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@enakai00
Created October 31, 2022 00:15
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QIQO 8-4.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": [],
"authorship_tag": "ABX9TyPIha4opkjktt7mJ36KN3eK",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/enakai00/c07dc25c59f2fc9e5d437511bf89a644/qiqo-8-4.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "mPYQfZUnXBgV"
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"plt.rcParams.update({'font.size': 12})"
]
},
{
"cell_type": "code",
"source": [
"J = 0.01\n",
"alpha = 0.1\n",
"omega1 = 1\n",
"def eigenvalues(x):\n",
" omega2 = omega1 * x\n",
" D1 = (omega2-omega1)**2 + 4*J**2\n",
" D2 = (omega2-omega1-alpha)**2 + 8*J**2\n",
" E1 = omega1+omega2 - np.sqrt(D1)\n",
" E2 = omega1+omega2 + np.sqrt(D1)\n",
" E3 = -alpha+omega1+3*omega2 - np.sqrt(D2)\n",
" E4 = -alpha+omega1+3*omega2 + np.sqrt(D2)\n",
" return E1, E2, E3, E4"
],
"metadata": {
"id": "hz2Ki7XsXB34"
},
"execution_count": 4,
"outputs": []
},
{
"cell_type": "code",
"source": [
"fig = plt.figure(figsize=(7, 5))\n",
"subplot = fig.add_subplot(1, 1, 1)\n",
"xs = np.linspace(0.9, 1.5, 100)\n",
"es = [eigenvalues(x) for x in xs]\n",
"e1 = [es[n][0] for n in range(len(es))]\n",
"e2 = [es[n][1] for n in range(len(es))]\n",
"e3 = [es[n][2] for n in range(len(es))]\n",
"e4 = [es[n][3] for n in range(len(es))]\n",
"plt.plot(xs, e1, label='E1')\n",
"plt.plot(xs, e2, label='E2')\n",
"plt.plot(xs, e3, label='E3')\n",
"plt.plot(xs, e4, label='E4')\n",
"plt.plot([1+alpha/omega1, 1+alpha/omega1], [1.5, 6],\n",
" color='gray', linestyle='--', label='ω2=ω1+α')\n",
"plt.xlabel('ω2/ω1')\n",
"_ = plt.legend()\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 340
},
"id": "cbr_9lWIXGMj",
"outputId": "7eb0b511-60f8-4d76-821c-44c908413728"
},
"execution_count": 24,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
}
]
}
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