From e7bf50db590b23e8fd46b2294b3951ac251f7e19 Mon Sep 17 00:00:00 2001 From: Donjan Rodic <donjan@dyx.ch> Date: Tue, 15 Mar 2016 11:43:55 +0100 Subject: [PATCH] added exercise 3 solution --- examples/lanczos/Lanczos.ipynb | 10 +- .../TFIM_time_evolution/cpp/Makefile | 10 + .../TFIM_time_evolution/cpp/plotmagn.py | 17 + .../cpp/trFieldIsingTimeEvolution.cpp | 120 ++++++ .../trising-checkpoint.ipynb | 255 +++++++++++ .../TFIM_time_evolution/python/trising.ipynb | 255 +++++++++++ .../TFIM_time_evolution/python/trising.py | 87 ++++ .../python/trising_skeleton.py | 76 ++++ .../scattering-checkpoint.ipynb | 397 ++++++++++++++++++ .../ex03_solution/scattering/scattering.ipynb | 397 ++++++++++++++++++ 10 files changed, 1615 insertions(+), 9 deletions(-) create mode 100644 exercises/ex03_solution/TFIM_time_evolution/cpp/Makefile create mode 100644 exercises/ex03_solution/TFIM_time_evolution/cpp/plotmagn.py create mode 100644 exercises/ex03_solution/TFIM_time_evolution/cpp/trFieldIsingTimeEvolution.cpp create mode 100644 exercises/ex03_solution/TFIM_time_evolution/python/.ipynb_checkpoints/trising-checkpoint.ipynb create mode 100644 exercises/ex03_solution/TFIM_time_evolution/python/trising.ipynb create mode 100644 exercises/ex03_solution/TFIM_time_evolution/python/trising.py create mode 100644 exercises/ex03_solution/TFIM_time_evolution/python/trising_skeleton.py create mode 100644 exercises/ex03_solution/scattering/.ipynb_checkpoints/scattering-checkpoint.ipynb create mode 100644 exercises/ex03_solution/scattering/scattering.ipynb diff --git a/examples/lanczos/Lanczos.ipynb b/examples/lanczos/Lanczos.ipynb index 1c3504f..2d4ee46 100644 --- a/examples/lanczos/Lanczos.ipynb +++ b/examples/lanczos/Lanczos.ipynb @@ -116,16 +116,8 @@ "name": "python2" }, "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.8" + "version": "2.7.6" } }, "nbformat": 4, diff --git a/exercises/ex03_solution/TFIM_time_evolution/cpp/Makefile b/exercises/ex03_solution/TFIM_time_evolution/cpp/Makefile new file mode 100644 index 0000000..e185a51 --- /dev/null +++ b/exercises/ex03_solution/TFIM_time_evolution/cpp/Makefile @@ -0,0 +1,10 @@ + +magnetization.png: magnetization.txt + python3 plotmagn.py + +magnetization.txt: trFieldIsingTimeEvolution.x + ./trFieldIsingTimeEvolution.x > magnetization.txt + +trFieldIsingTimeEvolution.x: trFieldIsingTimeEvolution.cpp + g++ -O2 -o trFieldIsingTimeEvolution.x trFieldIsingTimeEvolution.cpp + diff --git a/exercises/ex03_solution/TFIM_time_evolution/cpp/plotmagn.py b/exercises/ex03_solution/TFIM_time_evolution/cpp/plotmagn.py new file mode 100644 index 0000000..be16ce5 --- /dev/null +++ b/exercises/ex03_solution/TFIM_time_evolution/cpp/plotmagn.py @@ -0,0 +1,17 @@ +import numpy as np +import matplotlib.pyplot as plt + +magn = np.loadtxt('magnetization.txt') +Nt = magn.shape[0] +N = magn.shape[1] +dt = 0.5 + +fig = plt.figure() +plt.pcolor(range(N+1),np.arange(Nt+1)*dt,magn) +plt.xlim([0,N]) +plt.ylim([0,Nt*dt]) +plt.xlabel('site') +plt.ylabel('time') +plt.colorbar() +plt.show() +fig.savefig('magnetization.png') diff --git a/exercises/ex03_solution/TFIM_time_evolution/cpp/trFieldIsingTimeEvolution.cpp b/exercises/ex03_solution/TFIM_time_evolution/cpp/trFieldIsingTimeEvolution.cpp new file mode 100644 index 0000000..e34750c --- /dev/null +++ b/exercises/ex03_solution/TFIM_time_evolution/cpp/trFieldIsingTimeEvolution.cpp @@ -0,0 +1,120 @@ +#include <valarray> +#include <vector> +#include <iostream> +#include <cmath> +#include <complex> + +typedef std::valarray< std::complex<double> > state_vector_t; +typedef std::vector<double> param_vector_t; +typedef unsigned state_t; +const std::complex<double> I(0.,1.); + + +template <class Vector> +void tstep_transv(unsigned l, const param_vector_t& cosinesPrecomputed, const Vector& sinesPrecomputed, Vector& x, Vector& tmp) +{ + state_t dim = 1 << l; + tmp *= 0; + for( int r = 0; r < l ; ++r ) + { + // diagonal + for( state_t s = 0; s < dim; ++s ) + tmp[s] = cosinesPrecomputed[r] * x[s]; + // off-diagonal + for( state_t s = 0; s < dim; ++s ) + tmp[s^(1<<r)] += sinesPrecomputed[r] * x[s]; + std::swap(x,tmp); + } +} + +param_vector_t precomputeCosines(const param_vector_t &hx, double dt){ + param_vector_t res(hx.size(),double(0.0)); + for(int r = 0; r<hx.size(); ++r){ + res[r] = std::cos(dt*hx[r]); + } + + return res; +} + +template <class Vector> +Vector precomputeSines(const param_vector_t &hx, double dt){ + Vector res(std::complex<double>(0.0,0.0), hx.size()); + for(int r = 0; r<hx.size(); ++r){ + res[r] = I * std::sin(dt*hx[r]); + } + + return res; +} + +template <class Vector> +void tstep_diag(unsigned l, const param_vector_t &j, double dt, Vector& x) +{ + state_t dim = 1 << l; + for( state_t s = 0; s < dim; ++s ) + { + double jtotal = 0.; + // +J for parallel, -J for antiparallel neighbors + for( int r = 0; r < l - 1; ++r ) + { + jtotal += ((s >> r)^(s >> (r+1)))&1 ? -j[r] : j[r]; // check if spins are parallel at site r and r+1 + } + x[s] *= std::exp(I*jtotal*dt); + } +} + +template <class Vector> +void evolve(unsigned l, const param_vector_t &j, const param_vector_t &hx, double dt, unsigned n, Vector& x) +{ + state_t dim = 1 << l; + state_vector_t tmp(x.size()); // memory for tstep_transv + param_vector_t cosinesPrecomputed = precomputeCosines(hx,dt); + Vector sinesPrecomputed = precomputeSines<Vector>(hx,dt); + tstep_diag(l,j,dt/2.,x); + for(int i=0 ; i<n-1 ; ++i){ + tstep_transv(l,cosinesPrecomputed,sinesPrecomputed,x,tmp); + tstep_diag(l,j,dt,x); + } + tstep_transv(l,cosinesPrecomputed,sinesPrecomputed,x,tmp); + tstep_diag(l,j,dt/2.,x); +} + +template <class Vector> +void printMagnetization(unsigned l, const Vector& v, std::ostream& outputStream) +{ + state_t dim = 1 << l; + for(int r=0; r<l; r++){ + double m(0); + for(long s=0; s<dim; s++){ + m += std::norm(v[s]) * 2. * ( (bool)(s&(1 << r)) -0.5); + } + outputStream << m << "\t\t"; + } + outputStream << std::endl; +} + +int main(){ + // ======== input + unsigned l = 11; // length of chain + param_vector_t j(l-1,1.0); // Ising coupling + param_vector_t hx(l,0.4); // transverse magnetic field + double tmax = 40.; // maximum time reached in time evolutin + double tmeas = 0.5; // time after which a measurment is performed + double dt = 0.1; // time step used for the evolution + unsigned nmeas = tmax/tmeas; // number of measurements + unsigned nstep = tmeas/dt; // number of steps between measurements + // ======== input + + // Starting configuration + state_t initialInd = 1<<5; + state_vector_t x(0., 1 << l); + x[initialInd] = 1; + printMagnetization(l,x,std::cout); + + // Do time evolution + for(int n=1; n<=nmeas; ++n){ + evolve(l, j, hx, dt, nstep, x); + printMagnetization(l,x,std::cout); + } + + return 0; +} diff --git a/exercises/ex03_solution/TFIM_time_evolution/python/.ipynb_checkpoints/trising-checkpoint.ipynb b/exercises/ex03_solution/TFIM_time_evolution/python/.ipynb_checkpoints/trising-checkpoint.ipynb new file mode 100644 index 0000000..9e3f39c --- /dev/null +++ b/exercises/ex03_solution/TFIM_time_evolution/python/.ipynb_checkpoints/trising-checkpoint.ipynb @@ -0,0 +1,255 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from cmath import exp\n", + "from math import sin, cos\n", + "%matplotlib inline\n", + "plt.rcParams['figure.figsize'] = 16, 9" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Time-evolution operator" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def evolve(l, j, hx, v, dt, n):\n", + " \"\"\" Evolve the state v in time by n * dt \"\"\"\n", + " dim = 1 << l\n", + " def tstep_diag(x, dt):\n", + " ## Apply diagonal part\n", + " for s in range(dim):\n", + " jtotal = 0.\n", + " for r in range(l-1):\n", + " jtotal += -j[r] if ((s >> r)^(s >> (r+1)))&1 else j[r]\n", + " x[s] = exp(-1j*jtotal*dt)*x[s]\n", + " return x\n", + " def tstep_transv(x, dt):\n", + " ## Apply transverse part succesively for each site\n", + " y = np.zeros_like(x)\n", + " for r in range(l):\n", + " cos_v = cos(dt*hx[r])\n", + " sin_v = sin(dt*hx[r])\n", + " ## diagonal\n", + " for s in range(dim):\n", + " y[s] = cos_v * x[s]\n", + " ## off-diagonal\n", + " for s in range(dim):\n", + " y[s^(1<<r)] += 1.j*sin_v * x[s]\n", + " ## swap vectors\n", + " tmp = x\n", + " x = y\n", + " y = tmp\n", + " return x\n", + " v = tstep_diag(v, dt/2.)\n", + " for i in range(int(n-1)):\n", + " v = tstep_transv(v, dt)\n", + " v = tstep_diag(v, dt)\n", + " v = tstep_transv(v, dt)\n", + " v = tstep_diag(v, dt/2.)\n", + " return v" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Measurements" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def magnetization(v, l):\n", + " \"\"\" Measure the magnetization per site for the state v \"\"\"\n", + " dim = 1 << l\n", + " m = np.zeros((l))\n", + " for r in range(l):\n", + " for s in range(dim):\n", + " m[r] += abs(v[s])**2 * 2. * ( bool(s&(1 << r)) -0.5)\n", + " return m" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Transverse field only" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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0AACAubhBRQsAAIDNWviK1os/deLYIQCwAJapX/96dmTX2CGwAPwskCSn1tgR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\n0QIAAOZj8dbR2jIqWgAAADO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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x10916c898>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "l = 11\n", + "dim = 1 << l\n", + "j = 0.00*np.ones((l-1)) # Ising coupling\n", + "hx = 2*np.pi*0.125*np.ones((l)) # transverse field strength Gamma\n", + "\n", + "## Starting configuration\n", + "ind = int('00000000000',base=2) # specify spin configuration: 0 = down, 1 = up\n", + "v = np.zeros((dim),dtype=complex)\n", + "v[ind] = 1.\n", + "\n", + "## Parameters for time evolution\n", + "tend = 20. # duration of the time evolution\n", + "tmeas = 0.5 # time after which a measurment is performed\n", + "dt = 0.1 # time step used for the evolution\n", + "nmeas = int((tend)/tmeas) # number of measurements\n", + "nstep = int((tmeas)/dt) # number of steps between measurments\n", + "\n", + "## measure magnetization\n", + "m=np.zeros((nmeas,l));\n", + "m[0,:] = magnetization(v, l)\n", + "\n", + "## Do time evolution\n", + "for t in range(1,nmeas):\n", + " # print(t*tmeas)\n", + " v=evolve(l,j,hx,v,dt,nstep)\n", + " m[t,:] = magnetization(v, l)\n", + "\n", + "## plot magnetization\n", + "plt.pcolor(np.array(range(l+1)),np.linspace(0.,tend,nmeas+1),m,\n", + " vmin=-1.0, vmax=1.0)\n", + "plt.xlabel('site')\n", + "plt.ylabel('time')\n", + "plt.axis([0,l,0,tend])\n", + "plt.title(\"Magnetisation, J = \"+str(j[0])+\" , hx = \"+str(hx[0]))\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ising coupling and transverse field" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+vneE7sZ0rYXV7Luld4L+bvum+/SO0N3+277WO0J3X9vf5+ABW3wOtn+T34UT\n8ze9I3T39hHtD97tI9Pbxjbvfbsrzr88V5x/xa6GXZ1k6eQWRyW5ZtmYq5I8JMk1VbUpyQNaa8tP\ngdotaym03lxVP5nkfUnu2LFwN9polXtWiO9J8qIkpyd5YZJ37/zlL1vjZgAAYG+1vOHwx72CLJRj\nTjw2x5x47NcfX3Da/1lp2IVJjquqYzKZPf15SU5ZNua9mdQmH07yw5lM2rdH1lJofS3JbyX597m7\nfdaSPHRXL6yqtyY5McnBVXVlklOT/EaSd1TVi5NcmckbAQAA9nI9jlaannP1siTnZDIZ4Btba5dU\n1WlJLmytvS/JGzNpMH0uyQ2ZFGN7ZC2F1i8nOa61dv3urry19iOrPHXS7q4LAABgFq21DyQ5ftmy\nU5fcvyPJc+e5zbUUWv+YZOs8NwoAAIzPthGdf7+WQusrST5RVX+Te56jNev07gAAAHu1tRRa75re\nAAAAZrZ9TeXH3mGX77S1duauxgAAAHC3VQutqnp7a+25VXVxvvFiXa219tj1jQYAAOxNxnSN1J11\ntH5++uclSX5lyfJK8pvrlggAAGCDW7XQaq1dO717XGvtHpdbrqpHrGsqAABgr6OjlaSq/k2Sn0ny\n0Kr65JKnNif5u/UOBgAAsFHt7NDBtyb5qyS/nuQVS5bf1lq7cV1TAQAAex3X0UrSWrslyS1JThku\nzkrGMwXkck/KR3pH6G5TtveO0N94/xf4Op+DZLvPgc9B4vsgPgeJ/YMkeXue3DsC7JKvbAAAYBBj\nuo7WvXoHAAAA2NuMp6QEAAC6GtOsgzpaAAAAc6ajBQAADEJHCwAAgJnpaAEAAIPQ0QIAAGBmOloA\nAMAgtuloAQAAMCsdLQAAYBDbR1R+jOedbkBH5JreEbq7T+7oHaG7Ow7unaC/A2+8vXeE7rY88IDe\nEbo77MZbekfozvdBcmBu6h2hu/2ztXcEYA0UWgAAwCDMOggAAMDMdLQAAIBB6GgBAAAwMx0tAABg\nEK6jBQAAwMx0tAAAgEGM6TpaOloAAABzNp6SEgAA6MqsgwAAAMxMRwsAABjEmDpaCi0AAGAQY5re\nfQMUWtt6B6CjB+WG3hG6u37/g3tH6O7IW3wOxjRL02rqjt4J+rv+gb4P/C4k1+SI3hEWgP1DFp9f\nbgAAYBBj+odDk2EAAADM2XhKSgAAoKsxTYahowUAADBnOloAAMAgdLQAAACYmY4WAAAwCB0tAACA\nvVxVHVTaAxs2AAAUVElEQVRV51TVZ6vq7Ko6YIUxj62qv6+qi6vqE1X13LWsW6EFAAAMYls2rett\nBq9Icm5r7fgk5yV55QpjvpLkBa21b03yvUl+v6oesKsVK7QAAICxOjnJmdP7ZyZ59vIBrbV/bK39\n0/T+tUmuS3LIrlbsHC0AAGAQ2xev/Di0tbYlSVprX6qqnRZQVXVCknvvKLx2ZuHeKXe7PMf2jtDd\n43JR7wjd3ZCDe0fo7shtN/SO0N3+2do7Qn/begfoz/dBcmi29I7Q3d/nyb0jwML4yvkfzdbzP7rT\nMVX1wSSHLV2UpCV59e5sq6oenORNSV6wlvEKLQAAYBDznnVwvxOflP1OfNLXH19/2uu/YUxr7Rmr\nvb6qtlTVYa21LVV1eCaHBa40bnOS9yV5VWvtwrVkc44WAAAwVu9J8qLp/RcmeffyAVV17yTvSnJm\na+0v1rpiHS0AAGAQC3gdrdOTvL2qXpzkyiQ/nCRV9YQkP9Vae0mS5yZ5apKDqurHMzns8EWttU/u\nbMUKLQAAYJRaazcmOWmF5R9L8pLp/bckecvurluhBQAADGLGa11tSM7RAgAAmDMdLQAAYBALeB2t\ndaOjBQAAMGfjKSkBAICuFnDWwXWjowUAADBnOloAAMAgdLQAAACY2QboaN23d4BuPppv7x2huxfk\nzb0jdHdd9u8dob/9egfo78Abb+8doT+fg1H9S/BqNufLvSN0Z/8gGfP+4Ua3/a7xfI/paAEAAMzZ\nBuhoAQAAe4Nt23S0AAAAmJGOFgAAMIjt28ZTfuhoAQAAzNl4SkoAAKCr7c7RAgAAYFY6WgAAwCB0\ntAAAAJiZjhYAADCIbXfqaAEAADAjHS0AAGAQd20fT/mxAd7pfXsH6Ob8u07sHaG72+51/94Rutuc\n23pH6O6mQ8b7PbDDQZ+6vXeE7m56tM+B74PktvhdsH+QbIhdWEbPpxQAABiGWQcBAACYlY4WAAAw\nDB0tAAAAZqWjBQAADGNb9U4wGB0tAACAOdPRAgAAhrGtd4Dh6GgBAADMmY4WAAAwDB0tAAAAZqWj\nBQAADGNEHa0NUGjd2TtANze866jeEbr7zL98ZO8I3Z20/a97R+juhk0H947Q3UE33t47Qnc358De\nEbo7dPt1vSN0d+6mp/eO0N0N7zqyd4QFcHXvAMxqRLv2Dh0EAACYsw3Q0QIAAPYK23sHGI6OFgAA\nwJzpaAEAAMMY0WQYOloAAABzpqMFAAAMQ0cLAACAWSm0AACAYWxb59tuqqqDquqcqvpsVZ1dVQfs\nZOzmqrq6qv5gLetWaAEAAGP1iiTnttaOT3JeklfuZOxrk5y/1hUrtAAAgGEsWEcryclJzpzePzPJ\ns1caVFVPSHJoknPWumKFFgAAMFaHtta2JElr7UtJDlk+oKoqyW8n+ZUktdYVm3UQAAAYxrxnHbz4\n/ORT5+90SFV9MMlhSxclaUlevcat/EySv2ytfXFSc62t2NoAhdbtvQP0c27vAP397b/8rt4Ruvv+\nO/6qd4TuNu2/vXcEFsCm+Bzse8fXekfo7m/397tg/yAZ9f4h9/StJ05uO5x12jcMaa09Y7WXV9WW\nqjqstbalqg5Pct0Kw74zyVOr6meSbE5y76q6rbX2qp1F2wCFFgAAsFdYvOtovSfJi5KcnuSFSd69\nfEBr7Ud33K+qFyZ5wq6KrMQ5WgAAwHidnuQZVfXZJCcl+Y1kMvlFVb1+T1asowUAAAzjzt4B7qm1\ndmMmBdby5R9L8pIVlp+Zu2cp3CkdLQAAgDnT0QIAAIYxonmNdLQAAADmTEcLAAAYxuLNOrhudLQA\nAADmTEcLAAAYho4WAAAAs9LRAgAAhjGijpZCa5Fd0DtAf2fnmb0jdPer+/9a7wjdHbj95t4R+jug\nd4D+fA6Srfvft3eE7vwuxP4BbBAKLQAAYBgj6mg5RwsAAGDOdLQAAIBh6GgBAAAwKx0tAABgGDpa\nAAAAzEpHCwAAGMadvQMMp1uhVVWXJ7klyV1J7mytndArCwAAwDz17GjdleTE1tpNHTMAAABD2d47\nwHB6nqNVnbcPAACwLnp2tFqSs6uqJXl9a+0NHbMAAADrbUSzDvYstJ7cWvtSVR2S5INVdUlr7YJv\nHPYHS+4/aXoDAIAx+fD0xkZRrbXeGVJVpya5rbX2u8uWt+SyTqkWwcN7B+jv7N4B+vvIP//W3hG6\ne+I/fqp3hO7aA3sn6K9u7J2gvwuPe3TvCN2dcM7FvSP098zeARbB53oHWADfnNZa9U6xO6qq5T+s\nc+3x2lqYv5cu50hV1f5Vdf/p/fsl+edJ7EkBAAB7hV6HDh6W5H9Nz8/aJ8lbWmvndMoCAAAMwTla\n66u19oUkj+uxbQAAgPXWczIMAABgTO7sHWA4rmMFAAAwZzpaAADAMLb3DjAcHS0AAIA509ECAACG\nMaJZB3W0AAAA5kxHCwAAGIaOFgAAALPaAB2tEZW93+Dy3gH6e8OxvRN09/5//v29I3T3xEs+1TtC\nd1t+8IDeEbo7/O9u6R2hu/cf5/sgb+gdYBFc3jvAAhjz/uEGN6LraG2AQgsAANgrmN4dAACAWelo\nAQAAwxjRUZ86WgAAAHOmowUAAAxDRwsAAIBZ6WgBAADDGNH07jpaAADAKFXVQVV1TlV9tqrOrqoV\nL1xZVQ+ZPv+ZqvpUVR29q3UrtAAAgGFsX+fb7ntFknNba8cnOS/JK1cZ96Ykp7fWHpnkhCTX7WrF\nCi0AAGCsTk5y5vT+mUmevXxAVX1Lkk2ttfOSpLW2tbX21V2t2DlaAADAMBZv1sFDW2tbkqS19qWq\nOmSFMd+c5Jaq+vMkxyY5N8krWmttZytWaAEAABvT9ecnN5y/0yFV9cEkhy1dlKQlefUat7JPkqcm\neVySq5K8PcmLkpyxqxctuBt7B+hoc+8A/Z3dO0B/b84Lekfo7tSc3jtCd5vvuK13BBaA74P4XUiS\n3No7wALwnbhhzbujdeCJk9sOl532DUNaa89Y7eVVtaWqDmutbamqw7PyuVdXJ7motXbF9DXvSvKk\n7KLQco4WAAAwVu/JpDuVJC9M8u4VxlyY5KCqOnj6+GlJPrOrFW+AjhYAALBXWLzraJ2e5O1V9eIk\nVyb54SSpqick+anW2ktaa3dV1b9Ncl5VJcnHkrxhVytWaAEAAKPUWrsxyUkrLP9YkpcsefzXSR67\nO+tWaAEAAMOY7VpXG5JztAAAAOZMRwsAABjG4l1Ha93oaAEAAMyZjhYAADAMHS0AAABmpaMFAAAM\nY/Guo7VudLQAAADmbAN0tG7tHaCjzb0D9HfbiP7ZYxX/9KZH9Y7Q3z/rHaC/+330rt4R+nt07wD9\n+T6I3wWmxrx/uMG5jhYAAACz2gAdLQAAYK9g1kEAAABmpaMFAAAMQ0cLAACAWeloAQAAwxjRxKE6\nWgAAAHOmowUAAAzDdbQAAACYlY4WAAAwDLMOAgAAMCsdLQAAYBgj6mhtgELryN4BOnpg7wAL4JLe\nAfr7b4/pnaC7C3/s0b0jdPfE//mp3hG6u/A0n4M8v3eAReB3wf4BbAwboNACAAD2Cq6jBQAAwKx0\ntAAAgGG4jhYAAACz0tECAACGMaJZB3W0AAAA5kxHCwAAGIaOFgAAALPS0QIAAIbhOloAAADMSkcL\nAAAYhutoAQAAMKtqrfXOsKqqasni5lt/l/QOsAD8HSQn9Q7Q3b9q7+0dobt3PvJHe0fo7jmf+dPe\nEbr78/rB3hEWwLm9AyyAb+kdYAH4O0gqrbXqnWJ3DLNvvzh/LzpaAAAAc6bQAgAAmDOFFgAAwJwp\ntAAAAOZMoQUAADBnCi0AAIA5c8FiAABgIHf2DnAPVXVQkrclOSbJ5Ume21q7ZYVxpyf5/iSV5IOt\ntV/Y1bp1tAAAgLF6RZJzW2vHJzkvySuXD6iq70zy5Nbao5M8OskJVfVdu1qxjhYAADCQbb0DLHdy\nku+e3j8zyfmZFF9LtST7VdV+mTSq9kmyZVcr1tECAADG6tDW2pYkaa19Kckhywe01j6USQF2bZIv\nJjm7tfbZXa1YRwsAABjI8OdoVdUHkxy2dFEmXapXr/H1D0vyiCRHTF97blWd3Vq7YGevW/xC60G9\nA3R0/SW9EyyAG3sHWADn9g7Q3Z+/6fm9I3R37iU/2jtCdz4HSfIXvQMsAL8Lif2DPOhbeifo7/re\nARbF3ybZab2T1tozVnuuqrZU1WGttS1VdXiS61YY9i+SfKi1dvv0NX+V5Dt2tWGHDgIAAAPZNufb\ndyb5lSW33faeJC+a3n9hknevMObKJN9dVZuq6t6ZnNO1y3/xUGgBAABjdXqSZ1TVZ5OclOQ3kqSq\nnlBVr5+OeWeSzye5OMlFSS5qrf3lrla8+IcOAgAAe4nFuo5Wa+3GTAqs5cs/luQl0/t3Jfnp3V23\njhYAAMCc6WgBAAADWayO1nrS0QIAAJgzHS0AAGAg23oHGIyOFgAAwJzpaAEAAANxjhYAAAAz0tEC\nAAAG4hwtAAAAZrT4Ha3rx3McJyt5YO8ALIJf6B2gv1t7B1gEPgck8btAEvuHG9p4/tvpaAEAAMzZ\n4ne0AACAvYRztAAAAJiRjhYAADAQ52gBAAAwIx0tAABgIM7RAgAAYEY6WgAAwECcowUAAMCMdLQA\nAICBOEcLAACAGW2AjtZf9A7Q0e29A8BiuGnM3wMTt/YOsAh8DuKTADv4Pti4nKMFAADAjDZARwsA\nANg7OEcLAACAGeloAQAAA3GOFgAAADPS0QIAAAaiowUAAMCMdLQAAICBmHUQAACAGeloAQAAA3GO\nFgAAADPS0QIAAAYynnO0NkChdWnvAADdXdE7wEK4uHcAAFizDVBoAQAAe4fxnKOl0AIAAAYynkMH\nTYYBAAAwZzpaAADAQMZz6KCOFgAAwJzpaAEAAANxjta6q6pnVdWlVXVZVb28Vw4AAGCcquo5VfWp\nqtpeVY/fybjdrl26FFpVda8kr0vyzCSPSnJKVT2iRxY2gi/0DsBC8Dkg8TnAZ4AJn4ON6851vu22\ni5P8iyT/e7UBs9YuvTpaJyT5XGvtitbanUnOSnJypywsvMt7B2AhXN47AAvh8t4B6O7y3gFYCJf3\nDsBeorX22dba55LUTobNVLv0OkfryCRXLXl8dSZvAAAA2GttyHO0ZqpdehVaK1WMbfAUAADAXq2q\nPpjksKWLMqk9/n1r7b1rWcUKy3ZZu/QqtK5OcvSSx0cluWbloa9Z/zRsAKseNsuojPdz8JreARbC\na6Z/jvdzwA4+AyQ+BxvSFclrjlnnbWxZvqC19ow9XOdu1C5361VoXZjkuKo6Jsm1SZ6X5JTlg1pr\nOztWEgAA2CBaa8f2zrALq9Uea6pdlusyGUZrbXuSlyU5J8mnk5zVWrukRxYAAGCcqurZVXVVku9I\n8r6q+qvp8gdX1fuS2WuXas2pUQAAAPPU7YLFO+NixlTVUVV1XlV9pqourqqf652JfqrqXlX18ap6\nT+8s9FFVB1TVO6rqkqr6dFU9qXcmhldVvzi9sOgnq+otVXWf3plYf1X1xqraUlWfXLLsoKo6p6o+\nW1VnV9UBPTPCShau0HIxY6a2Jfml1tojk3xnkpf6HIzazyf5TO8QdPVfkry/tfYtSR6bxOHmI1NV\nRyT52SSPb609JpPzzJ/XNxUDOSOT/cKlXpHk3Nba8UnOS/LKwVPBLixcoRUXMyZJa+1LrbVPTO9/\nOZOdqiP7pqKHqjoqyfcl+ZPeWeijqjYn+WettTOSpLW2rbV2a+dY9LEpyf2qap8k+2cNs36x8bXW\nLkhy07LFJyc5c3r/zCTPHjQUrMEiFlorXRDMDvaIVdWxSR6X5MN9k9DJ7yX5lbjW3pg9NMn1VXXG\n9BDS11fVfXuHYlittWuS/E6SK5N8McnNrbVz+6aio0Nba1uSyT/OJjmkcx74BotYaLmYMV9XVfdP\n8s4kPz/tbDEiVfX9SbZMu5uV1addZe+2T5LHJ/mj1trjk2zN5LAhRqSqDsyki3FMkiOS3L+qfqRv\nKoDVLWKhNdMFwdj7TA8NeWeSN7fW3t07D108JckPVdXnk/xZku+pqjd1zsTwrk5yVWvto9PH78yk\n8GJcTkry+dbajdOplv8iyZM7Z6KfLVV1WJJU1eFJruucB77BIhZaX78g2HQ2oeclMdPYOP2PJJ9p\nrf2X3kHoo7X2qtba0a21h2byXXBea+3HeudiWNPDg66qqm+eLnp6TI4yRlcm+Y6q2q+qKpPPgUlR\nxmP5UQ3vSfKi6f0XJvEPsiycfXoHWK61tr2qdlwQ7F5J3uhixuNTVU9J8vwkF1fVRZkcPvqq1toH\n+iYDOvm5JG+pqnsn+XySH++ch4G11j5SVe9MclGSO6d/vr5vKoZQVW9NcmKSg6vqyiSnJvmNJO+o\nqhdnUoT/cL+EsDIXLAYAAJizRTx0EAAAYENTaAEAAMyZQgsAAGDOFFoAAABzptACAACYM4UWAADA\nnCm0AFhVVb2+qh4xvf/K3nkAYKNwHS0A1qSqbmutbe6dAwA2Ah0tAJIkVbV/Vb2vqi6qqk9W1XOr\n6m+q6vFV9etJ7ltVH6+qN0/HP7+qPjxd9l+rqjq/BQBYGAotAHZ4VpIvtta+rbX2mCQf2PFEa+2V\nSba21h7fWnvB9HDCf53kya21xye5K8nzu6QGgAW0T+8AACyMi5P81rR79ZettQuWNamWPnh6kscn\nuXDaydovyZbBkgLAglNoAZAkaa19rqqekOT7kry2qs5LstqJvJXkzNbavx8sIABsIA4dBCBJUlUP\nTnJ7a+2tSX47k47VUl+rqk3T+3+d5DlVdcj0tQdV1dHDpQWAxabQAmCHb03ykaq6KMmvJnntsudf\nn+Tiqnpza+2SJP8hyTlV9X+TnJPk8EHTAsACM707AADAnOloAQAAzJlCCwAAYM4UWgAAAHOm0AIA\nAJgzhRYAAMCcKbQAAADmTKEFAAAwZwotAACAOfv/J5xgI7o6QG4AAAAASUVORK5CYII=\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x1091636a0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "l = 11\n", + "dim = 1 << l\n", + "j = 1.00*np.ones((l-1)) # Ising coupling\n", + "hx = 0.4*np.ones((l)) # transverse field strength Gamma\n", + "\n", + "## Starting configuration\n", + "ind = int('00000100000',base=2) # specify spin configuration: 0 = down, 1 = up\n", + "v = np.zeros((dim),dtype=complex)\n", + "v[ind] = 1.\n", + "\n", + "## Parameters for time evolution\n", + "tend = 20. # duration of the time evolution\n", + "tmeas = 0.5 # time after which a measurment is performed\n", + "dt = 0.1 # time step used for the evolution\n", + "nmeas = int((tend)/tmeas) # number of measurements\n", + "nstep = int((tmeas)/dt) # number of steps between measurments\n", + "\n", + "## measure magnetization\n", + "m=np.zeros((nmeas,l));\n", + "m[0,:] = magnetization(v, l)\n", + "\n", + "## Do time evolution\n", + "for t in range(1,nmeas):\n", + " # print(t*tmeas)\n", + " v=evolve(l,j,hx,v,dt,nstep)\n", + " m[t,:] = magnetization(v, l)\n", + "\n", + "## plot magnetization\n", + "plt.pcolor(np.array(range(l+1)),np.linspace(0.,tend,nmeas+1),m,\n", + " vmin=-1.0, vmax=1.0)\n", + "plt.xlabel('site')\n", + "plt.ylabel('time')\n", + "plt.axis([0,l,0,tend])\n", + "plt.title(\"Magnetisation, J = \"+str(j[0])+\" , hx = \"+str(hx[0]))\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "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": "3.4.3" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/exercises/ex03_solution/TFIM_time_evolution/python/trising.ipynb b/exercises/ex03_solution/TFIM_time_evolution/python/trising.ipynb new file mode 100644 index 0000000..9e3f39c --- /dev/null +++ b/exercises/ex03_solution/TFIM_time_evolution/python/trising.ipynb @@ -0,0 +1,255 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from cmath import exp\n", + "from math import sin, cos\n", + "%matplotlib inline\n", + "plt.rcParams['figure.figsize'] = 16, 9" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Time-evolution operator" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def evolve(l, j, hx, v, dt, n):\n", + " \"\"\" Evolve the state v in time by n * dt \"\"\"\n", + " dim = 1 << l\n", + " def tstep_diag(x, dt):\n", + " ## Apply diagonal part\n", + " for s in range(dim):\n", + " jtotal = 0.\n", + " for r in range(l-1):\n", + " jtotal += -j[r] if ((s >> r)^(s >> (r+1)))&1 else j[r]\n", + " x[s] = exp(-1j*jtotal*dt)*x[s]\n", + " return x\n", + " def tstep_transv(x, dt):\n", + " ## Apply transverse part succesively for each site\n", + " y = np.zeros_like(x)\n", + " for r in range(l):\n", + " cos_v = cos(dt*hx[r])\n", + " sin_v = sin(dt*hx[r])\n", + " ## diagonal\n", + " for s in range(dim):\n", + " y[s] = cos_v * x[s]\n", + " ## off-diagonal\n", + " for s in range(dim):\n", + " y[s^(1<<r)] += 1.j*sin_v * x[s]\n", + " ## swap vectors\n", + " tmp = x\n", + " x = y\n", + " y = tmp\n", + " return x\n", + " v = tstep_diag(v, dt/2.)\n", + " for i in range(int(n-1)):\n", + " v = tstep_transv(v, dt)\n", + " v = tstep_diag(v, dt)\n", + " v = tstep_transv(v, dt)\n", + " v = tstep_diag(v, dt/2.)\n", + " return v" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Measurements" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def magnetization(v, l):\n", + " \"\"\" Measure the magnetization per site for the state v \"\"\"\n", + " dim = 1 << l\n", + " m = np.zeros((l))\n", + " for r in range(l):\n", + " for s in range(dim):\n", + " m[r] += abs(v[s])**2 * 2. * ( bool(s&(1 << r)) -0.5)\n", + " return m" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Transverse field only" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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0AACAubhBRQsAAIDNWviK1os/deLYIQCwAJapX/96dmTX2CGwAPwskCSn1tgR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\n0QIAAOZj8dbR2jIqWgAAADO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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x10916c898>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "l = 11\n", + "dim = 1 << l\n", + "j = 0.00*np.ones((l-1)) # Ising coupling\n", + "hx = 2*np.pi*0.125*np.ones((l)) # transverse field strength Gamma\n", + "\n", + "## Starting configuration\n", + "ind = int('00000000000',base=2) # specify spin configuration: 0 = down, 1 = up\n", + "v = np.zeros((dim),dtype=complex)\n", + "v[ind] = 1.