diff --git a/exercises/ex03_solution/cpp/Makefile b/exercises/ex03_solution/cpp/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..e185a516ebe196b58364364c6c0f1253fd332cb4
--- /dev/null
+++ b/exercises/ex03_solution/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/cpp/magnetization.png b/exercises/ex03_solution/cpp/magnetization.png
new file mode 100644
index 0000000000000000000000000000000000000000..380f251e27b38789edd42027dff695657c47b68b
Binary files /dev/null and b/exercises/ex03_solution/cpp/magnetization.png differ
diff --git a/exercises/ex03_solution/cpp/plotmagn.py b/exercises/ex03_solution/cpp/plotmagn.py
new file mode 100644
index 0000000000000000000000000000000000000000..be16ce5d7ee7f1cc3bca2b137e89289288d9eba0
--- /dev/null
+++ b/exercises/ex03_solution/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/cpp/trFieldIsingTimeEvolution.cpp b/exercises/ex03_solution/cpp/trFieldIsingTimeEvolution.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..e34750ce94c8808b0a5ef1da2abe01c996bf1c96
--- /dev/null
+++ b/exercises/ex03_solution/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/scattering.ipynb b/exercises/ex03_solution/scattering.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..c274d984e1fa219feba5f30f30c3fc00191e4673
--- /dev/null
+++ b/exercises/ex03_solution/scattering.ipynb
@@ -0,0 +1,406 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "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": 19,
+   "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": 20,
+   "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": 21,
+   "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": 22,
+   "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": 23,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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pWpCFMBsXuMU2yHRbjz/AQvfYY4+FvfaCJUsqF84ypPTXYH8oC38oC38oC38o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c6SVCENuUpdLtFUNVrSJFWjq9q4Ik9eFMmLIjmTXHK4okCRKrblYAsXm8gTKHr/gQAUklAnFSKR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\nja4kSZIkqaLY6EqSJEmSKsr/B0D/3Iw/p4ixAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x113017b00>"
+      ]
+     },
+     "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": 24,
+   "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": 25,
+   "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": 26,
+   "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": 27,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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0YexVIXIckwsAAAAgKl7Glc2st6TLJH1gZoslOUm/kXSpmR0lqVTScknDfdSH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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x113027ac8>"
+      ]
+     },
+     "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": 28,
+   "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": 29,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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aGhooLi6mrq6O/Px86urqaG1tJRgMsnz5clasWEFVVRX5+flOr0LSmdFyw95E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Tdxb62ihhivYYtMSiKEEALwuj4niZIkSgczlzu0cRjxq77DpNnHIA9zgCHSRLCOG/NbR5JqYjL2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\nAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x114965e80>"
+      ]
+     },
+     "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": 30,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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Ru1K3qsMKK6Td+bo7cnLHHWnN4R13FFuXVOsOOQT+53/ghBNyV1Jf5syBww6D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\nPZNtd+UQQm9SwL0sxngDQIz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Vqlo7uSGkkeXrrstdSWP6wx9gk03S9+Hhhw24kiRJKk+I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\nSUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x112f589b0>"
+      ]
+     },
+     "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()"
+   ]
+  },
+  {
+   "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": "3.4.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/exercises/ex03_solution/trising.ipynb b/exercises/ex03_solution/trising.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..d9841cbf6b37bd77874bc4795cc6d0f706656bf0
--- /dev/null
+++ b/exercises/ex03_solution/trising.ipynb
@@ -0,0 +1,265 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "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": 2,
+   "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)] += 1j*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": 3,
+   "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": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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2fZppeC6TYQyzM70xyXOHytbWDQwDAADYuLVmEt7nfGXLK1pVdWAmSdZru/tNw+adVXV4\nd++syWKM16zzXgkZAACsobvXXWpkEd22ah6z3+3s7o0s9j7tykxmdF1xZCbDIfbJPLoO/kGSD3X3\nS6e2vTmTNVVOy2SNkjet8b6JQ+VaS+/LJye3PHnsKBibzwGJzwE+A0z4HCTX7lc5VpLJ2hgnb/E5\nTp4sn7GWyvprYL45kzUEXz8sWfG5lWFO+2JLE62qeniSH8lkXZH3ZVKCe2EmCdafVNUzklye5Ie2\nMg4AAGB8c5sgYkpVvS7JsUluX1WXZ7L+4s2SdHe/orvfVlVPqKqPZjK9+4/N4rxbeq3d/XdJdqyz\n+9FbeW4AAIDu/uENtHn2rM87RlIJe+egY8eOgEXgc0Dic4DPABM+B/utg8YOYI6qe3HHQFVVG6MF\nAACrXFv73WQYVdWnbfE5np/FmSRERQsAAJiLZUo+5rKOFgAAwDJZpqQSAAAY0TKN0VLRAgAAmDEV\nLQAAYC6WKflQ0QIAAJixZUoqAQCAES3TGK2FT7Re/KkTxw4BAFgQu7Jj7BBgIZy6ECtFsTsLn2gB\nAADbwzIlH8ZoAQAAzNgyJZUAAMCIlmmMlooWAADAjKloAQAAc7FMyYeKFgAAwIwtU1IJAACMyBgt\nAAAANk1FCwAAmAsVLQAAADZNRQsAAJiLZUo+qrvHjmFdVdX9kLGjAACAxVLnJ91dY8exN6qq37bF\n53hCFue+LFNSCQAAjMgYLQAAADZNRQsAAJiLZUo+VLQAAABmbJmSSgAAYETLNEZLogUAAMzFMiUf\nug4CAADM2DIllQAAwIiWqeugihYAAMCMqWgBAABzsUzJh4oWAADAjC1TUgkAAIxomcZoLXyidcr5\nY0cAAACwdxY+0QIAALaHZUo+jNECAACYsWVKKgEAgBEt0xgtFS0AAIAZU9ECAADmQkULAACATZNo\nAQAAc3HgFj/WU1WPq6qLq+rDVfX8NfbfparOrqr3VtUFVfX4fb1WiRYAALBtVdUBSV6W5LFJ7pfk\n+Kq6z6pmL0ry+u4+OsnxSX5nX89rjBYAADAXB2119nHDmluPSfKR7r4sSarqjCTHJbl4qs2NSW4z\nPL9tkk/saygSLQAAYDs7IskVU6+vzCT5mnZKkrOq6meS3CLJo/f1pBItAABgLg4cp6JVa2zrVa+P\nT/Lq7v7Nqnpokj/MpJvhpi18onXSQ8aOAAAAFsvJ548dwWL4213JuTfusdmVSe469frIJJ9c1eaZ\nmYzhSne/u6puXlWHdve1m41t4RMtAABgezhox2yP98gdySOnXv/ql9dsdl6Se1TVUUmuSvLkTCpY\n0y7LpLvg6VV13yTfsC9JVmLWQQAAYBvr7l1Jnp3krCQXJjmjuy+qqlOq6nuGZj+X5Mer6oIkf5Tk\naft63upe3T1xcVRVt66DAABwE3V+0t1rjT1aWFXVXzl4a89xs88vzn1R0QIAAJgxY7QAAIC52PJ1\ntBaIihYAAMCMLVFOCQAAjGrGsw4uMhUtAACAGVPRAgAA5mOJsg8VLQAAgBlbopwSAAAY1RJlHypa\nAAAAM7bwOeWJ57147BAAYCHsyK6xQwAWRZ06dgSbs/DZx+yoaAEAAMzYEuWUAADAqKyjBQAAwGap\naAEAAPOxRNmHihYAAMCMLVFOCQAAjGqJsg8VLQAAgBlbopwSAAAYlVkHAQAA2CwVLQAAYD6WKPtQ\n0QIAAJix6u6xY1hXVXUOXdz4AABgFNdWurvGDmNvVFX3Q7f4HO/OwtwXFS0AAIAZW6JekgAAwKjM\nOggAAMBmqWgBAADzsUTZh4oWAADAjC1RTgkAAIxqibKPJbpUAABgVEuUfeg6CAAAMGNLlFMCAACj\nMr07AAAAm6WiBQAAzMcSZR8qWgAAADO2+DnltaeMHQEAADALi599zIyKFgAAwIwtUU4JAACMyqyD\nAAAAbJaKFgAAMB9LlH2oaAEAAMzYEuWUAADAqJYo+1DRAgAAmDGJFgAAMB87tvixjqp6XFVdXFUf\nrqrnr9PmSVV1YVV9oKr+cF8vdYmKdwAAwLKpqgOSvCzJo5J8Msl5VfWm7r54qs09kjw/ybd39xeq\n6tB9Pa9ECwAAmI9xso9jknykuy9Lkqo6I8lxSS6eavPjSV7e3V9Iku6+dl9PqusgAACwnR2R5Iqp\n11cO26bdK8m9q+rcqvr7qnrsvp5URQsAAJiPGWcf53wiOeeTe2xWa2zrVa8PTHKPJN+Z5K5J/raq\n7rdS4dqMxU+0Dj1p7AgAAGCxXHvy2BEshGOPmDxWnPJPaza7MpPkacWRmYzVWt3mH7r7xiSXVtUl\nSe6ZZO0jboCugwAAwHwcuMWPtZ2X5B5VdVRV3SzJk5O8eVWbv0jyyCQZJsK4Z5KP7culSrQAAIBt\nq7t3JXl2krOSXJjkjO6+qKpOqarvGdqcmeTTVXVhkv+b5Oe6+7P7ct7qXt09cXFUVefQxY0PAABG\ncW2lu9cae7Swqqr7uVt8jpdmYe6LihYAAMCMLf5kGAAAwPawRNmHihYAAMCMLVFOCQAAjGqJsg8V\nLQAAgBlbopwSAAAY1Y6xA5gfFS0AAIAZU9ECAADmY4myj4W/1Bd/6sSxQwBgAexapv4mrGtHdo0d\nwuj8LJAkpy7EkrzszsInWgAAwDaxRNmHMVoAAAAztkQ5JQAAMKolyj5UtAAAAGZsiXJKAABgVEs0\nl4uKFgAAwIypaAEAAPOxRNnHlla0qupVVbWzqt4/te2kqrqyqt47PB63lTEAAADM21bnlK9O8ttJ\nXrNq+290929s8bkBAIBFoqI1G919bpLPrrHLWtYAAMC2NdZkGD9dVRdU1e9X1cEjxQAAAMzTji1+\nLJAxine/k+SXurur6peT/EaSZ67X+K9P/puvPj/q2KNyt2OP2voIAQBggVx2zqW57JzLxg6DvTD3\nRKu7PzX18pVJ3rK79n/9l+d+7cX0cwAAWFL77TgcY7RmqjL1WaiqO07t+4EkH5xDDAAAAHOzpTll\nVb0uybFJbl9Vlyc5Kcl/qKoHJbkxyaVJfmIrYwAAABbEElW0tvRSu/uH19j86q08JwAAwNiWKKcE\nAABGtWAzA26lsaZ3BwAA2LZUtAAAgPlYouxjiS4VAAAY1RJlH7oOAgAAzNgS5ZQAAMColij7UNEC\nAACYsSXKKQEAgFEt0fTuC59onXL+2BEAAADsnYVPtAAAgG1iibIPY7QAAABmbIlySgAAYFRLlH2o\naAEAAMzYEuWUAADAqJZo1kEVLQAAgBlT0QIAAOZjibIPFS0AAGBbq6rHVdXFVfXhqnr+btr9YFXd\nWFVH7+s5lyinBAAARjVC9lFVByR5WZJHJflkkvOq6k3dffGqdrdK8pwk757FeVW0AACA7eyYJB/p\n7su6+/okZyQ5bo12L0lyWpJ/m8VJJVoAAMB87Njix9qOSHLF1Osrh21fVVUPSnJkd79t3y7wa3Qd\nBAAA9kvnvDc55317bFZrbOuv7qyqJL+Z5Gl7eM9eqe7ec6uRVFX3Q8aOAgAAFkudn3T3PicD81RV\n3TMZ/bSbczz06+9LVT00ycnd/bjh9QlJurtPG17fJslHk3wpkwTrjkk+neT7uvu9m41FRQsAANjO\nzktyj6o6KslVSZ6c5PiVnd39hSR3WHldVe9K8rPdveda2W5ItAAAgPkYIfvo7l1V9ewkZ2UyR8Wr\nuvuiqjolyXnd/dbVb4mugwAAsHz2266D52/xOR6yOPdFRQsAAJiPJco+TO8OAAAwY0uUUwIAAKNa\nf62rbUdFCwAAYMZUtAAAgPlYouxDRQsAAGDGliinBAAARrVE2YeKFgAAwIwtfE554nkvHjsEABbA\njuwaO4TR7Vqm6bpYl58FkiR16tgRbM4S/TOmogUAADBjC1/RAgAAtoklyj5UtAAAAGZsiXJKAABg\nVEuUfahoAQAAzNgS5ZQAAMColij7UNECAACYsSXKKQEAgDG1dbQAAADYLBUtAABgLnYtUfahogUA\nADBjS5RTAgAAY1qmilZ199gxrKuqOocubnwAADCKayvdXWOHsTeqqv/1y1t7jpvfMgtzX5YopwQA\nAMZ0w46tHrl04xYff+OM0QIAAJgxFS0AAGAudh241enHV7b4+BunogUAADBjKloAAMBc7NqxY+wQ\n5kZFCwAAYMZUtAAAgLnYleWpaEm0AACAubhhiRItXQcBAABmTEULAACYi11LlH6oaAEAAMzY4qeU\n154ydgQAAMAMLNNkGCpaAAAAM7b4FS0AAGBbUNECAABg01S0AACAuVDRAgAAYNNUtAAAgLm4QUUL\nAACAzZJoAQAAc7ErB27pYz1V9biquriqPlxVz19j//Oq6sKquqCq3lFVd9nXa5VoAQAA21ZVHZDk\nZUkem+R+SY6vqvusavbeJA/u7gcl+dMkv76v5zVGCwAAmIuRZh08JslHuvuyJKmqM5Icl+TilQbd\n/ddT7d+d5Ef29aQqWgAAwHZ2RJIrpl5fOWxbzzOTvH1fT6qiBQAAzMWsK1rnn/PlnH/OdXtqVmts\n6zUbVv1okgcnecQ+hpbqXvMcC6GqOocubnwAADCKayvdvVYCsbCqqt/b993ScxxdF33dfamqhyY5\nubsfN7w+IUl392mr2j06yUuTfGd3f3pfY1HRAgAA5mKkdbTOS3KPqjoqyVVJnpzk+OkGVfWtSX4v\nyWNnkWQlxmgBAADbWHfvSvLsJGcluTDJGd19UVWdUlXfMzT7tSS3TPKGqnpfVf3Fvp5X10EAANjf\n7KddB/+hH7Sl5/j2umBh7ouKFgAAwIwZowUAAMzFSOtojUJFCwAAYMZUtAAAgLlQ0QIAAGDTVLQA\nAIC5UNECAABg01S0AACAubhBRQsAAIDNWviK1os/deLYIQCwAJapX/96dmTX2CGwAPwskCSn1tgR\nbM6uxU8/ZkZFCwAAYMaWJ6UEAABGtUwVWRUtAACAGVPRAgAA5kJFCwAAgE1T0QIAAObCOloAAABs\nmooWAAAwF9bRAgAAYNOWJ6UEAABGZdZBAAAANm3hK1q/9O9PHTsEAABYKPvrb8gqWgAAAGzawle0\nAACA7cE6WgAAAGyaihYAADAX1tECAABg05YnpQQAAEZl1kEAAAA2TUULAACYCxUtAAAANk1FCwAA\nmItlqmhJtAAAgLmwYDEAAACbtvAVrVPOHzsCAABgFixYDAAAwKYtT0oJAACMapkmw1DRAgAAmLE9\nVrSq6l5JfjfJ4d19/6p6QJLv6+5f3vLoAACAbUNF66ZemeQFSa5Pku5+f5Inb2VQAAAA+7ONjNG6\nRXe/p6qmt92wRfEAAADblHW0buraqrp7kk6SqvrBJFdt5OBV9aqq2llV75/adkhVnVVVl1TVmVV1\n8KYiBwAA2ICqelxVXVxVH66q56+x/2ZVdUZVfaSq/qGq7rqv59xIovXTSf53kvtU1SeS/NckP7nB\n4786yWNXbTshyTu7+95Jzs6kWyIAALDN7cqBW/pYS1UdkORlmeQl90tyfFXdZ1WzZyb5THffM8lv\nJfm1fb3WPSZa3f2x7n50ksOS3Ke7v6O7L93Iwbv73CSfXbX5uCSnD89PT/LEjYcLAACwV45J8pHu\nvqy7r09yRiY5ybTpHOWNSR61ryfdyKyDt03y1CR3S3Lgylit7v6ZTZ7zDt29czjG1VV12CaPAwAA\n7EdGmnXwiCRXTL2+MpPka8023b2rqj5XVbfr7s9s9qQbmQzjbUneneQDSW7c7IkAAABGUGts6z20\nqTXa7JWNJFo37+6f3ZeTrLKzqg7v7p1Vdcck1+yucd/pa8+PvXVy7G1mGAkAAOwHzvlCcs4XpzZs\naGq6xTPritZl51yay865bE/NrkwyPbnFkUk+uarNFUnukuSTVbUjyW26e/UQqL1S3btP1KrqeUm+\nlOStSf5tZftGy2hVdbckb+nubxlen5bJQLPThhk/DunuE9Z5b/dDNnIWAABYHnV+0t1rVWoWVlX1\nC/vFW3qOU+slX3dfhsTpkkzGXV2V5D1Jju/ui6ba/FSS+3f3T1XVk5M8sbv3ae3gjVS0vpLk15Oc\nmK+VzzrJN+3pjVX1uiTHJrl9VV2e5KQkv5rkDVX1jCSXJ/mhvQ8bAADY34wxRmsYc/XsJGdlMhng\nq7r7oqrqOHg+AAAUlElEQVQ6Jcl53f3WJK9K8tqq+kiSTyfZpyQr2Vii9d+S3KO7r93bg3f3D6+z\n69F7eywAAIDN6O6/SnLvVdtOmnr+b0meNMtzbiTR+miS62Z5UgAAYPncMM6sg6PYSKL15SQXVNW7\nctMxWpud3h0AAGBb20ii9RfDAwAAYNN2bSj92B72eKXdffqe2gAAAPA16yZaVfUn3f2kqvpAvn6x\nru7uB25taAAAwHYyxqyDY9ldReu5w58XJfn5qe2V5Ne2LCIAAID93LqJVnevrDd9j+6+yXLLVXWf\nLY0KAADYdlS0klTVTyb5qSTfVFXvn9p16yR/t9WBAQAA7K9213XwdUnenuRXkpwwtf2L3f2ZLY0K\nAADYdqyjlaS7P5/k80mOn184X+/E81485ulhdDuya+wQRrdM3QxYn58FPwtM+FkgSVKnjh0Be7A8\nE9kDAACjWqZ1tA4YOwAAAIDtZnlSSgAAYFTL1AVaRQsAAGDGVLQAAIC5UNECAABg01S0AACAuVDR\nAgAAYNNUtAAAgLm4QUULAACAzVLRAgAA5mLXEqUfC3+lpx72S2OHAAAAC+bUsQNgDxY+0QIAALYH\nsw4CAACwaSpaAADAXKhoAQAAsGkqWgAAwFxYRwsAAIBNU9ECAADmYpnW0VLRAgAAmLHlSSkBAIBR\nmXUQAACATVPRAgAA5mKZKloSLQAAYC6WaXr3xU+0rj1l7AgAAAD2yuInWgAAwLZgencAAAA2bXlS\nSgAAYFTLNBmGihYAAMCMqWgBAABzoaIFAADApqloAQAAc6GiBQAAsM1V1SFVdVZVXVJVZ1bVwWu0\neWBV/X1VfaCqLqiqJ23k2BItAABgLm7Iji19bMIJSd7Z3fdOcnaSF6zR5stJntLd35Lk8Ul+q6pu\ns6cDS7QAAIBldVyS04fnpyd54uoG3f3R7v6X4flVSa5JctieDmyMFgAAMBe7Fi/9uEN370yS7r66\nqnabQFXVMUkOWkm8dmfhrvTrHHrS2BEAAMBiufbksSNYCF8+5/xcd875u21TVe9Icvj0piSd5EV7\nc66qulOS1yR5yobad/feHH+uqqpz6OLGBwAAo7i20t01dhh7o6r6Xv3PW3qOD9cD9+q+VNVFSY7t\n7p1Vdcck7+ru+67R7tZJzkny37v7zzZybGO0AACAZfXmJE8fnj8tyZtWN6iqg5L8RZLTN5pkJftD\n10EAAGBbWMB1tE5L8idV9Ywklyf5oSSpqgcn+YnuflaSJyX5jiSHVNWPZdLt8Ond/f7dHVjXQQAA\n2N/sp10H794f3NJz/Evdf2Hui4oWAAAwF5tc62q/ZIwWAADAjKloAQAAc7GA62htGRUtAACAGVue\nlBIAABjVAs46uGVUtAAAAGZMRQsAAJgLFS0AAAA2beErWi/+1IljhwAAAAvlJQuxJO/e23WjihYA\nAACbtPAVLQAAYHu44QYVLQAAADZJRQsAAJiLXTcsT/qhogUAADBjy5NSAgAAo9pljBYAAACbpaIF\nAADMhYoWAAAAm6aiBQAAzMUN16toAQAAsEkqWgAAwFzcuGt50o/q7rFjWFdVdT9k7CgAAGCx1PlJ\nd9fYceyNqup84l+39iRH3Hxh7svypJQAAMC4zDoIAADAZqloAQAA86GiBQAAwGapaAEAAPNxw0LM\nUzEXKloAAAAzpqIFAADMxw1jBzA/KloAAAAzpqIFAADMh4oWAAAAm6WiBQAAzMcSVbQWPtE65fyx\nIwAAAGbi+rEDmB9dBwEAAGZs4StaAADANrFr7ADmR0ULAABgxlS0AACA+ViiyTBUtAAAAGZMRQsA\nAJgPFS0AAAA2S6IFAADMxw1b/NhLVXVIVZ1VVZdU1ZlVdfBu2t66qq6sqv+1kWNLtAAAgGV1QpJ3\ndve9k5yd5AW7afuSJOds9MASLQAAYD4WrKKV5Lgkpw/PT0/yxLUaVdWDk9whyVkbPbBECwAAWFZ3\n6O6dSdLdVyc5bHWDqqok/yPJzyepjR7YrIMAAMB8zHrWwQ+ck3zwnN02qap3JDl8elOSTvKiDZ7l\np5L8ZXd/YpJzbSzZqu7e4PHnr6q6HzJ2FAAAsFjq/KS7N1xdWQRV1XnTFucex9Ve3ZequijJsd29\ns6rumORd3X3fVW3+MMl3JLkxya2THJTkd7r7hbs7tooWAAAwH4u3jtabkzw9yWlJnpbkTasbdPeP\nrjyvqqclefCekqzEGC0AAGB5nZbkMVV1SZJHJ/nVZDL5RVW9Yl8OrOsgAADsZ/bbroNnbHHu8eS9\n6zq4lVS0AAAAZswYLQAAYD52jR3A/KhoAQAAzJiKFgAAMB+LN+vgllHRAgAAmDEVLQAAYD5UtAAA\nANgsFS0AAGA+lqiitfCJ1onnvXjsEBjRjmWaA5R17cqOsUNgAfj3gMS/B0z49yBJnTp2BOzBwida\nAADANrFEFS1jtAAAAGZMRQsAAJgPFS0AAAA2S0ULAACYDxUtAAAANktFCwAAmI/rxw5gfkZLtKrq\n0iSfT3Jjkuu7+5ixYgEAAJilMStaNyY5trs/O2IMAADAvCzRWtNjjtGqkc8PAACwJcasaHWSM6uq\nk7yiu185YiwAAMBWW6JZB8dMtB7W3VdX1WFJ3lFVF3X3uasb/c3Jf/3V50cde1SOOvZucwwRAADG\nd+k5l+Wycy4bOwz2QnX32DGkqk5K8sXu/o1V2zuHjh8fAAAslGsr3V1jh7E3qqrz4i3+3f4li3Nf\nRhkjVVW3qKpbDc9vmeS7knxwjFgAAABmbayug4cn+fNhfNaBSf6ou88aKRYAAGAejNHaWt398SQP\nGuPcAAAAW23MyTAAAIBlcv3YAcyPdawAAABmTEULAACYj11jBzA/KloAAAAzpqIFAADMxxLNOqii\nBQAAMGMqWgAAwHyoaAEAALBZi1/RuvaUsSMAAABmYYnW0Vr8RAsAANgeTO8OAADAZqloAQAA82Ey\nDAAAADZLRQsAAJgPFS0AAAA2S0ULAACYjyWa3l1FCwAAWEpVdUhVnVVVl1TVmVV18Drt7jLs/1BV\nfbCq7rqnY0u0AACA+di1xY+9d0KSd3b3vZOcneQF67R7TZLTuvubkxyT5Jo9HViiBQAALKvjkpw+\nPD89yRNXN6iq+ybZ0d1nJ0l3X9fd/7qnAxujBQAAzMfizTp4h+7emSTdfXVVHbZGm3sl+XxV/WmS\nuyV5Z5ITurt3d2CJFgAAsH+69pzk0+fstklVvSPJ4dObknSSF23wLAcm+Y4kD0pyRZI/SfL0JK/e\n7Xn3kIiNqqo6hy5ufAAAMIprK91dY4exN6qq8/gt/t3+7Xt3X6rqoiTHdvfOqrpjknd1931Xtfm2\nJL/S3Y8cXv9okm/r7ufs7tjGaAEAAMvqzZlUp5LkaUnetEab85IcUlW3H14/MsmH9nRgXQcBAID5\nWLx1tE5L8idV9Ywklyf5oSSpqgcn+YnuflZ331hVP5fk7KpKkn9K8so9HVjXQQAA2N/sr10HH73F\nv9u/c3Hui4oWAAAwH5tb62q/ZIwWAADAjKloAQAA87F462htGRUtAACAGVPRAgAA5kNFCwAAgM1S\n0QIAAOZj8dbR2jIqWgAAADO28BWtF3/qxLFDYES7smPsEEa3Y5kWnAAANuQlC7Ek7yYs0a81KloA\nAAAztvAVLQAAYJsw6yAAAACbpaIFAADMh4oWAAAAm6WiBQAAzId1tAAAANgsFS0AAGA+rKMFAADA\nZqloAQAA82HWQQAAADZLRQsAAJiPJapoVXePHcO6qqr7IWNHAQAAi6XOT7q7xo5jb1RV505bnHtc\nVQtzX1S0AACA+bCOFgAAAJulogUAAMyHdbQAAADYLBUtAABgPpZo1kEVLQAAgBlT0QIAAOZDRQsA\nAIDNUtECAADmwzpaAAAAbJaKFgAAMB/W0QIAAGCzFr6idcr5Y0cAAADMRI8dwPyoaAEAAMyYRAsA\nAGDGJFoAAAAzJtECAACYMYkWAADAjEm0AAAAZmzhp3cHAAC2i+vHDuAmquqQJK9PclSSS5M8qbs/\nv0a705J8d5JK8o7u/q97OraKFgAAsKxOSPLO7r53krOTvGB1g6r69iQP6+77J7l/kmOq6jv3dGAV\nLQAAYE5uGDuA1Y5L8ojh+elJzskk+ZrWSW5eVTfPpFB1YJKdezqwihYAALCs7tDdO5Oku69Octjq\nBt397kwSsKuSfCLJmd19yZ4OrKIFAADMyfzHaFXVO5IcPr0pkyrVizb4/rsnuU+SOw/vfWdVndnd\n5+7ufQufaJ30kLEjAACAxXLy+WNHsCj+Nslu851092PW21dVO6vq8O7eWVV3THLNGs2+P8m7u/v/\nDe95e5KH7unEug4CAABzcsOMH9+e5OenHnvtzUmePjx/WpI3rdHm8iSPqKodVXVQJmO6LtrTgSVa\nAADAsjotyWOq6pIkj07yq0lSVQ+uqlcMbd6Y5GNJPpDkfUne191/uacDV3dvTcgzUFXdug4CAMBN\n1PlJd9fYceyNqurk6i0+yx0X5r6oaAEAAMzYwk+GAQAAbBfzn3VwLCpaAAAAM6aiBQAAzMkNYwcw\nNypaAAAAM6aiBQAAzIkxWgAAAGySihYAADAnxmgBAACwSQtf0frF8144dggAALBY6tSxI9gkY7QA\nAADYpIWvaAEAANuFMVoAAABskooWAAAwJ8ZoAQAAsEkqWgAAwJwYowUAAMAmqWgBAABzYowWAAAA\nm6SiBQAAzIkxWgAAAGxSdffYMayrqjqHLm58AAAwimsr3V1jh7E3qqqTt23xWZ6wMPdFRQsAAGDG\njNECAADmxBgtAAAANklFCwAAmBPraAEAALBJKloAAMCcqGgBAACwSSpaAADAnJh1EAAAgE1S0QIA\nAObEGC0AAAA2SUULAACYk+UZo7X4ida1p4wdAQAAwF5Z/EQLAADYJpZnjJZECwAAmJPl6TpoMgwA\nAIAZU9ECAADmZHm6DqpoAQAAzJiKFgAAMCfGaG25qnpcVV1cVR+uquePFQcAALCcquoHq+qDVbWr\nqo7eTbu9zl1GSbSq6oAkL0vy2CT3S3J8Vd1njFjYH3x87ABYCD4HJD4H+Aww4XOw/7p+ix977QNJ\nvj/JX6/XYLO5y1gVrWOSfKS7L+vu65OckeS4kWJh4V06dgAshEvHDoCFcOnYATC6S8cOgIVw6dgB\nsE109yXd/ZEktZtmm8pdxhqjdUSSK6ZeX5nJBQAAANvWfjlGa1O5y1iJ1loZY889CgAAYFurqnck\nOXx6Uya5x4nd/ZaNHGKNbXvMXcZKtK5Mctep10cm+eTaTU/e+mjYD6zbbZal4nNA4nOAzwATPgf7\nocuSk4/a4nPsXL2hux+zj8fci9zla8ZKtM5Lco+qOirJVUmenOT41Y26e3d9JQEAgP1Ed99t7Bj2\nYL3cY0O5y2qjTIbR3buSPDvJWUkuTHJGd180RiwAAMByqqonVtUVSR6a5K1V9fZh+52q6q3J5nOX\n6jY0CgAAYJZGW7B4dyxmTFUdWVVnV9WHquoDVfUzY8fEeKrqgKp6b1W9eexYGEdVHVxVb6iqi6rq\nwqr6trFjYv6q6nnDwqLvr6o/qqqbjR0TW6+qXlVVO6vq/VPbDqmqs6rqkqo6s6oOHjNGWMvCJVoW\nM2ZwQ5Kf7e5vTvLtSX7a52CpPTfJh8YOglG9NMnbuvu+SR6YRHfzJVNVd07ynCRHd/cDMhln/uRx\no2JOXp3J74XTTkjyzu6+d5Kzk7xg7lHBHixcohWLGZOku6/u7guG51/K5JeqI8aNijFU1ZFJnpDk\n98eOhXFU1a2T/H/d/eok6e4buvsLI4fFOHYkuWVVHZjkFtnArF/s/7r73CSfXbX5uCSnD89PT/LE\nuQYFG7CIidZaC4L5BXuJVdXdkjwoyT+OGwkj+c0kPx9r7S2zb0pybVW9euhC+oqq+saxg2K+uvuT\nSf5nksuTfCLJ57r7neNGxYju0N07k8mXs0kOGzke+DqLmGhZzJivqqpbJXljkucOlS2WSFV9d5Kd\nQ3Wzsv60q2xvByY5OsnLu/voJNdl0m2IJVJVt82kinFUkjsnuVVV/fC4UQGsbxETrU0tCMb2M3QN\neWOS13b3m8aOh1E8PMn3VdXHkvxxkv9QVa8ZOSbm78okV3T3+cPrN2aSeLFcHp3kY939mWGq5T9L\n8rCRY2I8O6vq8CSpqjsmuWbkeODrLGKi9dUFwYbZhJ6cxExjy+kPknyou186diCMo7tf2N137e5v\nyuTfgrO7+6ljx8V8Dd2Drqiqew2bHhWToyyjy5M8tKpuXlWVyefApCjLY3Wvhjcnefrw/GlJfCHL\nwjlw7ABW6+5dVbWyINgBSV5lMePlU1UPT/IjST5QVe/LpPvoC7v7r8aNDBjJzyT5o6o6KMnHkvzY\nyPEwZ939nqp6Y5L3Jbl++PMV40bFPFTV65Icm+T2VXV5kpOS/GqSN1TVMzJJwn9ovAhhbRYsBgAA\nmLFF7DoIAACwX5NoAQAAzJhECwAAYMYkWgAAADMm0QIAAJgxiRYAAMCMSbQAWFdVvaKq7jM8f8HY\n8QDA/sI6WgBsSFV9sbtvPXYcALA/UNECIElSVbeoqrdW1fuq6v1V9aSqeldVHV1Vv5LkG6vqvVX1\n2qH9j1TVPw7bfreqauRLAICFIdECYMXjknyiu7+1ux+Q5K9WdnT3C5Jc191Hd/dThu6E/ynJw7r7\n6CQ3JvmRUaIGgAV04NgBALAwPpDk14fq1V9297mrilTTLx6V5Ogk5w2VrJsn2Tm3SAFgwUm0AEiS\ndPdHqurBSZ6Q5CVVdXaS9QbyVpLTu/vEuQUIAPsRXQcBSJJU1Z2S/L/ufl2S/5FJxWraV6pqx/D8\n/yb5wao6bHjvIVV11/lFCwCL7f9v5w5tGwpgAAo+b5ElOmJDskVot8gIJVVU0HF+UEixFQXcURPT\nJ0sWWgA8fVTfM/NTnavLv/m1+p2Zr+M4/qrP6jYz9+pWnV66LQC8Me/dAQAAlrloAQAALBNaAAAA\ny4QWAADAMqEFAACwTGgBAAAsE1oAAADLhBYAAMAyoQUAALDsAWhrD+A6sKgjAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x106d07128>"
+      ]
+     },
+     "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": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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UeW5TRwsAAGDOdLQAAIBBrPt1tBaIjhYAAMCcjaimBAAAuprzrIOLTEcLAABgznS0AACA\nYYyo+tDRAgAAmLMR1ZQAAEBXI6o+dLQAAADmbEQ15QZ0SO8AC+Co3gH6uyEH947Q3W3Z3DtCd9vG\nNE3TKnwOfB8k8buQ2D9Ikut7B2BmI6o+dLQAAADmbEQ1JQAA0NWIDtDQ0QIAAJgzHS0AAGAYI6o+\ndLQAAADmbEQ1JQAA0NWIqg8dLQAAgDkbUU0JAAB0ZdZBAAAAZqWjBQAADGNE1YeOFgAAwJyNqKbc\ngO7sHWAB+IRmy9bDekfo7vb99+8dobt987XeEbq7PT4Hvg/idyGxf8DGNqL/h3W0AAAA5mxENSUA\nANCVWQcBAACYlY4WAAAwjBFVHzpaAAAAczaimhIAAOhqRNXHiN4qAADQ1YiqD4cOAgAAzNmIakoA\nAKAr07sDAAAwKx0tAABgGCOqPnS0AAAA5mxENeUGdEfvAAvgQb0D9Lf1tvv2jtDd1v337x2hu4Nz\nQ+8I3W2Nz4Hvg/hdSOwfsLGNqPrQ0QIAAJizEdWUAABAV2YdBAAAYFY6WgAAwDBGVH3oaAEAAMzZ\niGpKAACgqxFVHzpaAAAAc6bQAgAAhrFpnW+rqKpnVdWlVXVZVb18lTHPrapPV9XFVfWne/pWR9S8\nAwAAxqaq7pXkdUmenuSaJBdW1btba5cuGXNckpcn+c7W2q1VtceXR1doAQAAw+hTfZyQ5HOttSuS\npKrOSnJykkuXjPnJJH/UWrs1SVpr1+/pRh06CAAA7M2OTHLVksdXT5ct9c1Jjq+qC6rq76vqmXu6\nUR0tAABgGHOuPs7/YnL+NbscVissa8se75PkuCTfleToJH9bVY/a0eGaxQYotO7dO0A/R/UOsACO\n7R2ARXBbNveO0N3+2do7Qnc+ByTxu5DYP0iSq0a8f8g9nHjk5LbDaR9bcdjVmRRPOxyVyblay8f8\nQ2vtriSXV9Vnkzw8ycprXAOHDgIAAMPYZ51vK7swyXFVdUxV3SfJ85K8Z9mYdyV5WpJMJ8J4eJLP\n78lbVWgBAAB7rdba9iQvS3JOkk8nOau1dklVnVZVPzAdc3aSG6rq00n+Osm/ba3dtCfb3QCHDgIA\nAHuFnVzraj211j6Q5Phly05d9viXk/zyvLapowUAADBnOloAAMAwRlR96GgBAADM2YhqSgAAoKsR\nVR86WgAAAHM2opoSAADoqtOsgz3oaAEAAMyZjhYAADCMEVUfG+Ct3tk7QD8b4L/Ouvtq7wD9bT7o\ntt4RutuUbb0jdHdotvSO0J3Pge+DJLnlq/frHaE/+wcZ9f4hG4b/VQEAgGGMqPpwjhYAAMCcjaim\nBAAAuhpR9aGjBQAAMGcjqikBAICuXEcLAACAWeloAQAAwxhR9bGuHa2qemNVbamqTy5ZdmpVXV1V\nH5/enrWeGQAAAIa23jXlGUn+MMmbli3/3dba767ztgEAgEWiozUfrbULkty0wlO1ntsFAADoqddk\nGC+tqk9U1Z9U1QGdMgAAAEPatM63BdKjeffHSX6ttdaq6j8m+d0kP7H68D9Ycv9J0xsAAIzJh6c3\nNorBC63W2v9b8vANSd6781f8zLLH2+acaIGN6K2u6qu9A/R32H2u6x2hu825rXeE7r7t1k/1jtDd\n5gf4HPg+SG756uG9I/Rn/yDj/Et4wvS2w+t6BdkzztGaq8qSc7Kqauk35L9MYu8BAADYq6xrTVlV\nb01yYpKDq+rKJKcm+Z6qelySu5JcnuSn1jMDAACwIEbU0VrXt9pa+5EVFp+xntsEAADobUQ1JQAA\n0NWCzQy4nnpN7w4AALDX0tECAACGMaLqY0RvFQAA6GpE1YdDBwEAAOZsRDUlAADQ1YiqDx0tAACA\nORtRTQkAAHQ1oundFVqL7PDeARbAfr0D9HdErukdobsDc3PvCN3t84XeCfo78LE+B74Pksv2e0zv\nCP3ZP4ANQaEFAAAMY0TVh3O0AAAA5mxENSUAANDViKoPHS0AAIA5G1FNCQAAdDWiWQd1tAAAAOZM\nRwsAABjGiKoPHS0AAGCvVlXPqqpLq+qyqnr5TsY9p6ruqqrH7+k2R1RTAgAAXXWoPqrqXklel+Tp\nSa5JcmFVvbu1dumycfdP8rNJPjSP7epoAQAAe7MTknyutXZFa+3OJGclOXmFca9NcnqSO+axUYUW\nAAAwjE3rfFvZkUmuWvL46umyr6uqxyU5qrX2/j17g3dz6CAAALAhnf/x5PyLdjmsVljWvv5kVSX5\nvSQv3MVrdssGKLQ2QMT1sq13gAXwoN4B+jsi1/SO0N1D7vGPUCN1S+8A/fkcJF/O5t4R+vO7YP8g\nyaj3Dze6Of+nO/GEyW2H085YcdjVSY5e8vio5B47WJuTPCrJ+dOi6/Ak766qH2qtfXzWbD6lAADA\n3uzCJMdV1TFJrk3yvCSn7HiytXZrkkN3PK6qv0nyS621XffKdkKhBQAADKND9dFa215VL0tyTiZz\nVLyxtXZJVZ2W5MLW2vuWvyTjOHQQAABgdq21DyQ5ftmyU1cZ+7R5bFOhBQAADGNE1Yfp3QEAAOZs\nRDUlAADQ1erXutrr6GgBAADMmY4WAAAwjBFVHzpaAAAAczaimhIAAOhqRNWHjhYAAMCcjaim3ICu\n7x2gv/see1PvCN0dnBt6R+ju+FzWO0J/X+0doD+fg+S6HNY7Qnd+F5Lbrz+odwSYnVkHAQAAmJWO\nFgAAMIwRVR86WgAAAHM2opoSAADoakTVh44WAADAnI2opgQAALoaUfWhowUAADBnI6opAQCAnprr\naAEAADArHS0AAGAQ20dUfehoAQAAzNmIakoAAKCnMXW0RvRW2Yge9oB/7B2huwNzc+8I3R0Xn4Pc\nr3eA/nwOkovzrb0jdOd3IflUntg7ArAGCi0AAGAQ2zat95lLd63z+tfOOVoAAABzpqMFAAAMYvs+\n611+fG2d1792OloAAABzpqMFAAAMYvumTb0jDEZHCwAAYM50tAAAgEFsz3g6WgotAABgENtGVGg5\ndBAAAGDOdLQAAIBBbB9R+aGjBQAAMGfjKSk3ov16B+jvkflM7wjdbc5tvSN097Dt/9Q7Qn9H9A7Q\nn89BsnmT7wO/C8mn9nti7wgwszFNhqGjBQAAMGc6WgAAwCB0tAAAAJiZjhYAADAIHS0AAABmpqMF\nAAAMYpuOFgAAALNSaAEAAIPYnn3W9baaqnpWVV1aVZdV1ctXeP4Xq+rTVfWJqvpgVT1kT9+rQgsA\nANhrVdW9krwuyTOTPCrJKVX1iGXDPp7kCa21xyX58yS/tafbdY4WAAAwiE6zDp6Q5HOttSuSpKrO\nSnJykkt3DGit/e8l4z+U5Pl7ulEdLQAAYG92ZJKrljy+erpsNT+R5K/2dKM6WgAAwCDm3dH66Plf\nyUfP37qrYbXCsrbiwKofTfKEJN+9h9E2QqF1794B+rl/7wD9HZ/Lekfo7tBs6R2huwfc+LXeEbrb\ndnDvBP35HCSHHuL7wO9C7B8kGfX+Iffw7SfeL99+4v2+/vj1p12/0rCrkxy95PFRSa5ZPqiqTkry\nyiTf1Vq7c0+zbYBCCwAA2Bt0uo7WhUmOq6pjklyb5HlJTlk6oKq+Lcl/S/LM1toN89ioc7QAAIC9\nVmtte5KXJTknyaeTnNVau6SqTquqH5gO+80k90vyjqq6qKretafb1dECAAAGsbNrXa2n1toHkhy/\nbNmpS+4/Y97b1NECAACYMx0tAABgEJ2uo9WFjhYAAMCc6WgBAACD0NECAABgZjpaAADAIHS0AAAA\nmJmOFgAAMIhtOloAAADMSkdrkR2/6yF7u8OypXeE7o7OVb0jsADu2Ne/i+1zx129I3Tn+yD5cjb3\njtCf/YPkvb0DMKvtIyo//HIDAADM2XhKSgAAoCuzDgIAADAzHS0AAGAQOloAAADMTEcLAAAYhOto\nAQAAMDMdLQAAYBCuowUAAMDMxlNSAgAAXZl1EAAAgJnpaC2y7+kdoL/75vbeEbp7SK7qHaG7bfv2\nTsAi8DnwfZAkX8g39Y7Qn/2D5Ld7B2BWOloAAADMTEcLAAAYhOtoAQAAMDMdLQAAYBCuowUAAMDM\nxlNSAgAAXZl1EAAAgJnpaAEAAIPQ0QIAAGBmOloAAMAgxtTRUmgBAACDcMFiAAAAZrYBOlp39g7Q\nzaHfd2XvCCyAh2y9uneE7rbe7z69I3S37x1f6x2hO58D3wdJkv17B+jP/kFy3Yj3Dzc6FywGAABg\nZuMpKQEAgK7GNBmGjhYAAMCc7bKjVVXfnOS/JjmstfboqnpMkh9qrf3HdU8HAADsNXS07ukNSV6Z\n6awUrbVPJnneeoYCAADYyNZyjtb+rbWPVNXSZdvWKQ8AALCXch2te7q+qh6WpCVJVT0nybVrWXlV\nvbGqtlTVJ5csO6iqzqmqz1bV2VV1wEzJAQAA1qCqnlVVl1bVZVX18hWev09VnVVVn6uqf6iqo/d0\nm2sptF6a5L8neURVfTHJLyT5N2tc/xlJnrls2SuSnNtaOz7JeZkclggAAOzltmefdb2tpKruleR1\nmdQlj0pySlU9Ytmwn0hyY2vt4Ul+P8lv7ul73WWh1Vr7fGvtpCSHJHlEa+2prbXL17Ly1toFSW5a\ntvjkJGdO75+Z5NlrjwsAALBbTkjyudbaFa21O5OclUlNstTSGuWdSZ6+pxtdy6yDByb5sSTHJtln\nx7larbWfm3Gbh7bWtkzX8aWqOmTG9QAAABtIp1kHj0xy1ZLHV2dSfK04prW2vapurqoHttZunHWj\na5kM4/1JPpTk4iR3zbohAACADmqFZW0XY2qFMbtlLYXWfq21X9qTjSyzpaoOa61tqarDk1y38+G/\nv+T+CfnG4nPvdWL+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 0x106cebfd0>"
+      ]
+     },
+     "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": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "## Exact solution of 1D transverse field Ising model:\n",
+    "https://www.math.ucdavis.edu/~bxn/pfeuty1970.pdf"
+   ]
+  },
+  {
+   "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": "3.4.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}