Eq_two_min_with_phot.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Upload required packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import time\n",
    "import pickle\n",
    "import matplotlib.pyplot as plt\n",
    "from pylab import figure, plot, show, savefig\n",
    "import sys\n",
    "import os.path\n",
    "from finite_T_min_init import *\n",
    "from model_parameters import *\n",
    "plt.rcParams.update({'font.size': 15})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set up physical parameters and run precalcs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "phys_params = give_parameters()\n",
    "phys_params['target particle real space density n_0'] = 0.4\n",
    "phys_params['photon cut-off freq'] = 1.55\n",
    "\n",
    "extra_param = setting_up_grids__and_k_vect_len(phys_params)\n",
    "phys_params.update(extra_param)\n",
    "\n",
    "cs = cosine(phys_params[\"k-grid\"])\n",
    "\n",
    "attract_potential = Coulomb_modified(phys_params) \n",
    "phys_params[\"cosine\"] = cs\n",
    "phys_params[\"Coulomb interaction in real space\"] = attract_potential\n",
    "\n",
    "k = phys_params[\"k-grid\"]\n",
    "zero_ind = phys_params['zero momentum index']\n",
    "num_of_vars = phys_params['number of variables']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define normal and full energy functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "En_normal = lambda var_s: vMFFE_normal(var_s, phys_params, q)\n",
    "E_coh = lambda var_s: vMFFE(var_s, phys_params, q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define Q-vector array covering both small and large values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "q_array_1 = np.linspace(-2e-4, 1e-4, 41)[:-1]\n",
    "q_array_2 = np.logspace(-4, -1, 20)[:-1]\n",
    "q_array_3 = np.linspace(0.1, 2.0, 21)\n",
    "\n",
    "q_array = np.append(q_array_1, q_array_2)\n",
    "q_array = np.append(q_array, q_array_3)\n",
    "q_array = np.append(q_array, q_array[::-1][1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set up zero arrays for collecting results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "Eq = np.zeros([len(q_array)])\n",
    "solution_q = np.zeros([len(q_array), num_of_vars])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run minimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step 1 out of 159\n",
      "E = -16.283434700488357\n",
      "q is -0.0002\n",
      "--- 630.2339551448822 seconds ---\n",
      " \n",
      "\n",
      "step 2 out of 159\n",
      "E = -16.283437362968925\n",
      "q is -0.00019250000000000002\n",
      "--- 49.37351894378662 seconds ---\n",
      " \n",
      "\n",
      "step 3 out of 159\n",
      "E = -16.283439908167193\n",
      "q is -0.000185\n",
      "--- 60.246195793151855 seconds ---\n",
      " \n",
      "\n",
      "step 4 out of 159\n",
      "E = -16.283442336068674\n",
      "q is -0.0001775\n",
      "--- 47.918431997299194 seconds ---\n",
      " \n",
      "\n",
      "step 5 out of 159\n",
      "E = -16.283444646659376\n",
      "q is -0.00017\n",
      "--- 57.12693405151367 seconds ---\n",
      " \n",
      "\n",
      "step 6 out of 159\n",
      "E = -16.283446883507487\n",
      "q is -0.0001625\n",
      "--- 66.38126492500305 seconds ---\n",
      " \n",
      "\n",
      "step 7 out of 159\n",
      "E = -16.283448986721346\n",
      "q is -0.000155\n",
      "--- 54.58631229400635 seconds ---\n",
      " \n",
      "\n",
      "step 8 out of 159\n",
      "E = -16.28345094555886\n",
      "q is -0.0001475\n",
      "--- 58.796494007110596 seconds ---\n",
      " \n",
      "\n",
      "step 9 out of 159\n",
      "E = -16.283452787007644\n",
      "q is -0.00014\n",
      "--- 52.23582696914673 seconds ---\n",
      " \n",
      "\n",
      "step 10 out of 159\n",
      "E = -16.28345451106789\n",
      "q is -0.0001325\n",
      "--- 61.64062714576721 seconds ---\n",