\n", + "\n", + "## Parameters for time evolution\n", + "tend = 20. # duration of the time evolution\n", + "tmeas = 0.5 # time after which a measurment is performed\n", + "dt = 0.1 # time step used for the evolution\n", + "nmeas = int((tend)/tmeas) # number of measurements\n", + "nstep = int((tmeas)/dt) # number of steps between measurments\n", + "\n", + "## measure magnetization\n", + "m=np.zeros((nmeas,l));\n", + "m[0,:] = magnetization(v, l)\n", + "\n", + "## Do time evolution\n", + "for t in range(1,nmeas):\n", + " # print(t*tmeas)\n", + " v=evolve(l,j,hx,v,dt,nstep)\n", + " m[t,:] = magnetization(v, l)\n", + "\n", + "## plot magnetization\n", + "plt.pcolor(np.array(range(l+1)),np.linspace(0.,tend,nmeas+1),m,\n", + " vmin=-1.0, vmax=1.0)\n", + "plt.xlabel('site')\n", + "plt.ylabel('time')\n", + "plt.axis([0,l,0,tend])\n", + "plt.title(\"Magnetisation, J = \"+str(j[0])+\" , hx = \"+str(hx[0]))\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ising coupling and transverse field" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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GMaJZB3W0AAAA5kxHCwAAGIaOFgAAALPS0QIAAIbhOloAAADMSkcL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\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x1091636a0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "l = 11\n", + "dim = 1 << l\n", + "j = 1.00*np.ones((l-1)) # Ising coupling\n", + "hx = 0.4*np.ones((l)) # transverse field strength Gamma\n", + "\n", + "## Starting configuration\n", + "ind = int('00000100000',base=2) # specify spin configuration: 0 = down, 1 = up\n", + "v = np.zeros((dim),dtype=complex)\n", + "v[ind] = 1.\n", + "\n", + "## Parameters for time evolution\n", + "tend = 20. # duration of the time evolution\n", + "tmeas = 0.5 # time after which a measurment is performed\n", + "dt = 0.1 # time step used for the evolution\n", + "nmeas = int((tend)/tmeas) # number of measurements\n", + "nstep = int((tmeas)/dt) # number of steps between measurments\n", + "\n", + "## measure magnetization\n", + "m=np.zeros((nmeas,l));\n", + "m[0,:] = magnetization(v, l)\n", + "\n", + "## Do time evolution\n", + "for t in range(1,nmeas):\n", + " # print(t*tmeas)\n", + " v=evolve(l,j,hx,v,dt,nstep)\n", + " m[t,:] = magnetization(v, l)\n", + "\n", + "## plot magnetization\n", + "plt.pcolor(np.array(range(l+1)),np.linspace(0.,tend,nmeas+1),m,\n", + " vmin=-1.0, vmax=1.0)\n", + "plt.xlabel('site')\n", + "plt.ylabel('time')\n", + "plt.axis([0,l,0,tend])\n", + "plt.title(\"Magnetisation, J = \"+str(j[0])+\" , hx = \"+str(hx[0]))\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "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": "3.4.3" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/exercises/ex03_solution/TFIM_time_evolution/python/trising.py b/exercises/ex03_solution/TFIM_time_evolution/python/trising.py new file mode 100644 index 0000000..8ef28e1 --- /dev/null +++ b/exercises/ex03_solution/TFIM_time_evolution/python/trising.py @@ -0,0 +1,87 @@ +import numpy as np +import matplotlib.pyplot as plt +from cmath import exp +from math import sin, cos + +def evolve(l, j, hx, v, dt, n): + """ Evolve the state v in time by n * dt """ + dim = 1 << l + def tstep_diag(x, dt): + # Apply diagonal part + for s in range(dim): + jtotal = 0. + for r in range(l-1): + jtotal += -j[r] if ((s >> r)^(s >> (r+1)))&1 else j[r] + x[s] = exp(-1.j*jtotal*dt)*x[s] + return x + def tstep_transv(x, dt): + # Apply transverse part succesively for each site + y = np.zeros_like(x) + for r in range(l): + cos_v = cos(dt*hx[r]) + sin_v = sin(dt*hx[r]) + # diagonal + for s in range(dim): + y[s] = cos_v * x[s] + # off-diagonal + for s in range(dim): + y[s^(1<<r)] += 1.j*sin_v * x[s] + # swap vectors + tmp = x + x = y + y = tmp + return x + v = tstep_diag(v, dt/2.) + for i in range(int(n-1)): + v = tstep_transv(v, dt) + v = tstep_diag(v, dt) + v = tstep_transv(v, dt) + v = tstep_diag(v, dt/2.) + return v + +def magnetization(v, l): + """ Measure the magnetization per site for the state v """ + dim = 1 << l + m = np.zeros((l)) + for r in range(l): + for s in range(dim): + m[r] += abs(v[s])**2 * 2. * ( bool(s&(1 << r)) -0.5) + return m + + +l = 9 +dim = 1 << l +j = 1.00*np.ones((l-1)) # Ising coupling +hx = 0.40*np.ones((l)) # transverse field strength Gamma + +# Starting configuration +ind = int('0000001000000',base=2) # specify spin configuration: 0 = down, 1 = up +v = np.zeros((dim),dtype=complex) +v[ind] = 1. + +# Parameters for time evolution +tend = 20. # duration of the time evolution +tmeas = 0.5 # time after which a measurment is performed +dt = 0.1 # time step used for the evolution +nmeas = int((tend)/tmeas) # number of measurements +nstep = int((tmeas)/dt) # number of steps between measurments + +# measure magnetization +m=np.zeros((nmeas,l)); +m[0,:] = magnetization(v, l) + +# Do time evolution +for t in range(1,nmeas): + print(t*tmeas) + v=evolve(l,j,hx,v,dt,nstep) + m[t,:] = magnetization(v, l) + +# plot magnetization +plt.pcolor(np.array(range(l+1)),np.linspace(0.,tend,nmeas),m, + vmin=-1.0, vmax=1.0) +plt.xlabel('site') +plt.ylabel('time') +plt.axis([0,l,0,tend]) +plt.title("Magnetisation, J = "+str(j[0])+" , hx = "+str(hx[0])) +plt.colorbar() +plt.show() diff --git a/exercises/ex03_solution/TFIM_time_evolution/python/trising_skeleton.py b/exercises/ex03_solution/TFIM_time_evolution/python/trising_skeleton.py new file mode 100644 index 0000000..0abce03 --- /dev/null +++ b/exercises/ex03_solution/TFIM_time_evolution/python/trising_skeleton.py @@ -0,0 +1,76 @@ +# ---- CQP FS16, Ex3.1 skeleton ---- +# ---------------------------------- +import numpy as np +import matplotlib.pyplot as plt + +def evolve(l, j, hx, v, dt, n): + """ Evolve the state v in time by n * dt + + Parameters: + l length of chain + j Ising coupling for each neighbors, 1-d numpy array with length at least l-1 + hx transverse field for each site, 1-d numpy array with length at least l + v the state at time t, complex 1-d numpy array with length at least 1 << l + dt timestep + n number of consecutive timesteps + + Return: + v the state at time t+n*dt + """ + # Implement the time evolution of the state v here. + # Use the split-operator scheme we discussed in the + # exercise class. + return v + + +def magnetization(v, l): + """ Measure the magnetization per site for the state v + + Parameters: + v the state to be measured, complex 1-d numpy array with length at least 1 << l + l length of chain + + Return: + m the magnetization at each site, 1-d numpy array with length l + """ + # Implement the measurement of the magnetization here. + return m + + + +l = 9 # length of chain +dim = 1 << l +j = 1.00*np.ones((l)) # Ising coupling +hx = 0.40*np.ones((l-1)) # transverse field strength Gamma + +# Starting configuration +ind = int('000010000',base=2) # specify spin configuration: 0 = down, 1 = up +v = np.zeros((dim),dtype=complex) +v[ind] = 1. # start time evolution with a single basis state + +# Parameters for time evolution +tend = 10. # duration of the time evolution +tmeas = 0.5 # time after which a measurment is performed +dt = 0.1 # time step used for the evolution +nmeas = int((tend)/tmeas) # number of measurements +nstep = int((tmeas)/dt) # number of steps between measurements + +# measure magnetization +m=np.zeros((nmeas,l)); +m[0,:] = magnetization(v, l) + +# Do time evolution +for t in range(1,nmeas): + print(t*tmeas) + v=evolve(l,j,hx,v,dt,nstep) + m[t,:] = magnetization(v, l) + +# plot magnetization +plt.pcolor(np.array(range(l+1)),np.linspace(0.,tend,nmeas),m, + vmin=-1.0, vmax=1.0) +plt.xlabel('site') +plt.ylabel('time') +plt.axis([0,l,0,tend]) +plt.title("Magnetisation, J = "+str(j[0])+" , hx = "+str(hx[0])) +plt.colorbar() +plt.show() diff --git a/exercises/ex03_solution/scattering/.ipynb_checkpoints/scattering-checkpoint.ipynb b/exercises/ex03_solution/scattering/.ipynb_checkpoints/scattering-checkpoint.ipynb new file mode 100644 index 0000000..1a1d623 --- /dev/null +++ b/exercises/ex03_solution/scattering/.ipynb_checkpoints/scattering-checkpoint.ipynb @@ -0,0 +1,397 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline --no-import-all\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.cm as cm\n", + "from numpy import sqrt, exp, sinh\n", + "from scipy import constants, special\n", + "plt.rcParams['figure.figsize'] = 16, 9" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Numerov" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def numerov_step(k0, k1, k2, psi0, psi1, dx):\n", + " \"\"\"compute psi2 via a single numerov step\"\"\"\n", + " dx_sqr = dx**2\n", + " c0 = (1 + 1/12. * dx_sqr * k0)\n", + " c1 = 2 * (1 - 5/12. * dx_sqr * k1)\n", + " c2 = (1 + 1/12. * dx_sqr * k2)\n", + " return (c1 * psi1 - c0 * psi0) / c2\n", + "\n", + "def numerov(ks, psi0, psi1, dx):\n", + " \"\"\"compute psis = [psi0, psi1, psi2, ...] for ks = [k0, k1, ...] via iterated numerov steps\"\"\"\n", + " n = len(ks)\n", + " psis = np.zeros(n, dtype=np.complex128)\n", + " psis[0] = psi0\n", + " psis[1] = psi1\n", + " for i in range(2, n):\n", + " psis[i] = numerov_step(ks[i-2], ks[i-1], ks[i], psis[i-2], psis[i-1], dx)\n", + " return psis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Scattering Computations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Discretization parameters:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "r_min = 0.5\n", + "r_max = 5\n", + "r_steps = 1000\n", + "rs, dr = np.linspace(r_min, r_max, r_steps, retstep=True)\n", + "\n", + "l_max = 10\n", + "ls = np.arange(0, l_max+1)\n", + "l_colors = colors = cm.rainbow(ls / float(l_max))\n", + "\n", + "Es = np.linspace(0.1, 3.5, 200)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lennard--Jones potential:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "eps = 5.9\n", + "\n", + "def V_LJ(r):\n", + " \"\"\"r is in units of sigma, result is in meV\"\"\"\n", + " s = (1./r)**6\n", + " return eps * (s**2 - 2*s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Effective potential for $u_l(r)$:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "hbar_sqr_over_2m = 1/6.12\n", + "\n", + "def V_eff(l):\n", + " def V(r):\n", + " return V_LJ(r) + hbar_sqr_over_2m * l*(l+1) / r**2\n", + " return V" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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atWupq6sr+NoTTzyRvfbai5tuuonLL7+cz33ucxx//PHDMMrCqINbBeKZKcpB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qZcpa3WcUWJiqhRtmomr8d1DcADPDVzFySEwC6MYhdGKY0+FNtl0MRvXcZvzuCtn6Fx9esEnUWc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HX9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\nuugWvmDLAAAAAElFTkSuQmCC\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x10976fa90>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.title(r'Effective potential')\n", + "plt.xlabel(r'$r / \\sigma$')\n", + "plt.ylabel(r'$V_l(r)$ [meV]')\n", + "plt.ylim(-6.5, 15)\n", + "for l, color in zip(ls, l_colors):\n", + " plt.plot(rs, V_eff(l)(rs), label='$l = %d$' % l, color=color)\n", + "plt.grid()\n", + "plt.legend()\n", + "plt.savefig('potential.pdf')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Asymptotic solution for $r \\rightarrow 0$:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "C = np.sqrt(eps / (25 * hbar_sqr_over_2m))\n", + "\n", + "def inner_solution(r):\n", + " return np.exp(-C * r**(-5))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Spherical Bessel functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def bessel_j(l, x):\n", + "\treturn special.sph_jn(l, x)[0][-1]\n", + "\n", + "def bessel_n(l, x):\n", + "\treturn special.sph_yn(l, x)[0][-1]\n", + "\n", + "assert np.isclose(bessel_j(5, 1.5), 6.69620596e-4)\n", + "assert np.isclose(bessel_n(5, 1.5), -94.2361101)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Phase shift:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def delta(E, l):\n", + " # integrate radial solution using numerov\n", + " ks = (E - V_eff(l)(rs)) / hbar_sqr_over_2m\n", + " psi0 = inner_solution(r_min)\n", + " psi1 = inner_solution(r_min + dr)\n", + " psis = numerov(ks, psi0, psi1, dr)\n", + " \n", + " # compute phase shift\n", + " r1, r2 = r_max - dr, r_max\n", + " u1, u2 = psis[-2:]\n", + " K = (r1*u2) / (r2*u1)\n", + " k = np.sqrt(E / hbar_sqr_over_2m)\n", + " numerator = K * bessel_j(l, k*r1) - bessel_j(l, k*r2)\n", + " denominator = K * bessel_n(l, k*r1) - bessel_n(l, k*r2)\n", + " return np.arctan((numerator / denominator).real)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Partial scattering cross section for fixed $l$:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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XXACDB8M++8Bbb8WuSJIkSUpXLpfDPNPw65DL5aAZWdXOraKq27l1LFmSJElScxluFZUL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\nNUi9zeGo2LdwM3fXl8xc9leyCrK4b8jvmNztBsKJwu02IbG0lPJ93+Z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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x10995fa90>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def partial(E, l):\n", + " k_sqr = E / hbar_sqr_over_2m\n", + " return 4*np.pi/k_sqr * (2*l + 1) * np.sin(delta(E, l))**2\n", + "\n", + "plt.title('Partial scattering cross sections')\n", + "plt.xlabel('$E$ [meV]')\n", + "plt.ylabel(r'$\\sigma_{tot} / \\sigma^2$')\n", + "for l in [4, 5, 6]:\n", + " plt.plot(Es, [partial(E, l) for E in Es], label=\"$l = %d$\" % l)\n", + "plt.legend()\n", + "plt.savefig('partial.pdf')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Total scattering cross section for various values of $l_{\\max}$:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "partials = [np.array([partial(E, l) for E in Es]) for l in range(l_max + 1)]" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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tKQwkIiIiIiLpzO7idiGwDTgx/vMDhIvbKcCrXe/lDGQETczsrMgzuJw4WlXc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\nMmlLgNvb7dTZade7OqGryy53dkJXl61RUlICRcU27BYXO34I9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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x1099990d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.title('Total scattering cross section for various values of the cutoff $l_{\\max}$')\n", + "plt.xlabel('$E$ [meV]')\n", + "plt.ylabel(r'$\\sigma_{tot} / \\sigma^2$')\n", + "for l_max, color in zip(ls, l_colors):\n", + " plt.plot(Es, sum(partials[l] for l in range(l_max+1)), label=\"$l_{\\max} = %d$\" % l_max, color=color)\n", + "plt.legend()\n", + "plt.savefig('total.pdf')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The figure that we display in the exercise:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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uu+b/GptuGkaiNtssubqkYrbPPnDiiXDccbErKX1z5sB3vxs+pBszBnr0iF2R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\nN5RScbv2WvjZz8KZzZIkSUq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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x10995ae10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def total(E):\n", + " return sum(partial(E, l) for l in range(l_max+1))\n", + "\n", + "#plt.title('Total scattering cross section for $r_{\\min} = 0.5 \\sigma$, $r_{\\max} = 5 \\sigma$, $l_{\\max} = %d$' % l_max)\n", + "plt.xlabel('$E$ [meV]')\n", + "plt.ylabel(r'$\\sigma_{tot} / \\sigma^2$')\n", + "plt.plot(Es, [total(E) for E in Es])\n", + "plt.savefig('example.pdf')\n", + "plt.show()" + ] + } + ], + "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": "3.4.3" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/exercises/ex03_solution/scattering/scattering.ipynb b/exercises/ex03_solution/scattering/scattering.ipynb new file mode 100644 index 0000000..5af9d86 --- /dev/null +++ b/exercises/ex03_solution/scattering/scattering.ipynb @@ -0,0 +1,397 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline --no-import-all\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.cm as cm\n", + "from numpy import sqrt, exp, sinh\n", + "from scipy import constants, special\n", + "plt.rcParams['figure.figsize'] = 16, 9" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Numerov" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def numerov_step(k0, k1, k2, psi0, psi1, dx):\n", + " \"\"\"compute psi2 via a single numerov step\"\"\"\n", + " dx_sqr = dx**2\n", + " c0 = (1 + 1/12. * dx_sqr * k0)\n", + " c1 = 2 * (1 - 5/12. * dx_sqr * k1)\n", + " c2 = (1 + 1/12. * dx_sqr * k2)\n", + " return (c1 * psi1 - c0 * psi0) / c2\n", + "\n", + "def numerov(ks, psi0, psi1, dx):\n", + " \"\"\"compute psis = [psi0, psi1, psi2, ...] for ks = [k0, k1, ...] via iterated numerov steps\"\"\"\n", + " n = len(ks)\n", + " psis = np.zeros(n, dtype=np.complex128)\n", + " psis[0] = psi0\n", + " psis[1] = psi1\n", + " for i in range(2, n):\n", + " psis[i] = numerov_step(ks[i-2], ks[i-1], ks[i], psis[i-2], psis[i-1], dx)\n", + " return psis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Scattering Computations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Discretization parameters:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "r_min = 0.5\n", + "r_max = 5\n", + "r_steps = 1000\n", + "rs, dr = np.linspace(r_min, r_max, r_steps, retstep=True)\n", + "\n", + "l_max = 10\n", + "ls = np.arange(0, l_max+1)\n", + "l_colors = colors = cm.rainbow(ls / float(l_max))\n", + "\n", + "Es = np.linspace(0.1, 3.5, 200)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lennard--Jones potential:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "eps = 5.9\n", + "\n", + "def V_LJ(r):\n", + " \"\"\"r is in units of sigma, result is in meV\"\"\"\n", + " s = (1./r)**6\n", + " return eps * (s**2 - 2*s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Effective potential for $u_l(r)$:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "hbar_sqr_over_2m = 1/6.12\n", + "\n", + "def V_eff(l):\n", + " def V(r):\n", + " return V_LJ(r) + hbar_sqr_over_2m * l*(l+1) / r**2\n", + " return V" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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ZUc6Rc0YLESFB0pAqntXtfLxQXdeFLrQtX+5joTtr1ix4+mn4zW9U6JaZfhvs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\nAj/+Mdx7b2muOczo3De/KA9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BflEe/lAW/lAW/lAW/lAWfhkueaxYsYIZM2a0e69w6XKh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\nDvKI4svv0dWY1XCv8hdb6DpcySjlwIrsK/FZB88cq3GUw/TxHnUKnHw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WU/Q26wbLpsN/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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7fa3e1ff0080>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.title(r'Effective potential')\n", + "plt.xlabel(r'$r / \\sigma$')\n", + "plt.ylabel(r'$V_l(r)$ [meV]')\n", + "plt.ylim(-6.5, 15)\n", + "for l, color in zip(ls, l_colors):\n", + " plt.plot(rs, V_eff(l)(rs), label='$l = %d$' % l, color=color)\n", + "plt.grid()\n", + "plt.legend()\n", + "plt.savefig('potential.pdf')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Asymptotic solution for $r \\rightarrow 0$:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "C = np.sqrt(eps / (25 * hbar_sqr_over_2m))\n", + "\n", + "def inner_solution(r):\n", + " return np.exp(-C * r**(-5))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Spherical Bessel functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def bessel_j(l, x):\n", + "\treturn special.sph_jn(l, x)[0][-1]\n", + "\n", + "def bessel_n(l, x):\n", + "\treturn special.sph_yn(l, x)[0][-1]\n", + "\n", + "assert np.isclose(bessel_j(5, 1.5), 6.69620596e-4)\n", + "assert np.isclose(bessel_n(5, 1.5), -94.2361101)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Phase shift:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def delta(E, l):\n", + " # integrate radial solution using numerov\n", + " ks = (E - V_eff(l)(rs)) / hbar_sqr_over_2m\n", + " psi0 = inner_solution(r_min)\n", + " psi1 = inner_solution(r_min + dr)\n", + " psis = numerov(ks, psi0, psi1, dr)\n", + " \n", + " # compute phase shift\n", + " r1, r2 = r_max - dr, r_max\n", + " u1, u2 = psis[-2:]\n", + " K = (r1*u2) / (r2*u1)\n", + " k = np.sqrt(E / hbar_sqr_over_2m)\n", + " numerator = K * bessel_j(l, k*r1) - bessel_j(l, k*r2)\n", + " denominator = K * bessel_n(l, k*r1) - bessel_n(l, k*r2)\n", + " return np.arctan((numerator / denominator).real)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Partial scattering cross section for fixed $l$:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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0IYZbZaaqqumdWzDcSpIkSdoww60y05yxZDDcSpIkSdoww60yY7iVJEmSlBbD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\nNUi9zeGo2LdwM3fXl8xc9leyCrK4b8jvmNztBsKJwu02IbG0lPJ93+Z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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x10995fa90>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def partial(E, l):\n", + " k_sqr = E / hbar_sqr_over_2m\n", + " return 4*np.pi/k_sqr * (2*l + 1) * np.sin(delta(E, l))**2\n", + "\n", + "plt.title('Partial scattering cross sections')\n", + "plt.xlabel('$E$ [meV]')\n", + "plt.ylabel(r'$\\sigma_{tot} / \\sigma^2$')\n", + "for l in [4, 5, 6]:\n", + " plt.plot(Es, [partial(E, l) for E in Es], label=\"$l = %d$\" % l)\n", + "plt.legend()\n", + "plt.savefig('partial.pdf')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Total scattering cross section for various values of $l_{\\max}$:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "partials = [np.array([partial(E, l) for E in Es]) for l in range(l_max + 1)]" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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tKQwkIiIiIiLpzO7idiGwDTgx/vMDhIvbKcCrXe/lDGQETczsrMgzuJw4WlXc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\nMmlLgNvb7dTZade7OqGryy53dkJXl61RUlICRcU27BYXO34I9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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x1099990d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.title('Total scattering cross section for various values of the cutoff $l_{\\max}$')\n", + "plt.xlabel('$E$ [meV]')\n", + "plt.ylabel(r'$\\sigma_{tot} / \\sigma^2$')\n", + "for l_max, color in zip(ls, l_colors):\n", + " plt.plot(Es, sum(partials[l] for l in range(l_max+1)), label=\"$l_{\\max} = %d$\" % l_max, color=color)\n", + "plt.legend()\n", + "plt.savefig('total.pdf')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The figure that we display in the exercise:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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uu+b/GptuGkaiNtssubqkYrbPPnDiiXDccbErKX1z5sB3vxs+pBszBnr0iF2R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\nN5RScbv2WvjZz8KZzZIkSUq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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x10995ae10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def total(E):\n", + " return sum(partial(E, l) for l in range(l_max+1))\n", + "\n", + "#plt.title('Total scattering cross section for $r_{\\min} = 0.5 \\sigma$, $r_{\\max} = 5 \\sigma$, $l_{\\max} = %d$' % l_max)\n", + "plt.xlabel('$E$ [meV]')\n", + "plt.ylabel(r'$\\sigma_{tot} / \\sigma^2$')\n", + "plt.plot(Es, [total(E) for E in Es])\n", + "plt.savefig('example.pdf')\n", + "plt.show()" + ] + } + ], + "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": "3.4.3" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} -- GitLab