: \n", - " [kr=1]: lam=[0.04000589]; gamma=[-0.93092396]; w0=[3.97254983e-13] with normalized RMSE 9.285525683845158e-05 \n", - " [ki=1]: lam=[-0.18222192]; gamma=[-1.75906526]; w0=[0.2573249] with normalized 0.00010330946735496302\n", - "4.900147895871912e-05 5.048232471495117e-05\n", - "Parameters: \n", - " [kr=2]: lam=[0.01838072 0.02128095]; gamma=[-0.51507656 -1.01867827]; w0=[8.51309254e-27 9.62371319e-01] with normalized RMSE 4.900147895871912e-05 \n", - " [ki=2]: lam=[-0.01388949 -0.18222192]; gamma=[-1.43428103 -1.25058808]; w0=[1.80554058 0.09348054] with normalized 5.048232471495117e-05\n", - "1.330034898743409e-05 8.63989350882291e-06\n", - "Parameters: \n", - " [kr=3]: lam=[ 0.04108793 0.00505854 -0.00938488]; gamma=[-1.31653847 -0.28450369 -4.7192565 ]; w0=[3.48775382e-30 3.10463013e-21 4.89079434e+00] with normalized RMSE 1.330034898743409e-05 \n", - " [ki=3]: lam=[-0.18222177 0.00571398 -0.18222192]; gamma=[-0.76580285 -4.16798074 -2.11513673]; w0=[0.01245922 4.73623557 0.31461097] with normalized 8.63989350882291e-06\n" - ] - } - ], - "source": [ - "obp=heom.OhmicBath(alpha,T,wc,s,sigmaz())" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "62db8a97-d209-4da8-8d77-5420409f0615", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "10.1%. Run time: 0.03s. Est. time left: 00:00:00:00\n", - "20.2%. Run time: 0.05s. Est. time left: 00:00:00:00\n", - "30.3%. Run time: 0.07s. Est. time left: 00:00:00:00\n", - "40.4%. Run time: 0.09s. Est. time left: 00:00:00:00\n", - "50.5%. Run time: 0.10s. Est. time left: 00:00:00:00\n", - "60.6%. Run time: 0.12s. Est. time left: 00:00:00:00\n", - "70.7%. Run time: 0.13s. Est. time left: 00:00:00:00\n", - "80.8%. Run time: 0.14s. Est. time left: 00:00:00:00\n", - "90.9%. Run time: 0.15s. Est. time left: 00:00:00:00\n", - "100.0%. Run time: 0.17s. Est. time left: 00:00:00:00\n", - "Total run time: 0.17s\n" - ] - } - ], - "source": [ - "options = {'nsteps':15000, 'store_states':True, 'rtol':1e-12, 'atol':1e-12, 'method':\"bdf\"}\n", - "HEOM_corr_fit = heom.HEOMSolver(Hsys, obp.Bath_corr, max_depth=4, options=options)\n", - "result_corr=HEOM_corr_fit.run(rho0,tlist)" - ] - }, - { - "cell_type": "markdown", - "id": "fd990fca-2f2d-4136-ba3e-dccfb0c38644", - "metadata": {}, - "source": [ - "Obtaining an Ohmic Bath via Spectral density\n", - "\n", - "If the Nk option is specified than the Ohmic bath is obtained by fitting the ohmic spectral density " - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "3fad860d-7493-41da-9a1f-af7fa545399e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Parameters [k=1]: lam=[0.09457431]; gamma=[1.77937269]; w0=[0.1], Obtain a normalized RMSE of 0.00014398392031896555\n", - "Parameters [k=2]: lam=[0.03403659 0.0501813 ]; gamma=[1.24962826 1.43433213]; w0=[0.1 1.80573812], Obtain a normalized RMSE of 7.11144005909762e-05\n", - "Parameters [k=3]: lam=[ 0.1166377 -0.05569386 0.00403361]; gamma=[2.13429216 4.17975311 0.73506751]; w0=[0.1 4.6678629 0.1 ], Obtain a normalized RMSE of 1.1895054823893679e-05\n", - "Parameters [k=4]: lam=[ 0.12176592 0.00923496 -0.06777512 0.00016261]; gamma=[2.29588017 1.00218298 4.29819614 0.30723335]; w0=[0.1 0.1 3.9838893 0.1 ], Obtain a normalized RMSE of 2.070455673673749e-06\n" - ] - } - ], - "source": [ - "obp2=heom.OhmicBath(alpha,T,wc,s,sigmaz(),Nk=4)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "fb547724-f89b-4375-89e7-43456df7041e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "10.1%. Run time: 0.07s. Est. time left: 00:00:00:00\n", - "20.2%. Run time: 0.16s. Est. time left: 00:00:00:00\n", - "30.3%. Run time: 0.23s. Est. time left: 00:00:00:00\n", - "40.4%. Run time: 0.29s. Est. time left: 00:00:00:00\n", - "50.5%. Run time: 0.35s. Est. time left: 00:00:00:00\n", - "60.6%. Run time: 0.42s. Est. time left: 00:00:00:00\n", - "70.7%. Run time: 0.49s. Est. time left: 00:00:00:00\n", - "80.8%. Run time: 0.55s. Est. time left: 00:00:00:00\n", - "90.9%. Run time: 0.62s. Est. time left: 00:00:00:00\n", - "100.0%. Run time: 0.67s. Est. time left: 00:00:00:00\n", - "Total run time: 0.67s\n" - ] - } - ], - "source": [ - "Ltot = liouvillian(Hsys) + obp2.terminator\n", - "HEOM_spectral_fit = heom.HEOMSolver(Ltot, obp2.Bath_spec, max_depth=4, options=options)\n", - "result_spectral=HEOM_spectral_fit.run(rho0,tlist)" - ] - }, - { - "cell_type": "markdown", - "id": "171fcb2c-d8d0-46a2-adb3-5ad699c6598f", - "metadata": {}, - "source": [ - "Let us see the results from both ways of obtaining the ohmic bath parameters " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "f6eaf004-e708-48cc-b833-bb9c77ac7d7c", - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "def projection(result,i,j):\n", - " return [result.states[k][i,j] for k in range(len(result.states))]" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "2cfea7ff-6de6-4dff-926d-39024b9d66a3", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/mcditoos/anaconda3/envs/qutip-dev/lib/python3.12/site-packages/matplotlib/cbook.py:1699: ComplexWarning: Casting complex values to real discards the imaginary part\n", - " return math.isfinite(val)\n", - "/home/mcditoos/anaconda3/envs/qutip-dev/lib/python3.12/site-packages/matplotlib/cbook.py:1345: ComplexWarning: Casting complex values to real discards the imaginary part\n", - " return np.asarray(x, float)\n", - "/home/mcditoos/anaconda3/envs/qutip-dev/lib/python3.12/site-packages/matplotlib/collections.py:194: ComplexWarning: Casting complex values to real discards the imaginary part\n", - " offsets = np.asanyarray(offsets, float)\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(tlist,projection(result_spectral,0,0))\n", - "plt.scatter(tlist,projection(result_corr,0,0),s=5,marker='x',color='red')\n", - "plt.xlabel('t')\n", - "plt.ylabel(r'$\\rho_{11}$')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "1ca0c6b1-5ecf-4397-bb41-19b932df241b", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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AJOKeFIhExGNURA9Ry5YFQ2bbtm2rkJpExDkoEImIx6jIIbMDBw5w9uzZCqlLRMynQCQiHqO8p90XV69ePerWrYthGOzcubOiShMRkykQiYjHuJLT7otYLBbNIxJxQwpEIuIxKmLIDDSxWsQdKRCJiMeoiCEz0MRqEXekQCQiHqMihsxAPUQi7kiBSEQ8Ql5eHpmZmUDFDZnt3r2bvLy8K65NRMynQCQiHqFouAyuPBCFh4dTvXp1cnNz2bt375WWJiJOQIFIRDxCUSCqVq0avr6+V7QtLy8vmjdvDmgekYi7UCASEY9QUfOHihRNrNY8IhH3oEAkIh6hok65L6KJ1SLuRYFIRDxCRZ1yX0SBSMS9KBCJiEeo6CGzokC0Y8cO7HZ7hWxTRMyjQCQiHqGih8waN26Mj48PmZmZJCYmVsg2RcQ8CkQi4hEqOhD5+voSFRUFaNhMxB0oEImIR6joOUSgeUQi7kSBSEQ8QkXPIYI/A9G6+M1k5eZX2HZFpOopEImIR6joITMAr9phAPy0aClz+g5lxa6UCtu2iFQtBSIR8QgVPWSWlZtP7idfA2Ac28/o3+exaeSj6ikScVEKRCLiESp6yCwlPZutUddiAU4AycDiiPakpGdXyPZFpGopEImIR6joIbNgfysDjmyhSeHzzcD1CfEE+1srZPsiUrUUiETEI1R0ILL5etP23WnUCAwH4O2rO9D23WnYfL0rZPsiUrUUiETEIxTNIarIs8y6RwUz8IF/AFCjZ1u6RwVX2LZFpGopEImI2zMMo1KuQwTQProdANu2bqnQ7YpI1VIgEhG3l5mZSX5+wdlfFR2IWrduDcDWrVsd7yEirkeBSETcXlHvkLe3N9WrV6/QbTdp0gSbzcbZs2fZt29fhW5bRKqOApGIuL3ip9xbLJYK3ba3tzctW7YEYMsWDZuJuCoFIhFxe5Vxleri2rRpA8DmzZsrZfsiUvkUiETE7VXWhOoiCkQirk+BSETcXmXc2LU4BSIR16dAJCJur7KHzIrONNu9ezdZWVmV8h4iUrkUiETE7VV2IKpfvz5169bFbrezffv2SnkPEalcCkQi4vYqew6RxWLRsJmIi1MgEhG3V9lziEDziERcnQKRiLi9yh4yAwUiEVenQCQibq+yh8zgz0CkizOKuCYFIhFxe1UxZNaqVSsADh8+zMmTJyvtfUSkcigQiYh7s9s5tW0bADW/+hrs9kp5G39/fyIjIwENm4m4IgUiEXFriQ8/QfrRowDUXfA5iQ8/UWnvpXlEIq5LgUhE3FZWbj7jzzTgeOHzQGD8mQZk5eZXyvspEIm4LgUiEXFbKenZdNixmqIZPUFA551rSUnPrpT308RqEdelQCQibivY38o7MbdhFD7/JOZO3u07lGB/a6W8X9EtPLZs2cLB1MxK64kSkYqnQCQibsvm680z10cA4GWryXvX/5NZQztj8/WulPdr1qwZ3j4+pKWl0X3i53T698+s2JNaKe8lIhXLx+wCREQqU2TNgrPKIuqHsP6ZfpUWhgDsFm986jQg/9hBIrYv564/zjDasLNuwg2V+r4icuUUiETEraWmFvTQhIbUq/RQkpKeTSvDYANwy9L3eRgwgJSxvYgIrF6p7y0iV0ZDZiLi1ooCUVBQUKW/V7C/FXtkwcTqPwqXrWvWpdLmLIlIxXG6QDRjxgwaNmyIzWaja9eurF279qLtFyxYQPPmzbHZbLRp04bvv//+vDbbt2/nlltuISAggBo1atC5c2cSEhIqaxdExIlUZSCy+Xozrn5B+IkvXBZb/bCGy0RcgFMFos8++4xx48YxadIkNmzYQLt27ejfvz8pKSmltl+5ciVDhgxhxIgRxMfHM2jQIAYNGlTilNe9e/fSo0cPmjdvztKlS9m0aRMTJkzAZrNV1W6JiImqMhAB3DD7LQB2WSyc+tfjhL85pUreV0SujMUwDOPSzapG165d6dy5M2+9VfCBYrfbCQ8P56GHHuKpp546r/3gwYPJzMzk22+/dSy75ppriI6OZtasWQDcdddd+Pr68tFHH5W7rvT0dAICAkhLS6vUeyGJSMUbPnw4c+fOJTY2ttTPkcoQFhbG0aNHWbFiBd26dauS9xSR85Xl+9tpeohycnKIi4ujX79+jmVeXl7069ePVatWlbrOqlWrSrQH6N+/v6O93W7nu+++Iyoqiv79+xMcHEzXrl1ZuHDhRWvJzs4mPT29xENEXFNV9xABtG/fHoD4+PhLtBQRZ+E0gSg1NZX8/HxCQkJKLA8JCSEpKanUdZKSki7aPiUlhdOnTzN58mQGDBjATz/9xG233cZf//pXli1bdsFaYmNjCQgIcDzCw8OvcO9ExCwKRCJyOZwmEFUGe+FdrW+99VYeffRRoqOjeeqpp7j55psdQ2qlGT9+PGlpaY5HYmJiVZUsIhXMzEC0cePGKntPEbkyTnMdoqCgILy9vUlOTi6xPDk5mdDQ0FLXCQ0NvWj7oKAgfHx8aNmyZYk2LVq0YPny5ResxWq1YrXqNFkRd3D8eMGtXQMDA6vsPYsC0ebNm8nNzcXX17fK3ltEysdpeoj8/Pzo2LEjS5YscSyz2+0sWbKEmJiYUteJiYkp0R5g8eLFjvZ+fn507tyZnTt3lmiza9cuIiMjK3gPRMTZ5OXlcfJkwa1dq7KHqFGjRgQEBJCTk8P27dur7H1FpPycpocIYNy4cQwbNoxOnTrRpUsXXn/9dTIzMxk+fDgAQ4cOpUGDBsTGxgIwduxYevXqxauvvsrAgQOZP38+69evZ/bs2Y5tPv744wwePJhrr72W3r17s2jRIr755huWLl1qxi6KSBU6ceIEABaLhTp16lTZ+1osFqKjo1m2bBnx8fG0bdu2yt5bRMrHaXqIoOA0+qlTpzJx4kSio6PZuHEjixYtckycTkhI4OjRo4723bp1Y968ecyePZt27drxxRdfsHDhQscdpwFuu+02Zs2axZQpU2jTpg3vvvsu//3vf+nRo0eV75+IVK2i+UN16tTBx6dqf//TxGoR1+JU1yFyVroOkYhr+u233+jVqxdRUVHnDZ1Xtg8//JBhw4Zx7bXXXvSsVhGpPC55HSIRkYpmxoTqIsXPNCs641VEnJcCkYi4LTNOuS/SvHlzrFYr6enp7N+/v8rfX0TKRoFIRNyWmYHI19fXMZ9R84hEnJ8CkYi4LTMDEWhitYgrUSASEbdl5hwiUCAScSUKRCLittRDJCKXS4FIRNyW2YGobdu2WCwWkpKSLniTahFxDgpEIuK2zA5ENWrUoFmzZoB6iUScnQKRiLgtswMR/Dls9uuKtWTl5ptWh4hcnAKRiLil3Nxc0tLSAPMmVQPUCY8CYMYXi+n0759ZsSfVtFpE5MIUiETELZl1Y9fisnLz+f6wX0Edh3dw/89zGf3hOvUUiTghBSIRcUtFw2V169bF29vblBpS0rO5b9d6ADJPH2fYyvmMXPIhKenZptQjIhemQCQibskZ5g8F+1vZ1ronkYXPNwDrmnUh2N9qWk0iUjoFIhFxS2ZflBHA5utNbPXDdC58vg6IrX4Ym685PVYicmEKRCLilpyhhwgg/M0pdOrTB4A1zZoT/uYUU+sRkdIpEImIW3KWQISXF9dMnAjAujOZ4KWPXRFnpJ9MEXFLThOIgA4dOmCxWEhMTNQVq0WclAKRiLglZwpEtWrVomXLlgCsW7fO5GpEpDQKRCLilpxhUnVxXbp0AWDt2rUmVyIipVEgEhG35Ew9RACdOxeca6YeIhHnpEAkIm7J2QJRUQ/RunXrMAzD5GpE5FwKRCLilpwtELVp0war1cqJEyfYt2+f2eWIyDmuKBDl5uaSmJjIzp07HfcNEhExW25uLunp6YDzzCHy8/MjOjoa0DwiEWdU5kCUkZHBzJkz6dWrF/7+/jRs2JAWLVpQr149IiMjue+++zRGLiKmKppQ7eXlRe3atc0tphhNrBZxXmUKRK+99hoNGzZkzpw59OvXj4ULF7Jx40Z27drFqlWrmDRpEnl5edxwww0MGDCA3bt3V1bdIiIX5Aw3di2NJlaLOC+fsjRet24dv/32G61atSr19S5duvDPf/6TWbNmMWfOHH7//XeaNm1aIYWKiFwuZ5s/VKSoh2jDhg3k5ubi6+trckUiUqRMgejTTz+9rHZWq5XRo0eXqyARkSvlrIGoadOmBAQEkJaWxtatWx1zikTEfDrLTETcjrNdlLGIl5cXnTp1AjRsJuJsyh2IpkyZwt13302fPn0YOHAgjz/+OKtWrarI2kREysVZe4hAE6tFnFW5A9H06dNJTU0lODgYgPnz59OjRw8GDBhAWlpahRUoIlJWrhCI1EMk4lzKNIeouMTExPOWrV69mgceeIAxY8bw8ccfX1FhIiLl5cyBqOhMsy1btrAj4RgN69fF5us8Z8KJeKoKnUN0zTXXMGfOHL7++uuK3KyISJk46xwigAYNGhAUEkp+fj7XPT2HTv/+mRV7Us0uS8TjlbuHqLg5c+ZQq1YtbDYbCxcudMoPIRHxHM7cQ5SVm0927UaQnETw9uWM3B/PaMPOugk3qKdIxEQVEojWrFnDggULOHXqFAMHDlQPkYiYypkDUUp6NteezeQ7oOWGb3gYMICUsb2ICKxucnUinqtChsxmzZpFamoq3377Lfv27WPDhg0VsVkRkXJx5kAU7G8lq2V3AFYWLlvXrAvB/lbzihKR8geia6+9ljVr1jieWywWbrzxRj7++GPGjx9fIcWJiJRVTk4OGRkZgHPOIbL5ejMjwhdvIBFIAGKrH9ZwmYjJyj1k1qpVK7p3706XLl24/fbbadOmDTVr1uTTTz/l7NmzFVmjiMhlc9YbuxbXbOY0or9ZQNzRo/x26yD+/uYUs0sS8Xjl7iGaOXMmf/zxB1FRUTz//PMMGDCAHj168J///IennnqqImsUEblsRcNlgYGBeHk56cX4vbzoceedAKy+qgE4a50iHuSKfgpbtWrF3LlzOXHiBDt27GD16tUcOXKEJ598sqLqExEpE2eeP1Rc9+4F84hWrFhhciUiAmUMRAkJCaUu9/b2Jioqii5duhASEuJYfvjw4SurTkSkjFJTUgAI8vODiRPBbje5otIVBaJNmzY55jyJiHnKFIg6d+7MqFGjLnrJ+bS0NN555x1at27Nf//73ysuUESkLI598AEAQX/8AS+8AM8+a25BFxAWFkajRo2w2+2sXr3a7HJEPF6ZJlVv27aNF198keuvvx6bzUbHjh0JCwvDZrNx8uRJtm3bxtatW+nQoQNTpkzhpptuqqy6RURKtdHmD0BY4fNNra+hrXnlXFT37t3Zv38/K1as4Prrrze7HBGPVqYeosDAQF577TWOHj3KW2+9RdOmTUlNTWX37t0A3HPPPcTFxbFq1SqFIRGpclm5+WxeWdCDXRSIVrz1CVm5+eYVdRFFw2bLly83uRIRKddp99WqVeNvf/sbf/vb3yq6HhGRcktJz2ZjtYIeov/GDKaGxcLrMXcxMD3bKa8CXRSIVq9eTV5eHj4+FXLzABEphzKfZTZmzBjee+89NmzYQG5ubmXUJCJSLsH+VozMEwAcimjD69f+nRo2P6e9CnSrVq0ICAggMzOTTZs2mV2OiEcr868j69evZ+7cuZw9exZfX19atmxJ+/btHY/o6Ghq1qxZGbWKiFyUzdcb3+w0sgHvmnWp4efD2/d2dNqrQHt5eRETE8OiRYtYsWIFHTp0MLskEY9V5kC0Zs0a7HY7O3bsID4+3vH46quvOHnyJF5eXjRp0oR+/frx0EMP0axZs8qoW0TkPGfOnOF0ehoAP/2/QTS5Kthpw1CR7t27OwLRQw89ZHY5Ih7LYhiGUVEbO3jwIPHx8cTFxbFo0SK2bt3KTz/9RI8ePSrqLUyRnp5OQEAAaWlp+Pv7m12OiFzA7t27iYqKokaNGmRkZGCxWMwu6ZJ+/fVX+vTpw1VXXUViYqLZ5Yi4lbJ8f1doIDrXCy+84PjNx5UpEIm4hqVLl9K7d2+ioqLYuXOn2eVclszMTGrXrk1eXh4HDx4kIiLC7JJE3EZZvr8r9QY6Q4cO5Y8//qjMtxARcThy5AhQcNFDV1GjRg3at28P6PR7ETNVaiCKjIzUFVhFpMoU3S6oQYMGJldSNkWn3y9assxpr5kk4u4q/RbLrVu3ruy3EBEBXDcQBTYq+Jz8+stvmNN3KCt2pZhckYjnqfRAJCJSVVwxEGXl5uMz7zsAMk4e5Z7f57Fp5KPqKRKpYgpEIuI2XHEOUUp6NmubdONqwA6sBBZHtCclPdvkykQ8i64TLyJuwxV7iIL9rVyfEE8dYB/wK3B9QrzTXl1bxF2ph0hE3ILdbnf0ELlSILL5etP23WnkN4sBYH7NurR9d5rTX1BSxN0oEImIW0hNTXXcXzE0NNTkasqme1QwExbNB+DQmVO0CvYzuSIRz6NAJCJuoah3KDg4GD8/1wsUjRtGEBUVhd1u57fffjO7HBGPo0