      " \n",
      "\n",
      "step 11 out of 159\n",
      "E = -16.283456117729035\n",
      "q is -0.000125\n",
      "--- 72.02875900268555 seconds ---\n",
      " \n",
      "\n",
      "step 12 out of 159\n",
      "E = -16.283457606981155\n",
      "q is -0.0001175\n",
      "--- 60.807268142700195 seconds ---\n",
      " \n",
      "\n",
      "step 13 out of 159\n",
      "E = -16.283458978814867\n",
      "q is -0.00010999999999999999\n",
      "--- 66.0268337726593 seconds ---\n",
      " \n",
      "\n",
      "step 14 out of 159\n",
      "E = -16.283460233221398\n",
      "q is -0.0001025\n",
      "--- 57.60451602935791 seconds ---\n",
      " \n",
      "\n",
      "step 15 out of 159\n",
      "E = -16.28346137019271\n",
      "q is -9.499999999999999e-05\n",
      "--- 53.74676585197449 seconds ---\n",
      " \n",
      "\n",
      "step 16 out of 159\n",
      "E = -16.283462390380354\n",
      "q is -8.75e-05\n",
      "--- 54.61527490615845 seconds ---\n",
      " \n",
      "\n",
      "step 17 out of 159\n",
      "E = -16.283463292694414\n",
      "q is -7.999999999999999e-05\n",
      "--- 79.27698278427124 seconds ---\n",
      " \n",
      "\n",
      "step 18 out of 159\n",
      "E = -16.283464077494994\n",
      "q is -7.25e-05\n",
      "--- 55.58334708213806 seconds ---\n",
      " \n",
      "\n",
      "step 19 out of 159\n",
      "E = -16.283464744781043\n",
      "q is -6.499999999999998e-05\n",
      "--- 69.99189305305481 seconds ---\n",
      " \n",
      "\n",
      "step 20 out of 159\n",
      "E = -16.28346529457546\n",
      "q is -5.749999999999999e-05\n",
      "--- 54.67080092430115 seconds ---\n",
      " \n",
      "\n",
      "step 21 out of 159\n",
      "E = -16.283465726882312\n",
      "q is -4.9999999999999996e-05\n",
      "--- 62.27545785903931 seconds ---\n",
      " \n",
      "\n",
      "step 22 out of 159\n",
      "E = -16.28346604169756\n",
      "q is -4.2499999999999976e-05\n",
      "--- 60.76774191856384 seconds ---\n",
      " \n",
      "\n",
      "step 23 out of 159\n",
      "E = -16.283466239066176\n",
      "q is -3.499999999999998e-05\n",
      "--- 49.25177812576294 seconds ---\n",
      " \n",
      "\n",
      "step 24 out of 159\n",
      "E = -16.283466318956947\n",
      "q is -2.749999999999999e-05\n",
      "--- 78.61107993125916 seconds ---\n",
      " \n",
      "\n",
      "step 25 out of 159\n",
      "E = -16.28346628131149\n",
      "q is -1.999999999999997e-05\n",
      "--- 59.76289486885071 seconds ---\n",
      " \n",
      "\n",
      "step 26 out of 159\n",
      "E = -16.283466126155673\n",
      "q is -1.2499999999999979e-05\n",
      "--- 56.968595027923584 seconds ---\n",
      " \n",
      "\n",
      "step 27 out of 159\n",
      "E = -16.283465853503866\n",
      "q is -4.999999999999986e-06\n",
      "--- 46.75907611846924 seconds ---\n",
      " \n",
      "\n",
      "step 28 out of 159\n",
      "E = -16.28346546334499\n",
      "q is 2.5000000000000066e-06\n",
      "--- 39.91423487663269 seconds ---\n",
      " \n",
      "\n",
      "step 29 out of 159\n",
      "E = -16.283464955681577\n",
      "q is 1.0000000000000026e-05\n",
      "--- 53.341968297958374 seconds ---\n",
      " \n",
      "\n",
      "step 30 out of 159\n",
      "E = -16.283464330510007\n",
      "q is 1.750000000000002e-05\n",
      "--- 54.381726026535034 seconds ---\n",
      " \n",
      "\n",
      "step 31 out of 159\n",
      "E = -16.283463587842697\n",
      "q is 2.500000000000001e-05\n",
      "--- 64.85316205024719 seconds ---\n",
      " \n",
      "\n",
      "step 32 out of 159\n",
      "E = -16.283462727681357\n",
      "q is 3.250000000000003e-05\n",
      "--- 52.325623989105225 seconds ---\n",
      " \n",
      "\n",
      "step 33 out of 159\n",
      "E = -16.283461750016038\n",
      "q is 4.0000000000000024e-05\n",
      "--- 62.19223690032959 seconds ---\n",
      " \n",
      "\n",
      "step 34 out of 159\n",
      "E = -16.283460654851936\n",
      "q is 4.750000000000004e-05\n",
      "--- 62.33582901954651 seconds ---\n",
      " \n",
      "\n",
      "step 35 out of 159\n",
      "E = -16.283459442192832\n",
      "q is 5.500000000000001e-05\n",
      "--- 53.8025860786438 seconds ---\n",
      " \n",
      "\n",
      "step 36 out of 159\n",
      "E = -16.28345811204318\n",
      "q is 6.250000000000003e-05\n",
      "--- 53.8267548084259 seconds ---\n",
      " \n",
      "\n",
      "step 37 out of 159\n",
      "E = -16.283456664408064\n",
      "q is 7.000000000000005e-05\n",
      "--- 55.88796091079712 seconds ---\n",
      " \n",
      "\n",
      "step 38 out of 159\n",
      "E = -16.28345509929322\n",
      "q is 7.750000000000001e-05\n",
      "--- 56.87525677680969 seconds ---\n",
      " \n",
      "\n",
      "step 39 out of 159\n",
      "E = -16.28345341693747\n",
      "q is 8.500000000000003e-05\n",
      "--- 51.987509965896606 seconds ---\n",
      " \n",
      "\n",
      "step 40 out of 159\n",
      "E = -16.283451617012073\n",
      "q is 9.250000000000005e-05\n",
      "--- 52.1489999294281 seconds ---\n",
      " \n",
      "\n",
      "step 41 out of 159\n",
      "E = -16.283449699620423\n",
      "q is 0.0001\n",
      "--- 62.141310930252075 seconds ---\n",
      " \n",
      "\n",
      "step 42 out of 159\n",
      "E = -16.28343614151268\n",
      "q is 0.0001438449888287663\n",
      "--- 76.0548632144928 seconds ---\n",
      " \n",
      "\n",
      "step 43 out of 159\n",
      "E = -16.2834096065313\n",
      "q is 0.00020691380811147902\n",
      "--- 56.451560258865356 seconds ---\n",
      " \n",
      "\n",
      "step 44 out of 159\n",
      "E = -16.283356913861468\n",
      "q is 0.00029763514416313193\n",
      "--- 46.179121017456055 seconds ---\n",
      " \n",
      "\n",
      "step 45 out of 159\n",
      "E = -16.283251166930146\n",
      "q is 0.00042813323987193956\n",
      "--- 51.15802788734436 seconds ---\n",
      " \n",
      "\n",
      "step 46 out of 159\n",
      "E = -16.283037541784953\n",
      "q is 0.0006158482110660267\n",
      "--- 68.12478375434875 seconds ---\n",
      " \n",
      "\n",
      "step 47 out of 159\n",
      "E = -16.28260474736712\n",
      "q is 0.0008858667904100823\n",
      "--- 62.60926389694214 seconds ---\n",
      " \n",
      "\n",
      "step 48 out of 159\n",
      "E = -16.28173037217393\n",
      "q is 0.0012742749857031334\n",
      "--- 80.92765688896179 seconds ---\n",
      " \n",
      "\n",
      "step 49 out of 159\n",
      "E = -16.27998351179989\n",
      "q is 0.0018329807108324356\n",
      "--- 57.37762999534607 seconds ---\n",
      " \n",
      "\n",
      "step 50 out of 159\n",
      "E = -16.276585939917062\n",
      "q is 0.0026366508987303583\n",
      "--- 58.9269859790802 seconds ---\n",
      " \n",
      "\n",
      "step 51 out of 159\n",
      "E = -16.270335860144176\n",
      "q is 0.00379269019073225\n",
      "--- 51.42906713485718 seconds ---\n",
      " \n",
      "\n",
      "step 52 out of 159\n",
      "E = -16.260003305782377\n",
      "q is 0.005455594781168515\n",
      "--- 53.17742896080017 seconds ---\n",
      " \n",
      "\n",
      "step 53 out of 159\n",
      "E = -16.245838697966295\n",
      "q is 0.007847599703514606\n",
      "--- 53.64147210121155 seconds ---\n",
      " \n",
      "\n",
      "step 54 out of 159\n",
      "E = -16.23135565947244\n",
      "q is 0.011288378916846883\n",
      "--- 38.440061807632446 seconds ---\n",
      " \n",
      "\n",
      "step 55 out of 159\n",
      "E = -16.22251834814394\n",
      "q is 0.01623776739188721\n",
      "--- 34.028738021850586 seconds ---\n",
      " \n",
      "\n",
      "step 56 out of 159\n",
      "E = -16.218669347016863\n",
