{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP example: Dynamics of a Spin Chain" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "J.R. Johansson and P.D. Nation\n", "\n", "For more information about QuTiP see [http://qutip.org](http://qutip.org)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from qutip import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hamiltonian:\n", "\n", "$\\displaystyle H = - \\frac{1}{2}\\sum_n^N h_n \\sigma_z(n) - \\frac{1}{2} \\sum_n^{N-1} [ J_x^{(n)} \\sigma_x(n) \\sigma_x(n+1) + J_y^{(n)} \\sigma_y(n) \\sigma_y(n+1) +J_z^{(n)} \\sigma_z(n) \\sigma_z(n+1)]$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def integrate(N, h, Jx, Jy, Jz, psi0, tlist, gamma, solver):\n", "\n", " si = qeye(2)\n", " sx = sigmax()\n", " sy = sigmay()\n", " sz = sigmaz()\n", "\n", " sx_list = []\n", " sy_list = []\n", " sz_list = []\n", "\n", " for n in range(N):\n", " op_list = []\n", " for m in range(N):\n", " op_list.append(si)\n", "\n", " op_list[n] = sx\n", " sx_list.append(tensor(op_list))\n", "\n", " op_list[n] = sy\n", " sy_list.append(tensor(op_list))\n", "\n", " op_list[n] = sz\n", " sz_list.append(tensor(op_list))\n", "\n", " # construct the hamiltonian\n", " H = 0\n", "\n", " # energy splitting terms\n", " for n in range(N):\n", " H += - 0.5 * h[n] * sz_list[n]\n", "\n", " # interaction terms\n", " for n in range(N-1):\n", " H += - 0.5 * Jx[n] * sx_list[n] * sx_list[n+1]\n", " H += - 0.5 * Jy[n] * sy_list[n] * sy_list[n+1]\n", " H += - 0.5 * Jz[n] * sz_list[n] * sz_list[n+1]\n", "\n", " # collapse operators\n", " c_op_list = []\n", "\n", " # spin dephasing\n", " for n in range(N):\n", " if gamma[n] > 0.0:\n", " c_op_list.append(np.sqrt(gamma[n]) * sz_list[n])\n", "\n", " # evolve and calculate expectation values\n", " if solver == \"me\":\n", " result = mesolve(H, psi0, tlist, c_op_list, sz_list)\n", " elif solver == \"mc\":\n", " ntraj = 250 \n", " result = mcsolve(H, psi0, tlist, c_op_list, sz_list, ntraj)\n", "\n", " return result.expect" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "#\n", "# set up the calculation\n", "#\n", "solver = \"me\" # use the ode solver\n", "#solver = \"mc\" # use the monte-carlo solver\n", "\n", "N = 10 # number of spins\n", "\n", "# array of spin energy splittings and coupling strengths. here we use\n", "# uniform parameters, but in general we don't have too\n", "h = 1.0 * 2 * np.pi * np.ones(N) \n", "Jz = 0.1 * 2 * np.pi * np.ones(N)\n", "Jx = 0.1 * 2 * np.pi * np.ones(N)\n", "Jy = 0.1 * 2 * np.pi * np.ones(N)\n", "# dephasing rate\n", "gamma = 0.01 * np.ones(N)\n", "\n", "# intial state, first spin in state |1>, the rest in state |0>\n", "psi_list = []\n", "psi_list.append(basis(2,1))\n", "for n in range(N-1):\n", " psi_list.append(basis(2,0))\n", "psi0 = tensor(psi_list)\n", "\n", "tlist = np.linspace(0, 50, 200)\n", "\n", "sz_expt = integrate(N, h, Jx, Jy, Jz, psi0, tlist, gamma, solver)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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3UIcmwOm3++Zs1uTBnvchfQJc8jbojCguD5a1ZbSuK0doVHhzQljTtIOishKS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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10,6))\n", "\n", "for n in range(N):\n", " ax.plot(tlist, np.real(sz_expt[n]), label=r'$\\langle\\sigma_z^{(%d)}\\rangle$'%n)\n", "\n", "ax.legend(loc=0)\n", "ax.set_xlabel(r'Time [ns]')\n", "ax.set_ylabel(r'\\langle\\sigma_z\\rangle')\n", "ax.set_title(r'Dynamics of a Heisenberg spin chain');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Software version:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
SoftwareVersion
QuTiP4.3.0.dev0+6e5b1d43
Numpy1.13.1
SciPy0.19.1
matplotlib2.0.2
Cython0.25.2
Number of CPUs2
BLAS InfoINTEL MKL
IPython6.1.0
Python3.6.2 |Anaconda custom (x86_64)| (default, Jul 20 2017, 13:14:59) \n", "[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]
OSposix [darwin]
Thu Jul 20 22:57:36 2017 MDT
" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qutip.ipynbtools import version_table\n", "\n", "version_table()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }