qutip.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'Qobj' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-ec328bd17048>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mqutip\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/gitrepos/floquet_theory/qutip.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     27\u001b[0m \u001b[0mpsi0\u001b[0m   \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     28\u001b[0m \u001b[0mpsi0\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 29\u001b[0;31m \u001b[0mpsi0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpsi0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     30\u001b[0m \u001b[0mH0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0mH1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1.0\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m4.0\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mq\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcosp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'Qobj' is not defined"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from qutip import *\n",
    "from scipy import *\n",
    "\n",
    "delta  = 0.2 * 2*pi; eps0  = 1.0 * 2*pi\n",
    "A      = 0.5 * 2*pi; \n",
    "tlist  = np.linspace(0.0, 10 * T, 101)\n",
    "psi0   = basis(2,0)\n",
    "omega  = 1.0 * 2*np.pi; A_vec = np.linspace(0, 10, 1001) * omega;\n",
    "T      = (2*pi)/omega\n",
    "psi0   = basis(2,0)\n",
    "\n",
    "q_energies = np.zeros((len(A_vec), 2))\n",
    "\n",
    "H0 = - delta/2.0 * sigmax() - eps0/2.0 * sigmaz()\n",
    "H1 = A/2.0 * sigmaz()\n",
    "args = {'w': omega}\n",
    "w = omega\n",
    "H = [H0, [H1, lambda t,args: np.sin(args['w'] * t)]]\n",
    "\n",
    "for idx, A in enumerate(A_vec):\n",
    "    H1 = A/2.0 * sigmax()\n",
    "    #H = [H0, [H1, lambda t, w: np.sin(w*t)]]\n",
    "    H = [H0, [H1, lambda t: np.sin(args['w'] * t)]]\n",
    "    f_modes, f_energies = floquet_modes(H, T, args, True)\n",
    "    q_energies[idx,:] = f_energies\n",
    "\n",
    "plt.plot(A_vec/omega,q_energies)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### use Qutip on mean field dynamics\n",
    "\n",
    "check T. Mori's paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'Qobj' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-3-823c6ad882b3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mqutip\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/gitrepos/floquet_theory/qutip.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     27\u001b[0m \u001b[0mpsi0\u001b[0m   \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     28\u001b[0m \u001b[0mpsi0\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 29\u001b[0;31m \u001b[0mpsi0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpsi0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     30\u001b[0m \u001b[0mH0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0mH1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1.0\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m4.0\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mq\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcosp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'Qobj' is not defined"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from qutip import *\n",
    "from scipy import *\n",
    "import math\n",
    "\n",
    "N =4; h = 25.0; h0 = 0.1;    \n",
    "q = np.linspace(-0.5, 0.5, N)\n",
    "cosp = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "cosp_init = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "omega = 1.0 * 2 * np.pi/4; A_vec = np.linspace(0, 10, 100) * omega;\n",
    "T = (2*np.pi)/omega\n",
    "tlist  = np.linspace(0.0, 10 * T, 101)\n",
    "args = {'w': omega}\n",
    "\n",
    "cospinit = 0.0\n",
    "for k in np.arange(N):\n",
    "    for m in np.arange(N):\n",
    "        for l in np.arange(N+1):\n",
    "            for j in np.arange(l+1):\n",
    "                cospinit = cospinit + np.array([pow((-1),(l+j))/math.factorial(2 * l)* math.comb(l,j)])\n",
    "        cosp[k,m] = cospinit\n",
    "        cospinit = 0.0\n",
    "                                                \n",
    "psi0 = basis(N,0)\n",
    "H0 = Qobj(-2*q*q)\n",
    "H1 = Qobj(- np.sqrt(1.0 - 4.0 * q * q) * cosp)\n",
    "\n",
    "\n",
    "for idw, wv in enumerate(w_vec):\n",
    "    H = [H0,[H1,lambda t,h0: h0+h*np.cos(args[w] * t)]]\n",
    "    f_modes, f_energies = floquet_modes(H, T, args, True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[1.]\n",
      " [0.]\n",
      " [0.]\n",
      " [0.]]\n"
     ]
    }
   ],
   "source": [
    "print(psi0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n",
      "[1.]\n",
      "[0.5]\n",
      "[1.]\n",
      "[1.04166667]\n",
      "[0.95833333]\n",
      "[1.]\n",
      "[0.99861111]\n",
      "[1.00277778]\n",
      "[0.99861111]\n",
      "[1.]\n",
      "[1.0000248]\n",
      "[0.9999256]\n",
      "[1.0000744]\n",
      "[0.9999752]\n",
      "[1.]\n"
     ]
    },
    {
     "ename": "Exception",
     "evalue": "Invalid td-list element.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mException\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-eae743742f5a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     32\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0midw\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mw\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw_vec\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     33\u001b[0m     \u001b[0mH\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mH0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mH1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mh0\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mh0\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcos\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 34\u001b[0;31m     \u001b[0mf_modes\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf_energies\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfloquet_modes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mH\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/.local/lib/python3.8/site-packages/qutip/floquet.py\u001b[0m in \u001b[0;36mfloquet_modes\u001b[0;34m(H, T, args, sort, U)\u001b[0m\n\u001b[1;32m    100\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mU\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    101\u001b[0m         \u001b[0;31m# get the unitary propagator\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 102\u001b[0;31m         \u001b[0mU\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpropagator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mH\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    103\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    104\u001b[0m     \u001b[0;31m# find the eigenstates for the propagator\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.8/site-packages/qutip/propagator.py\u001b[0m in \u001b[0;36mpropagator\u001b[0;34m(H, t, c_op_list, args, options, unitary_mode, parallel, progress_bar, _safe_mode, **kwargs)\u001b[0m\n\u001b[1;32m    127\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    128\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0m_safe_mode\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 129\u001b[0;31m         \u001b[0m_solver_safety_check\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mH\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc_ops\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mc_op_list\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0me_ops\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    130\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    131\u001b[0m     \u001b[0mtd_type\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_td_format_check\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mH\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc_op_list\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msolver\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'me'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.8/site-packages/qutip/solver.py\u001b[0m in \u001b[0;36m_solver_safety_check\u001b[0;34m(H, state, c_ops, e_ops, args)\u001b[0m\n\u001b[1;32m    912\u001b[0m             \u001b[0mHtype\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mH\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtype\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    913\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 914\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mException\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Invalid td-list element.'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    915\u001b[0m         \u001b[0;31m# Check all operators in list\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    916\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mii\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mH\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mException\u001b[0m: Invalid td-list element."
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from qutip import *\n",
    "from scipy import *\n",
    "import math\n",
    "\n",
    "N =4; h = 25.0; h0 = 0.1;    \n",
    "q = np.linspace(-0.5, 0.5, N)\n",
    "cosp = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "cosp_init = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "omega = 1.0 * 2 * np.pi; w_vec = np.linspace(0, 10, 100) * omega;\n",
    "T = (2*np.pi)/omega\n",
    "tlist  = np.linspace(0.0, 10 * T, 101)\n",
    "args = {'w': omega}\n",
    "\n",
    "cospinit = 0.0\n",
    "for k in np.arange(N):\n",
    "    for m in np.arange(N):\n",
    "        for l in np.arange(N+1):\n",
    "            for j in np.arange(l+1):\n",
    "                cospinit = cospinit + np.array([pow((-1),(l+j))/math.factorial(2 * l)* math.comb(l,j)])\n",
    "        cosp[k,m] = cospinit\n",
    "        cospinit = 0.0\n",
    "                                                \n",
    "psi0 = basis(N,0)\n",
    "H0 = Qobj(-2*q*q)\n",
    "H1 = Qobj(- np.sqrt(1.0 - 4.0 * q * q) * cosp)\n",
    "\n",
    "for idw, wv in enumerate(A_vec):\n",
    "    H = [H0,[H1,lambda t,h0: h0+h*np.cos(args[w] * t)]]\n",
    "    f_modes, f_energies = floquet_modes(H, T, args, True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'basis' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-2-9f5f5163f541>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mqutip\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/gitrepos/floquet_theory/qutip.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     23\u001b[0m         \u001b[0mcospinit\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 25\u001b[0;31m \u001b[0mpsi0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbasis\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     26\u001b[0m \u001b[0mH0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     27\u001b[0m \u001b[0mH1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1.0\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m4.0\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mq\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcosp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'basis' is not defined"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from qutip import *\n",
    "from scipy import *\n",
    "import math\n",
    "\n",
    "N =4    \n",
    "q = np.linspace(-0.5, 0.5, N)\n",
    "cosp = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "cosp_init = np.zeros((N,N)) + (1j) * np.zeros((N,N))\n",
    "omega = 1.0 * 2 * np.pi \n",
    "h = np.linspace(0, 10, 100)\n",
    "h0 = 0.1\n",
    "T = (2*np.pi)/omega\n",
    "tlist  = np.linspace(0.0, 10 * T, 101)\n",
    "args = {'w': omega}\n",
    "\n",
    "cospinit = 0.0\n",
    "for k in np.arange(N):\n",
    "    for m in np.arange(N):\n",
    "        for l in np.arange(N+1):\n",
    "            for j in np.arange(l+1):\n",
    "                cospinit = cospinit + np.array([pow((-1),(l+j))/math.factorial(2 * l)* math.comb(l,j)])\n",
    "        cosp[k,m] = cospinit\n",
    "        cospinit = 0.0\n",
    "                                                \n",
    "psi0 = basis(N,0)\n",
    "H0 = Qobj(-2*q*q)\n",
    "H1 = Qobj(- np.sqrt(1.0 - 4.0 * q * q) * cosp)\n",
    "\n",
    "for idw, wv in enumerate(h):\n",
    "    H = [H0,[H1,lambda t,h0: h0+h*np.cos(args[w] * t)]]\n",
    "    f_modes, f_energies = floquet_modes(H, T, args, True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'psi0' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-2-5daea079cfb8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpsi0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'psi0' is not defined"
     ]
    }
   ],
   "source": [
    "print(psi0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}