{ "metadata": { "name": "Lecture-Quantum-Monte-Carlo-Trajectories" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP lecture: Quantum Monte-Carlo Trajectories" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Author: J.R. Johansson, robert@riken.jp\n", "\n", "http://dml.riken.jp/~rob/\n", "\n", "Latest version of this ipython notebook lecture is available at: http://github.com/jrjohansson/qutip-lectures\n", "\n", "The example in this lecture is based on an example by P.D. Nation." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# setup the matplotlib graphics library and configure it to show figures inline in the notebook\n", "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", "For more information, type 'help(pylab)'.\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# make qutip available in the rest of the notebook\n", "from qutip import *\n", "\n", "#qutip.settings.qutip_graphics=False\n", "#qutip.settings.qutip_gui=False" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction to the Quantum Monte-Carlo trajectory method\n", "\n", "The Quantum Monte-Carlo trajectory method is an equation of motion for a single realization of the state vector $\\left|\\psi(t)\\right>$ for a quantum system that interacts with its environment. The dynamics of the wave function is given by the Schrodinger equation,\n", "\n", "