AkIm7BFecPnatPnz5Awe08RKRqOWUgmjFjBg0bNsRms9G1a1fWrl170fYLFiygefPm2Gw22rRpw/fff3/BtqNHj8ZisfD6669XcNUiYiZ3CES9e/cG4JdffjG5EhHP43SB6LPPPmPcuHFMmjSJDRs20K5dO/r3709KSukXKlu5ciVDhgxhxIgRxMfHM2jQIAYNGsSWLVvOa/vll1+yevVqlzolV0QuT1EgcuWf7+uuuw6ATZs2kZqaam4xIh7G6QLRa6+9xn333cfw4cNp2bIls2bNonr16rz//vultn/jjTcYMGAAjz/+OC1atOCFF16gQ4cOvPXWWyXaHT58mIceeohPPvkEX1/fqtgVEalCrniG2bmCg4MdV/dftmyZydWIeBanCkQ5OTnExcXRr18/xzIvLy/69evHqlWrSl1n1apVJdoD9O/fv0R7u93Ovffey+OPP06rVq0uWUd2djbp6eklHiLi3NxhyAw0bCZiFqcKRKmpqeTn5xMSElJieUhICElJSaWuk5SUdMn2L7/8Mj4+Pjz88MOXVUdsbCwBAQGOR3h4eBn3RESqmrsEIk2sFjGHUwWiyhAXF8cbb7zB3LlzsVgsl7XO+PHjSUtLczwSExMruUoRuVLuMIcIoFevXlgsFrZv387Ro0fNLkfEYzhVIAoKCsLb25vk5OQSy5OTky94obXQ0NCLtv/9999JSUkhIiICHx8ffHx8OHjwII899hgNGzYsdZtWqxV/f/8SDxFxXtnZ2Rw/fhxw/R6iOnXq0L59ewCWLl1qbjEiHsSpApGfnx8dO3ZkyZIljmV2u50lS5YQExNT6joxMTEl2gMsXrzY0f7ee+9l06ZNbNy40fEICwvj8ccf58cff6y8nRGRKlM0odpqtVK3bl2Tq7lyRfOINGwmUnWc7uau48aNY9iwYXTq1IkuXbrw+uuvk5mZyfDhwwEYOnQoDRo0IDY2FoCxY8fSq1cvXn31VQYOHMj8+fNZv349s2fPBiAwMJDAwMAS7+Hr60toaCjNmjWr2p0TkUpRfLjscofGnVmfPn149dVXNbFapAo5XSAaPHgwx44dY+LEiSQlJREdHc2iRYscE6cTEhLw8vqzY6tbt27MmzePZ555hqeffpqmTZuycOFCx6mrIuL+3OGU++J69uyJt7c3e/fuJSEhgYiICLNLEnF7FsMwDLOLcHbp6ekEBASQlpam+UQiTmjatGmMGzeOwYMHM3/+fLPLqRAxMTGsXr2aN8Y9wf/ZfPF54XnwcqpZDiJOryzf307XQyQiUlbucsp9cR1z7KwG4l6bgg+QmJZF+FtTzS5LxG3p1w0RcXnucsp9kazcfLbX6wDAz4ABjD/TgKzcfFPrEnFnCkQi4vLcbQ5RSno2N6UdpzpwBNgMdN65lpT0bJMrE3FfCkQi4vLcbcgs2N/K3OuH06hOQY/XMxHteLfvUIL9rSZXJuK+FIhExKUZhuF2gcjm682soZ05fs0gAJZY7Mwa2hmbr7e5hYm4MQUiEXFpJ0+eJCsrC4D69eubXE3F6d4kiF+mPQJAzuHttAn2M7cgETenQCQiLq1o/lDdunWpVq2aydVUrBbNmhIVFUVeXt55V+QXkYqlQCQiLs3dhsvOdeONNwLwww8/mFyJiHtTIBIRl+Zup9yfa8CAAQAsWrQIXUdXpPIoEImIS3P3HqJevXphs9lITExk27ZtZpcj4rYUiETEpbnbNYjOVa1aNXr37g1o2EykMikQiYhLS0w8BEBwqPucYXauomEzBSKRyqNAJCIua8WuFDYtWwHA1hnzWbErxeSKKkfRxOrff/+d06dPm1yNiHtSIBIRl5SVm8+mkY+Sc/okAPdt+41NIx91y/t9NW3alMaNG5Obm8svv/xidjkibkmBSERcUkp6NovCWpNc+DwcWBzR3m3v96XT70UqlwKRiLikYH8rbXcvByAACAKuT4h32/t9DbjhBgC++3IhuU//P7DbTa5IxL0oEImIS7L5elN9xB0AWOpexayed9P23Wlue7+vpt/+jBVITE5ib+xLJD78hNklibgVBSIRcVm+Z1IBuLbXNQxf8iHdo4JNrqhyZOXm83xuQ64rfP4NMP5MA7ecLyViFgUiEXFZe/bsAaBtq+Zu2zMEBfOlOu9cy62Fz/8HdN651m3nS4mYQYFIRFxWUSBq0qSJyZVUrmB/K+/2HUpqp4JItBqY2WWg286XEjGDj9kFiIiU1+7duwH3D0Q2X29mDe3MKIsXfkd2kHNkJzfXPurWvWIiVU09RCLikrKyskhMTAQKrtPj7ro3CWL9M/14bOTfAdi0YrHJFYm4FwUiEXFJ+/fvxzAMatWqRb169cwup0rYfL0Z/vfBAPz666+cPHnS5IpE3IcCkYi4pOLzhywWi8nVVJ2mTZvSunVr8vLy+Pbbb80uR8RtKBCJiEvylAnVpbntttsA+PLLL02uRMR9KBCJiEvylAnVpSkKRIsWLeLMmTMmVyPiHhSIRMQlFfUQecKE6nNFR0cTGRnJ2bNn+emnn8wuR8QtKBCJiEvy5CEzi8WiYTORCqZAJCIuJycnh4MHDwKeGYjgz2Gzr7/+mtzcXJOrEXF9CkQi4nL279+P3W6nRo0ahIaGml2OKbp37069evU4deoUy5YtM7scEZenQCQiLsdTT7kvztvbm1v+8hcAPnl9Onn/7xmw202uSsR1KRCJiMvx5PlDxfVILrgw44/ffY3lpRdJfPgJkysScV0KRCLichSIICs3nx8DY6gDHAWWAuPPNCArN9/cwkRclAKRiLgcBSJISc/mmj0buKPw+SdA551rSUnPNrMsEZelQCQiLqfoooyeeA2iIsH+Vt7tOxRrqz4AfOrty+xedxHsbzW5MhHXpEAkIi4lNzeXAwcOAJ7dQ2Tz9WbW0M4s+eu/8K5Vj6z8XIbUP47N19vs0kRckgKRiLiUgwcPkp+fT7Vq1ahfv77Z5Ziqe5Mg4ibcwH3/+DsAcb98Y3JFIq5LgUhEXErR/KHGjRvj5aWPMJuvNw+M/AcA33//PSdPnjS3IBEXpU8TEXEpnnwPswtp27YtrVu3Jicnhy+++MLsckRckgKRiLgUT77L/cXcc889AHzyyScmVyLimhSIRMSl6JT70g0ZMgSAZcuWkZiYaHI1Iq5HgUhEXMru3QWBKKJhI5MrcS6RkZH07NkTgE8//dTkakRcjwKRiLiMZTuS2LN3HwBjv09mxZ5UkytyLvcU9hJ98s47MHGi7m0mUgYKRCLiErJy87nvP4sw7Hng7Uu2LYBRH8XpVhXF3LFvH77Apj172PLCC/Dss2aXJOIyFIhExCWkpGeTnpQAQK2adXn093lkZuXoVhXFHOrcmxsL/z4X2NT6GhOrEXEtCkQi4hKC/a1ct6HgwoO905IZu3I+T6yar1tVFMrKzWfFW5/wz8LnHwBL3/xQPWgil0mBSERcgs3XG5qEAhBVuKz7g/foVhWFUtKzmRJzF3tj7sRWzZ9U4N91I9SDJnKZFIhExGUkbt0IQHTh87ZbVptVitMJ9rdSw+bH9F5Dsba/CYAzmxerB03kMikQiYhLyM/P54/C21J0+OQTmDBBk4aLsfl68/a9Hanh50PNtjcAFjIPbCTxwD6zSxNxCQpEIuISdu/eTWZmJtWrVydq8GB4/nnQvcxK6N4kiPXP9GPlvwfTf0B/AN555x2TqxJxDfo0ERGXEB8fDxTct8vbW/OGLsTm601EYHUeGD0agDlz5pCdrXlEIpeiQCQiLqEoELVv397kSlzDwIEDqV+/PqmpqXz11VdmlyPi9BSIRMQlFAWiDh06mFyJa/Dx8WHEiBEAzJ492+RqRJyfApGIOD3DMNiwYQOgHqKyGDlyJBaLhSVLljhuiisipVMgEhGnl5iYyIkTJ/Dx8aF169Zml+MyIiMjGdC/YHL16+OfIe//PaP7m4lcgI/ZBYiIXErRcFmrVq2wWnVdnbL4q8WPH4DPv/iMqcDRtCzC35pqdlkiTkc9RCLi9DShunyycvP5Jbgn4cAx4BNg/JkGup2HSCkUiETE6Wn+UPmkpGfTdXccYwufvwp03LFGt/MQKYUCkYg4PfUQlU+wv5V3+w4lv8vt+Pja2A68EdlSt/MQKYVTBqIZM2bQsGFDbDYbXbt2Ze3atRdtv2DBApo3b47NZqNNmzZ8//33jtdyc3N58sknadOmDTVq1CAsLIyhQ4dy5MiRyt4NEakAx44d49ChQwBER0ebW4yLsfl6M2toZz4ccB/Vo28EIPDAYt0QV6QUTheIPvvsM8aNG8ekSZPYsGED7dq1o3///qSkpJTafuXKlQwZMoQRI0YQHx/PoEGDGDRoEFu2bAHgzJkzbNiwgQkTJrBhwwb+97//sXPnTm655Zaq3C0RKaei3qGmTZtSq1Ytk6txPUW38/jx3cn4+PiwYfVyxxCkiBRjOJkuXboYY8aMcTzPz883wsLCjNjY2FLb33nnncbAgQNLLOvatasxatSoC77H2rVrDcA4ePDgZdWUlpZmAEZaWtpltReRijN58mQDMO68806zS3F5d999twEYd999t9mliFSJsnx/O1UPUU5ODnFxcfTr18+xzMvLi379+rFq1apS11m1alWJ9gD9+/e/YHuAtLQ0LBYLtWvXLvX17Oxs0tPTSzxExBy6QnXFeeyxx4CCnvjExESTqxFxLk4ViFJTU8nPzyckJKTE8pCQEJKSkkpdJykpqUzts7KyePLJJxkyZAj+/v6ltomNjSUgIMDxCA8PL8feiEhF0ITqitOhQwd69+5Nfn4+b775ptnliDgVpwpElS03N5c777wTwzCYOXPmBduNHz+etLQ0x0O/SYmYIyMjg127dgEKRBXlX//6FwCzp09n93+/0dWrRQo51ZWqg4KC8Pb2Jjk5ucTy5ORkQkNDS10nNDT0stoXhaGDBw/yyy+/XLB3CMBqtepquCJOYG1cweTfsAYNqFevnsnVuIcBAwbQtE4gu08eZ+HfbuFxIFFXrxZxrh4iPz8/OnbsyJIlSxzL7HY7S5YsISYmptR1YmJiSrQHWLx4cYn2RWFo9+7d/PzzzwQGBlbODohIhVmxJ5W/v/wZABk1rmLFnlSTK3IPOfkGga2uB+AV4DS6erUIOFkgAhg3bhzvvPMOH3zwAdu3b+eBBx4gMzOT4cOHAzB06FDGjx/vaD927FgWLVrEq6++yo4dO3j22WdZv349Dz74IFAQhv72t7+xfv16PvnkE/Lz80lKSiIpKYmcnBxT9lFELi4rN59RH8Vx+vBuALzqXc2oj+L0pV0BUtKzuSPfThMKbufxFtB551pdvVo8nlMNmQEMHjyYY8eOMXHiRJKSkoiOjmbRokWOidMJCQl4ef2Z47p168a8efN45plnePrpp2natCkLFy503BH78OHDfP3118D5F3X79ddfue6666pkv0Tk8qWkZ5OZlYP/3vWcBm5PTeSXrBxS0rOJCKxudnkuLdjfypx+/+Ca1AT27F7NCz5+RPb4G6N09WrxcBbDMAyzi3B26enpBAQEkJaWdtG5RyJSMbJy85nd+x4eW/EZecBB4LuedzN8yYe6ynIFWLEnlfs/WMvumaPJPZ7IiIef5N03JptdlkiFK8v3t9MNmYmI2Hy9qd6nHXlAKBAOdH/wHoWhCtK9SRBxE/vz+ssvAvDFB7M4efKkyVWJmEuBSESc0oFfC+5J2BewAG23rDa1Hndj8/Vm9PB7aNOmDWlpabz66qtmlyRiKgUiEXFKS/LyAOj79NMwYQI8+6y5BbkhLy8vnnvuOQDeeOMNNu5K0MR18ViaQ3QZNIdIpGqlpaVRt25d7HY7Bw8eJCIiwuyS3JZhGDRvE82urZto2vI6Hg0Mo+270+geFWx2aSJXTHOIRMSlLVu2DLvdTtOmTRWGKll2np2+1AHg0Lal3PL7PDaNfFQ9ReJxFIhExOkUXWy1b9++Jlfi/lLSsznabiDdgLPAU8DiiPa6LpF4HAUiEXE6RYGoX79+Jlfi/oL9rdyQuJE3KJi8/jHQeMtPBOu6ROJhFIhExKkcPXqUrVu3YrFY6N27t9nluD2brzdt353Gup53E9G4MwDf5h/Dz9ticmUiVUuBSEScyi+//AIU3N2+bt26JlfjGbpHBTN8yYf895vPqFWrFju2bGTu3LlmlyVSpRSIRMSpaP6QOWy+3nRs0YiJEycCMH78eNLT002uSqTqKBCJiNMwDIOff/4Z0Pwhszz88MNERUWRkpLCpOeeI+H4GZ1xJh5BgUhEnMaePXtITEzEz8+PHj16mF2OR/Lz82PatGkATJ/2OiOGP8ecvkNZsSvF5MpEKpcCkYg4jaLhspiYGKpX113tzdLn+v60qlOffMOO8c0URuvaROIBFIhExClk5ebzzQ8/AZo/ZLaU9GzCetyLDVgCvIuuTSTuT4FIREy3Yk8qHV/4iUU/FcwfCm7eyeSKPFuwv5XbTh3ixcLnjwEddy3XtYnErSkQiYipsnLzGf3hOm766nXsWRlYvX2Y/ke+hmdMVHRtImuPu6gbFEkG8LU1HauPvjLEfel/t4iYKiU9m5FLPiR4U8Fw2fX5edz36ycanjFZ96hgRvzyMQu++RKr1cra5b8yZ84cs8sSqTQKRCJiqmB/K+uadeHLwufXA+uaddHwjBOw+XrT55r2vPDCCwCMGzeONZt3q/dO3JICkYiYyubrzajcrayi4APpDiC2+mFsvt4mVyZFxo0bR8t2HUhLS+PWAbfwfp97dRq+uB0fswsQEfm1STgAPTt0ot6A/vi88LzJFUlxuXa43ac+e4HkIzswjuxg00gLHZd8qOAqbkM9RCJiKsMw+OjjjwEY+ehYfF78N3jpo8mZpKRns6X5dUwufP4o8HmNIM3zEreiTx0RMdXatWvZs2cP1atXZ9CgQWaXI6UI9rdyfUI8Y4HbgFxg86/v4Zt/xuTKRCqOApGImOrjwt6h2267jZo1a5pcjZSm6DT8WT3vJueO5wmy1eR4diaj7xvB2Zw83e9M3ILFMAzD7CKcXXp6OgEBAaSlpeHv7292OSJuIzc3l7CwMFJTU/nhhx8YMGCA2SXJRWTl5pOSns3hvVvpfW1PsrOzCek3ElvHQdS0+vD2vR3p3iTI7DJFHMry/a0eIhExzY8//khqairBwcG6u70LsPl6ExFYnZgunZn6WsENYI/9/B4RG77n/p/nMvrDdeopEpelQCQipikaLhsyZAg+Pjrp1ZX85c6hdAyKxI7BzsX/4S8r5zNyyYeaaC0uS4FIREyRnp7OV199BcC9995rcjVSViEBNhoPGE00kALcBCxv2FoX1BSXpUAkIqb4bMEXZGVl0axZczp06GB2OVJGNl9vpgak8h1wFbADOLR0FtnZ2ZpkLS5JfdQiUuVW7Erh1X89DUBUlh8rdx+je1SwyVVJWYW/OYW8ABsfNmjIrY+OYfWRQ0TG3EzATeOoZfPVJGtxKQpEIlKlsnLz+fXv97HrVDIAbxzcxKKRj+qqx67IywufF/9Nb+DTRldx8803k7blV0INL+4PqMdow866CTfouIpL0JCZiFSplPRs3juZggH0AxoBiyPaazKui2vT5VqGNOoIwM6tS8jXJGtxMQpEIlKlstNSSNy7FoAJhcuuT4jXZFwXF+xvxevau3iu8Pk44MO8szqu4jIUiESkSr3+6ivkG3aaBgTz+j2vMLPn3bR9d5qGVVyczdeb2OqHmcCfQXfD2q/4z/Q3yMrN10RrcXq6UvVl0JWqRSrGoUOHaNy4MTk5Ofy4+Geat48h2N+qMOQu7HbyJkzkWPfezHjpWV5csRyA2xu1x97tbq5PiKftu9M0gV6qTFm+vzWpWkSqzJQpU8jJyaFnz55c37cPFovF7JKkIhVOsq4PvHBjH+zPTCD2pRf57/54Xt4fz2hg1kg0gV6ckobMRKRKHDlyhNmzZwMwadIkhSE3Z7FYGPXoeJq1Lrgly5PAWOCnq9pporU4JQUiEakSU6ZMITs7m+7du9OnTx+zy5EqEBJg4+Ha9Xil8Pl0YO+Pb+Jj18UbxfkoEIlI5bLbOTT2Ed6eOROAic88o94hD2Hz9abde69To+fddOl5L75e3mw+cZiYq5sw+v7JzOk7lBW7UswuUwRQIBKRSpb48BO88uYbZOXkcA3Q/JvFZpckVah7VDDDl3zIgi9n8d3Pv1DTx0rC6RNs/d8LXPP7PDaNfFQ9ReIUFIhEpNJk5eYzYn8O0wufPw88ffYqfQF6GJuvNxGB1WnWthMxNz1CFJAAXAO8nXWW5LQsnZovptNZZiJSaQ4cPUH8L3MwgGHA9cC2nWtJSc8mIrC6ydVJVQv2t3LbyUTuAv4BfA38se5Lhv59CCnt/sFZi5WaVh/dA01MoUAkIpXm9dhJpGadprZfdY7f+hRvHt7Gu32HMkpXL/ZINl9v2r47jfkjwSs8mttXz2dhwiZ++/EbApf+QpveI7ktPVn3QBNT6MKMl0EXZhQpu8WLF3PDDTcAEPn3l6BBW/32L0DBUGpKejbB/lZ+/HU5w2+5iZPZZ/ABngDqXHMHd347l2B/q6OdwpGUhy7MKCKmOnXqFP/85z8BGDNmDFOnPaEvNnEomlME0L93D/re/jSWec+wAHgJ8N++DL9FS5i9y4/T2XkK0lIlFIhEpGLZ7Tx07bUcOnSIJnXq8HJsbIkvQJHibL7evFbnJOHA/4AxQFJaCmP/fgs9QpvQqOdQrj+8TcNoUukUiESkQr3U5wY+3rwZL+DDkyc5Mf45arw11eyyxImFvzmFvAAb3Xr0YdPi73goJZXPPvmQ5Ul7CFwwkf7AcLudxDE9sPp4q6dRKoUCkYhUmPfnfMD/W7YEgGeBGODvZxrwbm6+vsDkwgrvgRYKcGMf5ubmk5pagyM/zmQ78BBQa+sv7Ow9kJT2f+GGxI26SaxUOF2HSEQqxJdffsn9940ACr7Anilc3rnwNHuRy2Xz9WZOk+psAmYCwUBGRiqzt//OsXlPcPXv8/hjxCNk5ebr+kVSYdRDJCJX7KeffuKuu+4iPz+f2u36cXX1QG6/uhPX7Y/TafZSLkXDaIN69GHAt18zYNlmDm79hRXAAKD2tt85OO1dIr5ZxpLIDlyfEK9eI7kiOu3+Mui0e5ELsNtZOuwf3Ljgc7Kys/nb7bfz4L/fYsynf+jsIKkwWbn5zOk7lFt/n8erwCzgTOFrLYCxwD3ARz3v5u5Fc0g7m6d5RgLotHsRqQKGYRDb5waeW7aEHAp+a59cL5zGzUNZ/0w9nWYvFabogo5fjYT9Ee15du8q1rW6ioUfvcP2nLOMBh4H6iXt51DPQWxv0Uc9RlJmCkQiUmanT59mxMj7+LxwAvUg4BPg/uwIxwRqnWYvFal7VDAdl3zIwPRsgv0fBeA/245iWbWAWcAuIGP3Kl4Cum34AQNYMTSLjr9/DqCALpekQCQil89uZ9PoB/jbokXsTkzACwtTMBgHWPhzArXCkFSGc4N217lvsWmkLy3Do+m/6Qf+m3aM5MQtrARWApa1C5nfqy9tjmdzot1N3JS0g7bvTqNjo0AFJDmP5hBdBs0hEoHMzEye69ufGWtWcAYIAwa36UvDWvVY2qgj1+2P452+Q3XxPKlSRbcBCajmw7wBwxn0+zw+BeYBccXa+QA9gToN29M2qAF/NOtVYlit+O1E9P/XfZTl+1uB6DIoEImnysrN58iJTH5cOJ/nn3uWpKNHAehHwRDZ2GFT2RzZWhOoxSms2JXCppGPsjiiPdcnxGMfex9vPfcSls2L2X5O2yigL5DbvAc3vTOTpKdjHeupF8l9KBBVMAUi8UTLth7m47/dxWdHd5ORlgxAoLUGb2VncicFFzF7o9td3PS/2bp6sDiN4j09AHP6DuWB3+exB/gWeK9GXXZkniDvnPXaUNCDdA2wu8NNhFYP4OdzTudXL5LrUSCqYApE4hHsdvImTGRNw6b8771ZvLMhnozcggsq1gX6XN2ebYOfZdSyTzVEJi6jZK/RBgzD4J7l8/kV+BX4onoAR86knbdeXaALEA2kNOtGz1diOT1lJr9EdlQvkgtRIKpgCkTijop+261Xy4+D+/bw6X0PsHT5Un4r1iYEGAn8C/jnPa9w77i7mPDVVg2RiUsp3rMTt/94iWG15rNeZd0/x3D1mv+xClgNrLN4kWvYz9uODWgJNAfSIlpTv3pt9l3dhb+cOkTnOdMv2IukniXzKBBVMAUicWaX8wFc/LnVx4vPf17LTw8/xi95eaQnbuZE9hnH9rwouKZQi4i2xCZswrdw+cyedzN8yYeATmEW13buz8e5vUi5+Xl0W7mAdcAfwE+1Akk4m0F+Xs4Ft+nva+OqVq2pcTiV9ODGdMhOp8MTj1AvpD6psf9h+dVdCu7BNvtVun70Fqk9+hC0/Bd8XngevLwu+jOrn7Pyc/lANGPGDF555RWSkpJo164d06dPp0uXLhdsv2DBAiZMmMCBAwdo2rQpL7/8MjfddJPjdcMwmDRpEu+88w6nTp2ie/fuzJw5k6ZNm15WPQpEnqusYeNivxGWZ71LtYk7eJJRH8WV6LHBbmfTyEf5KTyaLntWcvyu20me+RZrfGx4HdnBIftZMjPSS+ynj8WLxv71uC8tmTuBcOCNmMH4+XixOEK3RRD3d6lepG2jxnHD8k/ZBuwAfqhdn+xTR9kBnLqM7duAUKCmXzWa5JwlBKgH+PTojX3QHZycu4DNV7WlT+p+aj7zDH5Tp5W8JUmTIPImTCwRpLLyjSr9fHJFLh2IPvvsM4YOHcqsWbPo2rUrr7/+OgsWLGDnzp0EB5//Ybxy5UquvfZaYmNjufnmm5k3bx4vv/wyGzZsoHXr1gC8/PLLxMbG8sEHH9CoUSMmTJjA5s2b2bZtGzab7ZI1VWYgqowvyYpsY/b7O13YgBLLHurThOm/7Llom1LXu+5q7JOeLXFWC1DiQ9hr0kTszz1fok1ebi7rRo5lcXBTohM2ML95d66LW8RG/2CCk3axrm4Y9RO34nUqiQP8eXuDc3l5+dDRnkcMBb1BMwe/yL6m0dz/y0cl5gctf6qvboMgHulSvUiGYfB/y+cDcBJ4uX1/fq0ZzF9//4gEIBH4rU4YZ8+kkZOdWeb3twABhY+8GrUJ869B8NHD+AM1gTMt2nEyM5+DgZG0Tk+m8ch7sdqqkfTOJ2yu35xrUvfhN/oBfN59jzVXteO6pO20mz4Zq9XK9jHjS4QtuPRnz3mB7LlnyZv0bMmeLrh0myruDXPpQNS1a1c6d+7MW2+9BYDdbic8PJyHHnqIp5566rz2gwcPJjMzk2+//dax7JprriE6OppZs2ZhGAZhYWE89thj/Otf/wIgLS2NkJAQ5s6dy1133XXJmiorEH364yqWPvokf9RrRLtj+7EMvhPjs88dzyPH/BOAgzPeN6VN0bIDM97nj6BGtEvdj9edd2D/fIHjecP/G17Q5j9zKrFNQ9ql7ifygYI2B2f+2aZo2YH/zGFTvUa0PbYfy51/w/j8CzYFNaRt6gEiRg8rWG/WXDYFNaJN6n68br8d+3//y+bAhrRJ3U/4/fcCkDD7IzYHNqT18f381CyGPttXsj2oIc2P7Wdpi25ggWu3rmBHUCRRqQf4uXEn+u5Zx87AcJqmJrA8qhMYBtfsWsvuOg1odDyRtVe3A8Og/d549geEcNXJI9gNO22O7iIXyAa21Iskz7ATnprIWSALSPW14ZWbxRkgAzhl8SKvlHkNF+MF+Ffzp8vZdJoC7YFPbnyEv6Yf5cEVnznazex5N81nT+OhT+M1P0jkAi7Vi7Rj9GM88Ps8R/uZPYcAFv7x+zySgaPAb4Hh1DqeSDKQCqwMDOeQjx+hyXs5QUG4OlsF++ID+AGGjy++Fm/8c7PwA3yBPB8rAXnZ+Ba2SwkIJrimjZqHE/ApXJYbUIeaaSfxAbyBrOat8LZY8N++BW8KPnuyAoOpdTzF8fx0h86c7hzDse+XsD+gPo3Tk/Du3RuWLmNv7TBusOfyty/mVWhPtMsGopycHKpXr84XX3zBoEGDHMuHDRvGqVOn+Oqrr85bJyIignHjxvHII484lk2aNImFCxfyxx9/sG/fPho3bkx8fDzR0dGONr169SI6Opo33njjvG1mZ2eTnZ3teJ6enk54eHiFBqKs3HzuiurIVwf+qJDtiWepQcFZMNm1AmmVcZxAoD7wW4ebaHf6BH/ftZpIoCEQf1Uruh7a6lh3Zs+7HR/eJX4D1GnFImVy8V6k0npfNvBWz7sZtfQTR0/s7D73MmbZJyWC1G8NWtD08HZOAWnAJ62v43RODt13rSQDOA2sD4rkqtSDZFDQE7w8rDn5eTk0TNnHWQpCVYq1Or7ZZzhLwS9eTvNlfwHjgfDCuYoV9fnjsjd3TU1NJT8/n5CQkBLLQ0JC2LFjR6nrJCUlldo+KSnJ8XrRsgu1OVdsbCzPPfdcufbhcqWkZ3MorAXdiwWig7XrE3nqqOP59noNAWhx7IApbarq/S3A9nqNCtvsd7Q5ULs+DUtsp2QbC7CtcFnLY/uxFLbbXyeMRiePONpsDb4agFYp+xxt9tVpwNUnDzvabAlpAkDb5D2ONnsCw4k6nuhos6lBcywWC+0PbcdCwW882+s1onXhe3sDaxpGY/Gy0H1fPF4U/ID93rQLFosX1+9a7fiNa29QJK1TD+ILWIH1jdrj7eVF371xVAOqAQmBEUQfT6A6UAtY2PkWrN6+jF39X8dE53W1Q+mccdzxb5QY04KEh59g08hHmVms+3vDud3fUcHEOO4L9Wf40T3IRC7fuT8vJe+39ufPVfFlbQ+eZJSPL6ez89jVuE3BkPq9nZg5khJDVluL/cz+ddarPDw/nvZLPuT3Rh3ptT+OvobBw6kHHe89s3F7wMIDKfscy9bUa+T4ZcgA3up+J3l2g3tXLSAbyAE+6DiQPMNg0IbvyQVygU1BkTROPUgukAd817w7ufn59N29mjwgH9hduz4Rp446ni+LaIeBna4Jm7EXLkusFURoRir5he+/vn4zEgOCuWnH79gLl626qhWdD23FDnQCPo5oz0CTbv/jVIHIWYwfP55x48Y5nhf1EFWkYH8rI7y9eKDYsjU169K1WACY2TwGsPBAsSBRlW2q9v2vKWyzv0xtSl2vRh26FgYigJnNunLeB0WN2nQtDEQAM6M6F7RJ3uNYtq66P53/zBokDhoIQPiMP695e6R+EGHF3jtxYN/CNvF/LruhZ8GyXasdy+JuvJm1B046PvAeLfab5JeFy2pMmsjOYh+K1xW2eXek9c9wM/tV8oqdsRL+wvOEe3md96Gcda3Cj0hVKO3nqviy7k2CWP9Mv/N6Yi/1MztraGdGWbwcQeqh665m5iTv83qjzg1WxX8Z6lDYZsFIX8ey6wuXrSvWs+U7aSIHiq3398JA1mnJhywtDGT/7X4Xj6yYz++FPV37+9yLxWLhhmJtPi5sU9Qb9kOfe3ls2Sc8UKx/Yw3Qtdi/VXJCvOOimlXNqQJRUFAQ3t7eJCcnl1ienJxMaGhoqeuEhoZetH3Rn8nJydSvX79Em+JDaMVZrVas1so9IDZfb9q+O+2i/3kv5z94ZbYx+/3NrrG0sAGQF2BzLAs7Z9JgaW1KW9bxhedplW9c9DfJCwWZ834DffHfhALc2KfE/6/iH8oKPyLO41KhqbTnpQWprB6X/ny4rM+Qy1jv3ED2ZJ8mTK/2j5I9XXDpNqX0hp37WWzacL3hZLp06WI8+OCDjuf5+flGgwYNjNjY2FLb33nnncbNN99cYllMTIwxatQowzAMw263G6GhocbUqVMdr6elpRlWq9X49NNPL6umtLQ0AzDS0tLKujuXdDYnzziYmmmczckr9bnZbcx+f7NrFBGRAlX5OV9RyvL97VSTqqHgtPthw4bx9ttv06VLF15//XU+//xzduzYQUhICEOHDqVBgwbExsYCBafd9+rVi8mTJzNw4EDmz5/PSy+9dN5p95MnTy5x2v2mTZuc4rR7ERERqRwuO6kaCk6jP3bsGBMnTiQpKYno6GgWLVrkmBSdkJCAl5eXo323bt2YN28ezzzzDE8//TRNmzZl4cKFjjAE8MQTT5CZmcn999/PqVOn6NGjB4sWLbqsMCQiIiLuz+l6iJyReohERERcT1m+v70u+qqIiIiIB1AgEhEREY+nQCQiIiIeT4FIREREPJ4CkYiIiHg8BSIRERHxeApEIiIi4vEUiERERMTjKRCJiIiIx3O6W3c4o6KLeaenp5tciYiIiFyuou/ty7kphwLRZcjIyAAgPDzc5EpERESkrDIyMggICLhoG93L7DLY7XaOHDlCrVq1sFgsFbrt9PR0wsPDSUxMdMv7pGn/XJ+776P2z/W5+z5q/8rPMAwyMjIICwsrcWP40qiH6DJ4eXlx1VVXVep7+Pv7u+V/9CLaP9fn7vuo/XN97r6P2r/yuVTPUBFNqhYRERGPp0AkIiIiHk+ByGRWq5VJkyZhtVrNLqVSaP9cn7vvo/bP9bn7Pmr/qoYmVYuIiIjHUw+RiIiIeDwFIhEREfF4CkQiIiLi8RSIRERExOMpEFWyF198kW7dulG9enVq165dapuEhAQGDhxI9erVCQ4O5vHHHycvL++i2z1x4gT33HMP/v7+1K5dmxEjRnD69OlK2IOyWbp0KRaLpdTHunXrLrjeddddd1770aNHV2Hll69hw4bn1Tp58uSLrpOVlcWYMWMIDAykZs2a3H777SQnJ1dRxZfvwIEDjBgxgkaNGlGtWjUaN27MpEmTyMnJueh6zn78ZsyYQcOGDbHZbHTt2pW1a9detP2CBQto3rw5NpuNNm3a8P3331dRpWUTGxtL586dqVWrFsHBwQwaNIidO3dedJ25c+eed6xsNlsVVVx2zz777Hn1Nm/e/KLruMrxg9I/TywWC2PGjCm1vSscv99++42//OUvhIWFYbFYWLhwYYnXDcNg4sSJ1K9fn2rVqtGvXz927959ye2W9ee4rBSIKllOTg533HEHDzzwQKmv5+fnM3DgQHJycli5ciUffPABc+fOZeLEiRfd7j333MPWrVtZvHgx3377Lb/99hv3339/ZexCmXTr1o2jR4+WeIwcOZJGjRrRqVOni6573333lVhvypQpVVR12T3//PMlan3ooYcu2v7RRx/lm2++YcGCBSxbtowjR47w17/+tYqqvXw7duzAbrfz9ttvs3XrVqZNm8asWbN4+umnL7musx6/zz77jHHjxjFp0iQ2bNhAu3bt6N+/PykpKaW2X7lyJUOGDGHEiBHEx8czaNAgBg0axJYtW6q48ktbtmwZY8aMYfXq1SxevJjc3FxuuOEGMjMzL7qev79/iWN18ODBKqq4fFq1alWi3uXLl1+wrSsdP4B169aV2LfFixcDcMcdd1xwHWc/fpmZmbRr144ZM2aU+vqUKVN48803mTVrFmvWrKFGjRr079+frKysC26zrD/H5WJIlZgzZ44REBBw3vLvv//e8PLyMpKSkhzLZs6cafj7+xvZ2dmlbmvbtm0GYKxbt86x7IcffjAsFotx+PDhCq/9SuTk5Bj16tUznn/++Yu269WrlzF27NiqKeoKRUZGGtOmTbvs9qdOnTJ8fX2NBQsWOJZt377dAIxVq1ZVQoUVa8qUKUajRo0u2saZj1+XLl2MMWPGOJ7n5+cbYWFhRmxsbKnt77zzTmPgwIEllnXt2tUYNWpUpdZZEVJSUgzAWLZs2QXbXOizyFlNmjTJaNeu3WW3d+XjZxiGMXbsWKNx48aG3W4v9XVXO36A8eWXXzqe2+12IzQ01HjllVccy06dOmVYrVbj008/veB2yvpzXB7qITLZqlWraNOmDSEhIY5l/fv3Jz09na1bt15wndq1a5focenXrx9eXl6sWbOm0msui6+//prjx48zfPjwS7b95JNPCAoKonXr1owfP54zZ85UQYXlM3nyZAIDA2nfvj2vvPLKRYc44+LiyM3NpV+/fo5lzZs3JyIiglWrVlVFuVckLS2NunXrXrKdMx6/nJwc4uLiSvzbe3l50a9fvwv+269atapEeyj4mXSVYwVc8nidPn2ayMhIwsPDufXWWy/4WeMsdu/eTVhYGFdffTX33HMPCQkJF2zryscvJyeHjz/+mH/+858XvZG4qx2/4vbv309SUlKJYxQQEEDXrl0veIzK83NcHrq5q8mSkpJKhCHA8TwpKemC6wQHB5dY5uPjQ926dS+4jlnee+89+vfvf8mb4959991ERkYSFhbGpk2bePLJJ9m5cyf/+9//qqjSy/fwww/ToUMH6taty8qVKxk/fjxHjx7ltddeK7V9UlISfn5+580hCwkJcbrjda49e/Ywffp0pk6detF2znr8UlNTyc/PL/VnbMeOHaWuc6GfSWc/Vna7nUceeYTu3bvTunXrC7Zr1qwZ77//Pm3btiUtLY2pU6fSrVs3tm7dWuk3sS6Prl27MnfuXJo1a8bRo0d57rnn6NmzJ1u2bKFWrVrntXfV4wewcOFCTp06xT/+8Y8LtnG143euouNQlmNUnp/j8lAgKoennnqKl19++aJttm/ffsmJf66kPPt86NAhfvzxRz7//PNLbr/4/Kc2bdpQv359+vbty969e2ncuHH5C79MZdm/cePGOZa1bdsWPz8/Ro0aRWxsrOmXnr+Q8hy/w4cPM2DAAO644w7uu+++i65r9vETGDNmDFu2bLno/BqAmJgYYmJiHM+7detGixYtePvtt3nhhRcqu8wyu/HGGx1/b9u2LV27diUyMpLPP/+cESNGmFhZxXvvvfe48cYbCQsLu2AbVzt+rkSBqBwee+yxiyZ4gKuvvvqythUaGnreTPmis49CQ0MvuM65E8ny8vI4ceLEBde5UuXZ5zlz5hAYGMgtt9xS5vfr2rUrUNBDURVfqFdyTLt27UpeXh4HDhygWbNm570eGhpKTk4Op06dKtFLlJycXGnH61xl3b8jR47Qu3dvunXrxuzZs8v8flV9/C4kKCgIb2/v887ou9i/fWhoaJnaO4MHH3zQcXJFWXsJfH19ad++PXv27Kmk6ipW7dq1iYqKumC9rnj8AA4ePMjPP/9c5l5VVzt+RcchOTmZ+vXrO5YnJycTHR1d6jrl+TkulwqbjSQXdalJ1cnJyY5lb7/9tuHv729kZWWVuq2iSdXr1693LPvxxx+dalK13W43GjVqZDz22GPlWn/58uUGYPzxxx8VXFnF+/jjjw0vLy/jxIkTpb5eNKn6iy++cCzbsWOH006qPnTokNG0aVPjrrvuMvLy8sq1DWc6fl26dDEefPBBx/P8/HyjQYMGF51UffPNN5dYFhMT45STcu12uzFmzBgjLCzM2LVrV7m2kZeXZzRr1sx49NFHK7i6ypGRkWHUqVPHeOONN0p93ZWOX3GTJk0yQkNDjdzc3DKt5+zHjwtMqp46dapjWVpa2mVNqi7Lz3G5aq2wLUmpDh48aMTHxxvPPfecUbNmTSM+Pt6Ij483MjIyDMMo+M/cunVr44YbbjA2btxoLFq0yKhXr54xfvx4xzbWrFljNGvWzDh06JBj2YABA4z27dsba9asMZYvX240bdrUGDJkSJXv34X8/PPPBmBs3779vNcOHTpkNGvWzFizZo1hGIaxZ88e4/nnnzfWr19v7N+/3/jqq6+Mq6++2rj22muruuxLWrlypTFt2jRj48aNxt69e42PP/7YqFevnjF06FBHm3P3zzAMY/To0UZERITxyy+/GOvXrzdiYmKMmJgYM3bhog4dOmQ0adLE6Nu3r3Ho0CHj6NGjjkfxNq50/ObPn29YrVZj7ty5xrZt24z777/fqF27tuPMznvvvdd46qmnHO1XrFhh+Pj4GFOnTjW2b99uTJo0yfD19TU2b95s1i5c0AMPPGAEBAQYS5cuLXGszpw542hz7v4999xzxo8//mjs3bvXiIuLM+666y7DZrMZW7duNWMXLumxxx4zli5dauzfv99YsWKF0a9fPyMoKMhISUkxDMO1j1+R/Px8IyIiwnjyySfPe80Vj19GRobjuw4wXnvtNSM+Pt44ePCgYRiGMXnyZKN27drGV199ZWzatMm49dZbjUaNGhlnz551bKNPnz7G9OnTHc8v9XNcERSIKtmwYcMM4LzHr7/+6mhz4MAB48YbbzSqVatmBAUFGY899liJ3xJ+/fVXAzD279/vWHb8+HFjyJAhRs2aNQ1/f39j+PDhjpDlDIYMGWJ069at1Nf2799f4t8gISHBuPbaa426desaVqvVaNKkifH4448baWlpVVjx5YmLizO6du1qBAQEGDabzWjRooXx0ksvlejNO3f/DMMwzp49a/zf//2fUadOHaN69erGbbfdViJkOIs5c+aU+v+1eGeyKx6/6dOnGxEREYafn5/RpUsXY/Xq1Y7XevXqZQwbNqxE+88//9yIiooy/Pz8jFatWhnfffddFVd8eS50rObMmeNoc+7+PfLII45/i5CQEOOmm24yNmzYUPXFX6bBgwcb9ev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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "w=np.linspace(-10,10,100)\n", - "plt.scatter(w,obp.corr_spectrum_approx(w),s=8)\n", - "plt.scatter(w,obp2.spec_spectrum_approx(w),s=5,marker='x',color='red')\n", - "plt.plot(w,obp.ohmic_power_spectrum(w),color='k')\n", - "plt.ylabel(r'$J( \\omega )$')\n", - "plt.xlabel(r'$\\omega$')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "c4cd4157-f1a3-4ed9-9293-45777606b5ca", - "metadata": {}, - "source": [ - "Both approaches of obtaining the Ohmic bath yield almost identical results, as expected " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6fa3988d-5117-4268-b494-1e349bff48b7", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "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": "3.12.0" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/.ipynb_checkpoints/RHS_heom-checkpoint.ipynb b/.ipynb_checkpoints/RHS_heom-checkpoint.ipynb deleted file mode 100644 index 363fcab7ed..0000000000 --- a/.ipynb_checkpoints/RHS_heom-checkpoint.ipynb +++ /dev/null @@ -1,6 +0,0 @@ -{ - "cells": [], - "metadata": {}, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/Fitting_HEOM.ipynb b/Fitting_HEOM.ipynb deleted file mode 100644 index b718031a83..0000000000 --- a/Fitting_HEOM.ipynb +++ /dev/null @@ -1,433 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "cb83932f", - "metadata": {}, - "outputs": [], - "source": [ - "from qutip import *\n", - "import numpy as np" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "3e389834", - "metadata": {}, - "outputs": [], - "source": [ - "# Defining the system Hamiltonian\n", - "eps = 0.2 # Energy of the 2-level system.\n", - "Del = 0 # Tunnelling term\n", - "Hsys = 0.5 * eps * sigmaz() + 0.5 * Del * sigmax()\n", - "# Initial state of the system.\n", - "rho0 = basis(2, 0) * basis(2, 0).dag()\n", - "tlist=np.linspace(0,10,1000)" - ] - }, - { - "cell_type": "markdown", - "id": "45b970e7-5064-479a-9450-48a533748716", - "metadata": {}, - "source": [ - "## Spectral density fitting" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "4d63e22e", - "metadata": {}, - "outputs": [], - "source": [ - "w = np.linspace(0, 20, 20000)\n", - "def ohmic_spectral_density(w, alpha, wc):\n", - " \"\"\" The Ohmic bath spectral density as a function of w\n", - " (and the bath parameters).\n", - " \"\"\"\n", - " return w * alpha * np.e**(-w / wc)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "3dac107b-86ff-4b6c-9662-a726080c617a", - "metadata": {}, - "outputs": [], - "source": [ - "alpha=0.05\n", - "T=1\n", - "wc=0.5" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "c9aa3205", - "metadata": {}, - "outputs": [], - "source": [ - "J=ohmic_spectral_density(w,alpha,wc)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "ca762b08", - "metadata": {}, - "outputs": [], - "source": [ - "obp=heom.FitSpectral(T, sigmax(), Nk=4)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "0b9dbb68-63a8-45fe-b8cc-eaca06211e57", - "metadata": {}, - "outputs": [], - "source": [ - "obp.get_fit(J,w,final_rmse=9e-6)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "c8349e53-001f-4ee5-80ed-fc03bd08e132", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "10.0%. 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Est. time left: 00:00:00:00\n", - "Total run time: 0.92s\n" - ] - } - ], - "source": [ - "options = {'nsteps':15000, 'store_states':True, 'rtol':1e-12, 'atol':1e-12, 'method':\"bdf\"}\n", - "HEOM_spectral_fit = heom.HEOMSolver(Hsys, obp.Bath_spec, max_depth=4, options=options,)\n", - "result_spectral=HEOM_spectral_fit.run(rho0,tlist)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "ba8ad1ba", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Results of the fitting the Spectral density with 4 terms: \n", - " \n", - " Parameters| lam | gamma | w0 \n", - " 1 | 7.67e-02 | 3.21e-01 |5.00e-02 \n", - " 2 |-8.19e-03 | 2.15e+00 |2.04e+00 \n", - " 3 |-7.58e-02 | 3.20e-01 |5.31e-02 \n", - " 4 | 1.52e-02 | 1.13e+00 |5.01e-02 \n", - " \n", - "A normalized RMSE of 2.28e-06 was obtained for the Spectral density \n", - " The current fit took 31.700378 seconds\n" - ] - } - ], - "source": [ - "obp.summary()" - ] - }, - { - "cell_type": "markdown", - "id": "a68fa018-26b0-4a38-9298-f4f54dccc7c1", - "metadata": {}, - "source": [ - "## Correlation Function Fitting" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "e1878268-b61c-4209-b86b-e1996a918ce4", - "metadata": {}, - "outputs": [], - "source": [ - "from mpmath import mp\n", - "alpha=0.05\n", - "T=1\n", - "wc=0.5" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "75f32f68-9729-462f-b168-02b730dd970f", - "metadata": {}, - "outputs": [], - "source": [ - "def ohmic_correlation(t, alpha, wc, beta, s=1):\n", - " \"\"\" The Ohmic bath correlation function as a function of t\n", - " (and the bath parameters).\n", - " \"\"\"\n", - " corr = (\n", - " (1 / np.pi) * alpha * wc**(1 - s) * beta**(-(s + 1)) * mp.gamma(s + 1)\n", - " )\n", - " z1_u = (1 + beta * wc - 1.0j * wc * t) / (beta * wc)\n", - " z2_u = (1 + 1.0j * wc * t) / (beta * wc)\n", - " # Note: the arguments to zeta should be in as high precision as possible.\n", - " # See http://mpmath.org/doc/current/basics.html#providing-correct-input\n", - " return np.array([\n", - " complex(corr * (mp.zeta(s + 1, u1) + mp.zeta(s + 1, u2)))\n", - " for u1, u2 in zip(z1_u, z2_u)\n", - " ], dtype=np.complex128)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "ba2d7d9a-cebf-4468-a7c7-2479953a73b5", - "metadata": {}, - "outputs": [], - "source": [ - "C=ohmic_correlation(tlist,alpha,wc,1/T)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "eac8b815", - "metadata": {}, - "outputs": [], - "source": [ - "obp2=heom.FitCorr(sigmax())" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "af7df643-faab-4a60-aaa2-ec423badf3a4", - "metadata": {}, - "outputs": [], - "source": [ - "obp2.fit_correlation(tlist,C,final_rmse=8e-5)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "551d18e6", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Fit correlation class instance: \n", - " \n", - "\n", - "Results of the fitting the Real Part with 3 terms: |\t Results of the fitting the Imaginary Part with 4 terms: \n", - " | \n", - " Parameters| lam | gamma | w0 | \t Parameters| lam | gamma | w0 \n", - " 1 | 3.54e-03 |-1.81e-01 |3.78e-14 |\t 1 |-1.29e-02 |-8.57e-01 |3.44e-01 \n", - " 2 |-6.46e-03 |-2.07e+00 |1.28e+00 | \t 2 | 1.17e-03 |-2.15e+00 |2.33e+00 \n", - " 3 | 1.95e-02 |-6.56e-01 |8.73e-11 | \t 3 |-1.89e-03 |-1.01e+00 |1.04e+00 \n", - " | \t 4 |-1.29e-02 |-3.93e-01 |2.36e-02 \n", - " | \n", - " A normalized RMSE of 3.21e-06 was obtained for the real part | \t A normalized RMSE of 2.23e-06 was obtained for the imaginary part \n", - "\t \t \t \t \t \t The current fit took 9.119783 seconds\n" - ] - } - ], - "source": [ - "obp2.summary()" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "ee42d781-9da8-48ce-86e6-79b9c3522864", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "10.0%. 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Est. time left: 00:00:00:00\n", - "Total run time: 0.26s\n" - ] - } - ], - "source": [ - "options = {'nsteps':15000, 'store_states':True, 'rtol':1e-12, 'atol':1e-12, 'method':\"bdf\"}\n", - "HEOM_corr_fit = heom.HEOMSolver(Hsys, obp2.Bath_corr, max_depth=4, options=options,)\n", - "result_corr=HEOM_corr_fit.run(rho0,tlist)" - ] - }, - { - "cell_type": "markdown", - "id": "5f8af268-5059-46a7-9d24-9a07a8a05d7b", - "metadata": {}, - "source": [ - "# Comparison between fits" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "2f29bd39-5a12-48f5-a78f-50a621b650eb", - "metadata": {}, - "outputs": [], - "source": [ - "def projection(result,i,j):\n", - " return [result.states[k][i,j] for k in range(len(result.states))]" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "930b28d4-90dd-4c8d-9568-20b33dde6fa7", - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "fea8022a-02f5-4043-871f-da8048a598b7", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/mcditoos/anaconda3/envs/qutip-dev/lib/python3.12/site-packages/matplotlib/cbook.py:1699: ComplexWarning: Casting complex values to real discards the imaginary part\n", - " return math.isfinite(val)\n", - "/home/mcditoos/anaconda3/envs/qutip-dev/lib/python3.12/site-packages/matplotlib/cbook.py:1345: ComplexWarning: Casting complex values to real discards the imaginary part\n", - " return np.asarray(x, float)\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(tlist,projection(result_corr,0,0))\n", - "plt.plot(tlist,projection(result_spectral,0,0),color='k')\n", - "plt.xlabel('t')\n", - "plt.ylabel(r'$\\rho_{11}$')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "bd2e4af7", - "metadata": {}, - "outputs": [], - "source": [ - "def ohmic_power_spectrum(w, alpha, wc, beta):\n", - " \"\"\" The Ohmic bath power spectrum as a function of w\n", - " (and the bath parameters).\n", - " \"\"\"\n", - " return (\n", - " w * alpha * np.e**(-abs(w) / wc) *\n", - " ((1 / (np.e**(w * beta) - 1)) + 1) * 2\n", - " )" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "86ef45f2-c782-4075-becb-2617381ff831", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/mcditoos/anaconda3/envs/qutip-dev/lib/python3.12/site-packages/matplotlib/collections.py:194: ComplexWarning: Casting complex values to real discards the imaginary part\n", - " offsets = np.asanyarray(offsets, float)\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "w=np.linspace(-10,10,1000)\n", - "plt.plot(w,ohmic_power_spectrum(w,alpha,wc,1/T),color='green')\n", - "plt.scatter(w,obp2.corr_spectrum_approx(w),color='red',s=4)\n", - "plt.scatter(w,obp.spec_spectrum_approx(w),color='k',s=4)\n", - "plt.ylabel(r'$P( \\omega )$')\n", - "plt.xlabel(r'$\\omega$')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "9db0ba4d", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "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": "3.12.0" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/OhmicBath.ipynb b/OhmicBath.ipynb deleted file mode 100644 index 3c8e64cfb2..0000000000 --- a/OhmicBath.ipynb +++ /dev/null @@ -1,306 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "2bb296b7-6f64-4660-a79a-30309e63153f", - "metadata": {}, - "outputs": [], - "source": [ - "from qutip import *\n", - "import numpy as np" - ] - }, - { - "cell_type": "markdown", - "id": "c4ed1d4b-69ee-495d-bdd4-e85d129bcea5", - "metadata": {}, - "source": [ - "Setting parameters" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "b52eb1f2-6579-4f8a-9329-8543d301090c", - "metadata": {}, - "outputs": [], - "source": [ - "# Defining the system Hamiltonian\n", - "Hsys = 0.5 * sigmaz()\n", - "# Initial state of the system.\n", - "rho0 = basis(2, 0) * basis(2, 0).dag()\n", - "tlist=np.linspace(0,10,100)\n", - "# defining Ohmic bath properties\n", - "alpha=0.05\n", - "T=1\n", - "wc=1\n", - "s=1\n" - ] - }, - { - "cell_type": "markdown", - "id": "7cad3ae4-1f51-4950-9d7f-b8c7ac6f0f77", - "metadata": {}, - "source": [ - "Obtaining an Ohmic Bath via Correlation functions" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "f3f59052-a687-4a00-8a0a-ece534e77433", - "metadata": {}, - "outputs": [], - "source": [ - "obp=heom.OhmicBath(T,sigmax(),alpha,wc,s,rmse=1e-4)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "b944e6df", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Fit correlation class instance: \n", - " \n", - "\n", - "Results of the fitting the Real Part with 3 terms: |\t Results of the fitting the Imaginary Part with 3 terms: \n", - " | \n", - " Parameters| lam | gamma | w0 | \t Parameters| lam | gamma | w0 \n", - " 1 | 4.12e-02 |-1.32e+00 |7.28e-18 |\t 1 |-5.16e-02 |-9.06e-01 |9.06e-02 \n", - " 2 |-9.70e-03 |-4.87e+00 |4.80e+00 | \t 2 | 3.78e-03 |-4.00e+00 |5.44e+00 \n", - " 3 | 5.10e-03 |-2.86e-01 |6.65e-18 | \t 3 |-5.16e-02 |-1.94e+00 |9.48e-01 \n", - " | \n", - " A normalized RMSE of 4.24e-05 was obtained for the real part | \t A normalized RMSE of 4.08e-05 was obtained for the imaginary part \n", - "\t \t \t \t \t \t The current fit took -0.994941 seconds\n" - ] - } - ], - "source": [ - "obp.summary()" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "62db8a97-d209-4da8-8d77-5420409f0615", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "10.1%. Run time: 0.04s. Est. time left: 00:00:00:00\n", - "20.2%. Run time: 0.06s. Est. time left: 00:00:00:00\n", - "30.3%. Run time: 0.08s. Est. time left: 00:00:00:00\n", - "40.4%. Run time: 0.10s. Est. time left: 00:00:00:00\n", - "50.5%. Run time: 0.13s. Est. time left: 00:00:00:00\n", - "60.6%. Run time: 0.15s. Est. time left: 00:00:00:00\n", - "70.7%. Run time: 0.17s. Est. time left: 00:00:00:00\n", - "80.8%. Run time: 0.20s. Est. time left: 00:00:00:00\n", - "90.9%. Run time: 0.22s. Est. time left: 00:00:00:00\n", - "100.0%. Run time: 0.24s. Est. time left: 00:00:00:00\n", - "Total run time: 0.24s\n" - ] - } - ], - "source": [ - "options = {'nsteps':15000, 'store_states':True, 'rtol':1e-12, 'atol':1e-12, 'method':\"bdf\"}\n", - "HEOM_corr_fit = heom.HEOMSolver(Hsys, obp.fit.Bath_corr, max_depth=4, options=options)\n", - "result_corr=HEOM_corr_fit.run(rho0,tlist)" - ] - }, - { - "cell_type": "markdown", - "id": "fd990fca-2f2d-4136-ba3e-dccfb0c38644", - "metadata": {}, - "source": [ - "Obtaining an Ohmic Bath via Spectral density\n", - "\n", - "If the spectral method is specified than the Ohmic bath is obtained by fitting the ohmic spectral density " - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "3fad860d-7493-41da-9a1f-af7fa545399e", - "metadata": {}, - "outputs": [], - "source": [ - "obp2=heom.OhmicBath(T,sigmax(),alpha,wc,s,Nk=4,method='spectral',rmse=3e-5)" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "d6cd7456", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Results of the fitting the Spectral density with 4 terms: \n", - " \n", - " Parameters| lam | gamma | w0 \n", - " 1 |-6.78e-02 | 4.30e+00 |3.98e+00 \n", - " 2 | 1.22e-01 | 2.30e+00 |1.00e-01 \n", - " 3 | 1.63e-04 | 3.07e-01 |1.00e-01 \n", - " 4 | 9.24e-03 | 1.00e+00 |1.00e-01 \n", - " \n", - "A normalized RMSE of 6.47e-06 was obtained for the Spectral density \n", - " The current fit took 0.465765 seconds\n" - ] - } - ], - "source": [ - "obp2.summary()" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "fb547724-f89b-4375-89e7-43456df7041e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "10.1%. Run time: 0.06s. Est. time left: 00:00:00:00\n", - "20.2%. Run time: 0.13s. Est. time left: 00:00:00:00\n", - "30.3%. Run time: 0.19s. Est. time left: 00:00:00:00\n", - "40.4%. Run time: 0.25s. Est. time left: 00:00:00:00\n", - "50.5%. Run time: 0.30s. Est. time left: 00:00:00:00\n", - "60.6%. Run time: 0.36s. Est. time left: 00:00:00:00\n", - "70.7%. Run time: 0.41s. Est. time left: 00:00:00:00\n", - "80.8%. Run time: 0.46s. Est. time left: 00:00:00:00\n", - "90.9%. Run time: 0.53s. Est. time left: 00:00:00:00\n", - "100.0%. Run time: 0.58s. Est. time left: 00:00:00:00\n", - "Total run time: 0.58s\n" - ] - } - ], - "source": [ - "HEOM_spectral_fit = heom.HEOMSolver(Hsys, obp2.fit.Bath_spec, max_depth=4, options=options)\n", - "result_spectral=HEOM_spectral_fit.run(rho0,tlist)" - ] - }, - { - "cell_type": "markdown", - "id": "171fcb2c-d8d0-46a2-adb3-5ad699c6598f", - "metadata": {}, - "source": [ - "Let us see the results from both ways of obtaining the ohmic bath parameters " - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "f6eaf004-e708-48cc-b833-bb9c77ac7d7c", - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "def projection(result,i,j):\n", - " return [result.states[k][i,j] for k in range(len(result.states))]" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "2cfea7ff-6de6-4dff-926d-39024b9d66a3", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/mcditoos/anaconda3/envs/qutip-dev/lib/python3.12/site-packages/matplotlib/cbook.py:1699: ComplexWarning: Casting complex values to real discards the imaginary part\n", - " return math.isfinite(val)\n", - "/home/mcditoos/anaconda3/envs/qutip-dev/lib/python3.12/site-packages/matplotlib/cbook.py:1345: ComplexWarning: Casting complex values to real discards the imaginary part\n", - " return np.asarray(x, float)\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(tlist,projection(result_spectral,0,0))\n", - "#plt.scatter(tlist,projection(result_corr,0,0),s=5,marker='x',color='red')\n", - "plt.xlabel('t')\n", - "plt.ylabel(r'$\\rho_{11}$')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "1ca0c6b1-5ecf-4397-bb41-19b932df241b", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/mcditoos/anaconda3/envs/qutip-dev/lib/python3.12/site-packages/matplotlib/collections.py:194: ComplexWarning: Casting complex values to real discards the imaginary part\n", - " offsets = np.asanyarray(offsets, float)\n" - ] - }, - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "w=np.linspace(-10,10,100)\n", - "plt.scatter(w,obp.fit.corr_spectrum_approx(w),s=8)\n", - "plt.scatter(w,obp2.fit.spec_spectrum_approx(w),s=5,marker='x',color='red')\n", - "plt.plot(w,obp.ohmic_power_spectrum(w),color='k')\n", - "plt.ylabel(r'$P( \\omega )$')\n", - "plt.xlabel(r'$\\omega$')\n", - "plt.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "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": "3.12.0" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/qutip/solver/heom/bofin_baths.py b/qutip/solver/heom/bofin_baths.py index f24501d058..c6154c0524 100644 --- a/qutip/solver/heom/bofin_baths.py +++ b/qutip/solver/heom/bofin_baths.py @@ -47,15 +47,12 @@ class BathExponent: Parameters ---------- - type : {"R", "I", "RI", "+", "-","Ra","Re","Ia","Ie"} or BathExponent.ExponentType + type : {"R", "I", "RI", "+", "-"} or BathExponent.ExponentType The type of bath exponent. "R" and "I" are bosonic bath exponents that appear in the real and imaginary parts of the correlation expansion. - When the RWA approximation is performed "Ra","Ia" and "Re","Ie" are bosonic bath exponents that appear in the real and - imaginary parts of the correlation expansion, for the absorption and emission parts respectively. - "RI" is combined bosonic bath exponent that appears in both the real and imaginary parts of the correlation expansion. The combined exponent has a single ``vk``. The ``ck`` is the coefficient in the real @@ -569,7 +566,7 @@ class DrudeLorentzBath(BosonicBath): bath an exponent is from. """ - def __init__(self, Q, lam, gamma, T, Nk, combine=True, tag=None, rwa=False): + def __init__(self, Q, lam, gamma, T, Nk, combine=True, tag=None): ck_real, vk_real, ck_imag, vk_imag = self._matsubara_params( lam=lam, gamma=gamma, @@ -1604,7 +1601,7 @@ def _matsubara_coefficients(self): self.Bath_corr = BosonicBath(self.Q, ckAR, vkAR, ckAI, vkAI) -class OhmicBath(FitCorr, FitSpectral): +class OhmicBath(BosonicBath): def __init__(self, T, Q, alpha, wc, s, Nk=4, method="correlation", rmse=1e-6): self.alpha = alpha self.wc = wc