NonMDynamics.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SwoKvbsOdOHe",
        "outputId": "e9255d4d-d69f-4659-d908-ed3601efa8fd"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting qutip\n",
            "  Downloading qutip-4.7.5-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (16.3 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m16.3/16.3 MB\u001b[0m \u001b[31m48.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: numpy>=1.16.6 in /usr/local/lib/python3.10/dist-packages (from qutip) (1.25.2)\n",
            "Requirement already satisfied: scipy>=1.0 in /usr/local/lib/python3.10/dist-packages (from qutip) (1.11.4)\n",
            "Requirement already satisfied: packaging in /usr/local/lib/python3.10/dist-packages (from qutip) (23.2)\n",
            "Installing collected packages: qutip\n",
            "Successfully installed qutip-4.7.5\n"
          ]
        }
      ],
      "source": [
        "!pip install qutip"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "import qutip as qt\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "#parameters  - Hamiltonian\n",
        "times = np.linspace(0, 1, 201)\n",
        "psi0 = qt.basis(2, 1)\n",
        "a0 = qt.destroy(2)\n",
        "H = a0.dag() * a0"
      ],
      "metadata": {
        "id": "a9E20-ECdXfD"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Rate functions\n",
        "gamma1 = \"kappa * nth\"\n",
        "gamma2 = \"kappa * (nth+1) + 12 * np.exp(-2*t**3) * (-np.sin(15*t)**2)\"\n",
        "# gamma2 becomes negative during some time intervals\n",
        "# nm_mcsolve integration\n",
        "ops_and_rates = []\n",
        "ops_and_rates.append([a0.dag(), gamma1])\n",
        "ops_and_rates.append([a0, gamma2])\n",
        "\n",
        "# Create an instance of Options class\n",
        "options = qt.Options(rhs_reuse=True)\n",
        "\n",
        "MCSol = qt.mcsolve(H, psi0, times, ops_and_rates,\n",
        "                   args={'kappa': 1.0 / 0.129, 'nth': 0.063},\n",
        "                   e_ops=[a0.dag() * a0, a0 * a0.dag()],\n",
        "                   options=options, ntraj=2500)\n",
        "\n",
        "# mesolve integration for comparison\n",
        "d_ops = [[qt.lindblad_dissipator(a0.dag(), a0.dag()), gamma1],\n",
        "         [qt.lindblad_dissipator(a0, a0), gamma2]]\n",
        "\n",
        "MESol = qt.mesolve(H, psi0, times, d_ops,\n",
        "                   e_ops=[a0.dag() * a0, a0 * a0.dag()],\n",
        "                   args={'kappa': 1.0 / 0.129, 'nth': 0.063})\n",
        "\n",
        "# Calculate total population\n",
        "total_population = np.array(MCSol.expect[0]) + np.array(MCSol.expect[1])\n",
        "\n",
        "# Plot results\n",
        "plt.figure()\n",
        "plt.plot(times, MCSol.expect[0], 'g', label='Population in |0>')\n",
        "plt.plot(times, MCSol.expect[1], 'b', label='Population in |1>')\n",
        "plt.plot(times, total_population, 'r', label='Total Population')\n",
        "plt.title('Monte Carlo time evolution')\n",
        "plt.xlabel('Time')\n",
        "plt.ylabel('Population')\n",
        "plt.legend()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 663
        },
        "id": "oat1x32vdn7J",
        "outputId": "2f8870ed-b7c4-4348-8f4a-3ba005f91317"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "10.0%. Run time:   6.24s. Est. time left: 00:00:00:56\n",
            "20.0%. Run time:  11.35s. Est. time left: 00:00:00:45\n",
            "30.0%. Run time:  16.50s. Est. time left: 00:00:00:38\n",
            "40.0%. Run time:  20.63s. Est. time left: 00:00:00:30\n",
            "50.0%. Run time:  24.72s. Est. time left: 00:00:00:24\n",
            "60.0%. Run time:  29.85s. Est. time left: 00:00:00:19\n",
            "70.0%. Run time:  33.72s. Est. time left: 00:00:00:14\n",
            "80.0%. Run time:  37.66s. Est. time left: 00:00:00:09\n",
            "90.0%. Run time:  42.69s. Est. time left: 00:00:00:04\n",
            "100.0%. Run time:  46.63s. Est. time left: 00:00:00:00\n",
            "Total run time:  46.66s\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}