      "q is 0.023357214690901212\n",
      "--- 23.56591296195984 seconds ---\n",
      " \n",
      "\n",
      "step 57 out of 159\n",
      "E = -16.217663211527704\n",
      "q is 0.03359818286283781\n",
      "--- 28.04079580307007 seconds ---\n",
      " \n",
      "\n",
      "step 58 out of 159\n",
      "E = -16.21758065677467\n",
      "q is 0.04832930238571752\n",
      "--- 124.09345531463623 seconds ---\n",
      " \n",
      "\n",
      "step 59 out of 159\n",
      "E = -16.217587431338668\n",
      "q is 0.06951927961775606\n",
      "--- 114.16103911399841 seconds ---\n",
      " \n",
      "\n",
      "step 60 out of 159\n",
      "E = -16.2175988779019\n",
      "q is 0.1\n",
      "--- 124.89747786521912 seconds ---\n",
      " \n",
      "\n",
      "step 61 out of 159\n",
      "E = -16.21762304896291\n",
      "q is 0.195\n",
      "--- 136.17540287971497 seconds ---\n",
      " \n",
      "\n",
      "step 62 out of 159\n",
      "E = -16.218418273362246\n",
      "q is 0.29000000000000004\n",
      "--- 103.00894594192505 seconds ---\n",
      " \n",
      "\n",
      "step 63 out of 159\n",
      "E = -16.220531270533897\n",
      "q is 0.385\n",
      "--- 71.99192810058594 seconds ---\n",
      " \n",
      "\n",
      "step 64 out of 159\n",
      "E = -16.22262351752679\n",
      "q is 0.48\n",
      "--- 25.429335117340088 seconds ---\n",
      " \n",
      "\n",
      "step 65 out of 159\n",
      "E = -16.224533713476525\n",
      "q is 0.575\n",
      "--- 34.23596000671387 seconds ---\n",
      " \n",
      "\n",
      "step 66 out of 159\n",
      "E = -16.226163754724116\n",
      "q is 0.67\n",
      "--- 33.162617921829224 seconds ---\n",
      " \n",
      "\n",
      "step 67 out of 159\n",
      "E = -16.227435587180366\n",
      "q is 0.765\n",
      "--- 42.86441111564636 seconds ---\n",
      " \n",
      "\n",
      "step 68 out of 159\n",
      "E = -16.228312272331372\n",
      "q is 0.86\n",
      "--- 33.011276960372925 seconds ---\n",
      " \n",
      "\n",
      "step 69 out of 159\n",
      "E = -16.228780036799456\n",
      "q is 0.955\n",
      "--- 42.737709045410156 seconds ---\n",
      " \n",
      "\n",
      "step 70 out of 159\n",
      "E = -16.22883131197654\n",
      "q is 1.05\n",
      "--- 32.6363308429718 seconds ---\n",
      " \n",
      "\n",
      "step 71 out of 159\n",
      "E = -16.228454664429634\n",
      "q is 1.145\n",
      "--- 42.9938440322876 seconds ---\n",
      " \n",
      "\n",
      "step 72 out of 159\n",
      "E = -16.22763280186456\n",
      "q is 1.2400000000000002\n",
      "--- 48.77235293388367 seconds ---\n",
      " \n",
      "\n",
      "step 73 out of 159\n",
      "E = -16.226351143434414\n",
      "q is 1.3350000000000002\n",
      "--- 73.21238875389099 seconds ---\n",
      " \n",
      "\n",
      "step 74 out of 159\n",
      "E = -16.22460447985293\n",
      "q is 1.4300000000000002\n",
      "--- 39.26074028015137 seconds ---\n",
      " \n",
      "\n",
      "step 75 out of 159\n",
      "E = -16.222395343545674\n",
      "q is 1.5250000000000001\n",
      "--- 84.93578124046326 seconds ---\n",
      " \n",
      "\n",
      "step 76 out of 159\n",
      "E = -16.219731620880978\n",
      "q is 1.62\n",
      "--- 34.44865393638611 seconds ---\n",
      " \n",
      "\n",
      "step 77 out of 159\n",
      "E = -16.2166244015581\n",
      "q is 1.715\n",
      "--- 40.107807874679565 seconds ---\n",
      " \n",
      "\n",
      "step 78 out of 159\n",
      "E = -16.21308179620319\n",
      "q is 1.81\n",
      "--- 39.04462718963623 seconds ---\n",
      " \n",
      "\n",
      "step 79 out of 159\n",
      "E = -16.209112443608824\n",
      "q is 1.905\n",
      "--- 46.79739689826965 seconds ---\n",
      " \n",
      "\n",
      "step 80 out of 159\n",
      "E = -16.20471229014988\n",
      "q is 2.0\n",
      "--- 62.360332012176514 seconds ---\n",
      " \n",
      "\n",
      "step 81 out of 159\n",
      "E = -16.20911261818989\n",
      "q is 1.905\n",
      "--- 73.31843185424805 seconds ---\n",
      " \n",
      "\n",
      "step 82 out of 159\n",
      "E = -16.213085602644426\n",
      "q is 1.81\n",
      "--- 46.1887891292572 seconds ---\n",
      " \n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step 83 out of 159\n",
      "E = -16.216626711362906\n",
      "q is 1.715\n",
      "--- 85.78460812568665 seconds ---\n",
      " \n",
      "\n",
      "step 84 out of 159\n",
      "E = -16.21973293585413\n",
      "q is 1.62\n",
      "--- 43.44888210296631 seconds ---\n",
      " \n",
      "\n",
      "step 85 out of 159\n",
      "E = -16.222396053751233\n",
      "q is 1.5250000000000001\n",
      "--- 72.12507700920105 seconds ---\n",
      " \n",
      "\n",
      "step 86 out of 159\n",
      "E = -16.22460493249844\n",
      "q is 1.4300000000000002\n",
      "--- 44.04298996925354 seconds ---\n",
      " \n",
      "\n",
      "step 87 out of 159\n",
      "E = -16.226351190865323\n",
      "q is 1.3350000000000002\n",
      "--- 47.965872049331665 seconds ---\n",
      " \n",
      "\n",
      "step 88 out of 159\n",
      "E = -16.22763235624377\n",
      "q is 1.2400000000000002\n",
      "--- 45.185949087142944 seconds ---\n",
      " \n",
      "\n",
      "step 89 out of 159\n",
      "E = -16.22845335337959\n",
      "q is 1.145\n",
      "--- 45.74708819389343 seconds ---\n",
      " \n",
      "\n",
      "step 90 out of 159\n",
      "E = -16.22882812072604\n",
      "q is 1.05\n",
      "--- 42.353408098220825 seconds ---\n",
      " \n",
      "\n",
      "step 91 out of 159\n",
      "E = -16.228776040047507\n",
      "q is 0.955\n",
      "--- 35.1703827381134 seconds ---\n",
      " \n",
      "\n",
      "step 92 out of 159\n",
      "E = -16.228307555734663\n",
      "q is 0.86\n",
      "--- 43.970781087875366 seconds ---\n",
      " \n",
      "\n",
      "step 93 out of 159\n",
      "E = -16.22743419410742\n",
      "q is 0.765\n",
      "--- 70.83629107475281 seconds ---\n",
      " \n",
      "\n",
      "step 94 out of 159\n",
      "E = -16.22616135641904\n",
      "q is 0.67\n",
      "--- 71.97574615478516 seconds ---\n",
      " \n",
      "\n",
      "step 95 out of 159\n",
      "E = -16.224530603719767\n",
      "q is 0.575\n",
      "--- 54.392494916915894 seconds ---\n",
      " \n",
      "\n",
      "step 96 out of 159\n",
      "E = -16.222617719049158\n",
      "q is 0.48\n",
      "--- 94.7766752243042 seconds ---\n",
      " \n",
      "\n",
      "step 97 out of 159\n",
      "E = -16.220514195448043\n",
      "q is 0.385\n",
      "--- 103.75711989402771 seconds ---\n",
      " \n",
      "\n",
      "step 98 out of 159\n",
      "E = -16.218398060626562\n",
      "q is 0.29000000000000004\n",
      "--- 151.18538308143616 seconds ---\n",
      " \n",
      "\n",
      "step 99 out of 159\n",
      "E = -16.2176201736855\n",
      "q is 0.195\n",
      "--- 93.51043796539307 seconds ---\n",
      " \n",
      "\n",
      "step 100 out of 159\n",
      "E = -16.217595540968222\n",
      "q is 0.1\n",
      "--- 55.21084213256836 seconds ---\n",
      " \n",
      "\n",
      "step 101 out of 159\n",
      "E = -16.21758367937088\n",
      "q is 0.06951927961775606\n",
      "--- 50.311278104782104 seconds ---\n",
      " \n",
      "\n",
      "step 102 out of 159\n",
      "E = -16.217578846295165\n",
      "q is 0.04832930238571752\n",
      "--- 57.05835270881653 seconds ---\n",
      " \n",
      "\n",
      "step 103 out of 159\n",
      "E = -16.217662970259113\n",
      "q is 0.03359818286283781\n",
      "--- 71.00448989868164 seconds ---\n",
      " \n",
      "\n",
      "step 104 out of 159\n",
      "E = -16.218668791597757\n",
      "q is 0.023357214690901212\n",
      "--- 50.71996283531189 seconds ---\n",
      " \n",
      "\n",
      "step 105 out of 159\n",
      "E = -16.22251694338378\n",
      "q is 0.01623776739188721\n",
      "--- 77.70153403282166 seconds ---\n",
      " \n",
      "\n",
      "step 106 out of 159\n",
      "E = -16.23213457248265\n",
      "q is 0.011288378916846883\n",
      "--- 188.9314250946045 seconds ---\n",
      " \n",
      "\n",
      "step 107 out of 159\n",
      "E = -16.246518876706403\n",
      "q is 0.007847599703514606\n",
      "--- 186.4385461807251 seconds ---\n",
      " \n",
      "\n",
      "step 108 out of 159\n",
      "E = -16.260491029606552\n",
      "q is 0.005455594781168515\n",
      "--- 221.06442308425903 seconds ---\n",
      " \n",
      "\n",
      "step 109 out of 159\n",
      "E = -16.270683180506335\n",
      "q is 0.00379269019073225\n",
      "--- 183.74654531478882 seconds ---\n",
      " \n",
      "\n",
      "step 110 out of 159\n",
      "E = -16.27681847724441\n",
      "q is 0.0026366508987303583\n",
      "--- 166.9191460609436 seconds ---\n",
      " \n",
      "\n",
      "step 111 out of 159\n",
      "E = -16.28013048178677\n",
      "q is 0.0018329807108324356\n",
      "--- 195.96087217330933 seconds ---\n",
      " \n",
      "\n",
      "step 112 out of 159\n",
      "E = -16.281816263966796\n",
      "q is 0.0012742749857031334\n",
      "--- 153.72024202346802 seconds ---\n",
      " \n",
      "\n",
      "step 113 out of 159\n",
      "E = -16.28264784667106\n",
      "q is 0.0008858667904100823\n",
      "--- 215.5408627986908 seconds ---\n",
      " \n",
      "\n",
      "step 114 out of 159\n",
      "E = -16.283050834375047\n",
      "q is 0.0006158482110660267\n",
      "--- 226.0942897796631 seconds ---\n",
      " \n",
      "\n",
      "step 115 out of 159\n",
      "E = -16.28324378317743\n",
      "q is 0.00042813323987193956\n",
      "--- 219.5221929550171 seconds ---\n",
      " \n",
      "\n",
      "step 116 out of 159\n",
      "E = -16.283335164609248\n",
      "q is 0.00029763514416313193\n",
      "--- 139.52074718475342 seconds ---\n",
      " \n",
      "\n",
      "step 117 out of 159\n",
      "E = -16.283377885796217\n",
      "q is 0.00020691380811147902\n",
      "--- 200.41295099258423 seconds ---\n",
      " \n",
      "\n",
      "step 118 out of 159\n",
      "E = -16.283397496131652\n",
      "q is 0.0001438449888287663\n",
      "--- 179.72295022010803 seconds ---\n",
      " \n",
      "\n",
      "step 119 out of 159\n",
      "E = -16.283406245311618\n",
      "q is 0.0001\n",
      "--- 217.3171579837799 seconds ---\n",
      " \n",
      "\n",
      "step 120 out of 159\n",
      "E = -16.283407340448672\n",
      "q is 9.250000000000005e-05\n",
      "--- 213.60463309288025 seconds ---\n",
      " \n",
      "\n",
      "step 121 out of 159\n",
      "E = -16.283408318259553\n",
      "q is 8.500000000000003e-05\n",
      "--- 205.74962711334229 seconds ---\n",
      " \n",
      "\n",
      "step 122 out of 159\n",
      "E = -16.283409178954145\n",
      "q is 7.750000000000001e-05\n",
      "--- 169.11173176765442 seconds ---\n",
      " \n",
      "\n",
      "step 123 out of 159\n",
      "E = -16.283409922137192\n",
      "q is 7.000000000000005e-05\n",
      "--- 220.1863350868225 seconds ---\n",
      " \n",
      "\n",
      "step 124 out of 159\n",
      "E = -16.283410548015155\n",
      "q is 6.250000000000003e-05\n",
      "--- 219.55600833892822 seconds ---\n",
      " \n",
      "\n",
      "step 125 out of 159\n",
      "E = -16.283411056515796\n",
      "q is 5.500000000000001e-05\n",
      "--- 199.31756806373596 seconds ---\n",
      " \n",
      "\n",
      "step 126 out of 159\n",
      "E = -16.283411447640667\n",
      "q is 4.750000000000004e-05\n",
      "--- 208.1975121498108 seconds ---\n",
      " \n",
      "\n",
      "step 127 out of 159\n",
      "E = -16.283411721401055\n",
      "q is 4.0000000000000024e-05\n",
      "--- 221.80421900749207 seconds ---\n",
      " \n",
      "\n",
      "step 128 out of 159\n",
      "E = -16.28341187782355\n",
      "q is 3.250000000000003e-05\n",
      "--- 191.48172688484192 seconds ---\n",
      " \n",
      "\n",
      "step 129 out of 159\n",
      "E = -16.28341191687638\n",
      "q is 2.500000000000001e-05\n",
      "--- 154.33823776245117 seconds ---\n",
      " \n",
      "\n",
      "step 130 out of 159\n",
      "E = -16.283411838552862\n",
      "q is 1.750000000000002e-05\n",
      "--- 215.71070098876953 seconds ---\n",
      " \n",
      "\n",
      "step 131 out of 159\n",
      "E = -16.28341164285644\n",
      "q is 1.0000000000000026e-05\n",
      "--- 235.81198573112488 seconds ---\n",
      " \n",
      "\n",
      "step 132 out of 159\n",
      "E = -16.28341132980918\n",
      "q is 2.5000000000000066e-06\n",
      "--- 206.03708481788635 seconds ---\n",
      " \n",
      "\n",
      "step 133 out of 159\n",
      "E = -16.28341089935804\n",
      "q is -4.999999999999986e-06\n",
      "--- 253.9668779373169 seconds ---\n",
      " \n",
      "\n",
      "step 134 out of 159\n",
      "E = -16.283410351527213\n",
      "q is -1.2499999999999979e-05\n",
      "--- 192.62938380241394 seconds ---\n",
      " \n",
      "\n",
      "step 135 out of 159\n",
      "E = -16.28340968631869\n",
      "q is -1.999999999999997e-05\n",
      "--- 196.8394479751587 seconds ---\n",
      " \n",
      "\n",
      "step 136 out of 159\n",
      "E = -16.283408903740046\n",
      "q is -2.749999999999999e-05\n",
      "--- 217.68830275535583 seconds ---\n",
      " \n",
      "\n",
      "step 137 out of 159\n",
      "E = -16.28340800378661\n",
      "q is -3.499999999999998e-05\n",
      "--- 158.7947940826416 seconds ---\n",
      " \n",
      "\n",
      "step 138 out of 159\n",
      "E = -16.283406986460744\n",
      "q is -4.2499999999999976e-05\n",
      "--- 180.04647612571716 seconds ---\n",
      " \n",
      "\n",
      "step 139 out of 159\n",
      "E = -16.283405851765867\n",
      "q is -4.9999999999999996e-05\n",
      "--- 234.50837397575378 seconds ---\n",
      " \n",
      "\n",
      "step 140 out of 159\n",
      "E = -16.28340459974847\n",
      "q is -5.749999999999999e-05\n",
      "--- 227.8014349937439 seconds ---\n",
      " \n",
      "\n",
      "step 141 out of 159\n",
      "E = -16.283403230376816\n",
      "q is -6.499999999999998e-05\n",
      "--- 158.6455430984497 seconds ---\n",
      " \n",
      "\n",
      "step 142 out of 159\n",
      "E = -16.283401743652163\n",
      "q is -7.25e-05\n",
      "--- 221.38854694366455 seconds ---\n",
      " \n",
      "\n",
      "step 143 out of 159\n",
      "E = -16.283400139598005\n",
      "q is -7.999999999999999e-05\n",
      "--- 214.77233219146729 seconds ---\n",
      " \n",
      "\n",
      "step 144 out of 159\n",
      "E = -16.283398418215832\n",
      "q is -8.75e-05\n",
      "--- 224.4402129650116 seconds ---\n",
      " \n",
      "\n",
      "step 145 out of 159\n",
      "E = -16.28339657951863\n",
      "q is -9.499999999999999e-05\n",
      "--- 190.71673393249512 seconds ---\n",
      " \n",
      "\n",
      "step 146 out of 159\n",
      "E = -16.283394623485158\n",
      "q is -0.0001025\n",
      "--- 202.35119009017944 seconds ---\n",
      " \n",
      "\n",
      "step 147 out of 159\n",
      "E = -16.283392550134096\n",
      "q is -0.00010999999999999999\n",
      "--- 212.7710828781128 seconds ---\n",
      " \n",
      "\n",
      "step 148 out of 159\n",
      "E = -16.283390359474506\n",
      "q is -0.0001175\n",
      "--- 148.9461510181427 seconds ---\n",
      " \n",
      "\n",
      "step 149 out of 159\n",
      "E = -16.283388051516237\n",
      "q is -0.000125\n",
      "--- 147.17354917526245 seconds ---\n",
      " \n",
      "\n",
      "step 150 out of 159\n",
      "E = -16.283385626269745\n",
      "q is -0.0001325\n",
      "--- 190.45237827301025 seconds ---\n",
      " \n",
      "\n",
      "step 151 out of 159\n",
      "E = -16.28338308374625\n",
      "q is -0.00014\n",
      "--- 212.52480673789978 seconds ---\n",
      " \n",
      "\n",
      "step 152 out of 159\n",
      "E = -16.28338042395776\n",
      "q is -0.0001475\n",
      "--- 231.73687291145325 seconds ---\n",
      " \n",
      "\n",
      "step 153 out of 159\n",
      "E = -16.283377646917007\n",
      "q is -0.000155\n",
      "--- 169.5811059474945 seconds ---\n",
      " \n",
      "\n",
      "step 154 out of 159\n",
      "E = -16.283374752637595\n",
      "q is -0.0001625\n",
      "--- 204.6911962032318 seconds ---\n",
      " \n",
      "\n",
      "step 155 out of 159\n",
      "E = -16.283371743475808\n",
      "q is -0.00017\n",
      "--- 199.91320872306824 seconds ---\n",
      " \n",
      "\n",
      "step 156 out of 159\n",
      "E = -16.283368615243745\n",
      "q is -0.0001775\n",
      "--- 202.5202181339264 seconds ---\n",
      " \n",
      "\n",
      "step 157 out of 159\n",
      "E = -16.283365369825532\n",
      "q is -0.000185\n",
      "--- 204.92637395858765 seconds ---\n",
      " \n",
      "\n",
      "step 158 out of 159\n",
      "E = -16.283362007237788\n",
      "q is -0.00019250000000000002\n",
      "--- 239.70634603500366 seconds ---\n",
      " \n",
      "\n",
      "step 159 out of 159\n",
      "E = -16.28335852749697\n",
      "q is -0.0002\n",
      "--- 213.5299949645996 seconds ---\n",
      " \n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(q_array)):\n",
    "    \n",
    "    start_time = time.time()  \n",
    "    \n",
    "    q = q_array[i]\n",
    "    other = { 'Is coherent?' : True, 'number of minimization repetitons' : 7, 'q-vector' : q }\n",
    "\n",
    "    # coherent solution with memory \n",
    "    if i == 0:\n",
    "        x_norm = initial_conditions_normal(phys_params, q)\n",
    "        init_with_mem = initial_conditions_coherent(phys_params, q, x_norm)\n",
    "    else:\n",
    "        init_with_mem = result_with_mem[1]\n",
    "    result_with_mem = get_new_minimum(init_with_mem, phys_params, other)\n",
    "    Eq[i] = result_with_mem[0]\n",
    "    solution_q[i,:] = result_with_mem[1]\n",
    "\n",
    "    \n",
    "        \n",
    "    print('step ' + str(i+1) + ' out of ' + str(len(q_array)))\n",
    "    print('E = ' + str(Eq[i]))\n",
    "    print('q is ' + str(q_array[i]))\n",
    "    print(\"--- %s seconds ---\" % (time.time() - start_time) + '\\n \\n')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# directory = 'results/two_min/'\n",
    "# if not os.path.exists(directory):\n",
    "#     os.makedirs(directory)\n",
    "\n",
    "# with open(directory + 'Energy', 'wb') as handle:\n",
    "#     pickle.dump(Eq, handle, protocol=pickle.HIGHEST_PROTOCOL)\n",
    "    \n",
    "# with open(directory + 'solution', 'wb') as handle:\n",
    "#     pickle.dump(solution_q, handle, protocol=pickle.HIGHEST_PROTOCOL)\n",
    "\n",
    "# with open(directory + 'Q_array', 'wb') as handle:\n",
    "#     pickle.dump(q_array, handle, protocol=pickle.HIGHEST_PROTOCOL)\n",
    "    \n",
    "# with open(directory + 'phys_params', 'wb') as handle:\n",
    "#     pickle.dump(phys_params, handle, protocol=pickle.HIGHEST_PROTOCOL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Upload results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# with open('results/two_min/Energy', 'rb') as handle:\n",
    "#     Energy = pickle.load(handle)\n",
    "\n",
    "# with open('results_new/two_min/solution', 'rb') as handle:\n",
    "#     Solution = pickle.load(handle)\n",
    "\n",
    "# with open('results_new/two_min/Q_array', 'rb') as handle:\n",
    "#     Q_array = pickle.load(handle)\n",
    "\n",
    "# with open('results_new/two_min/phys_params', 'rb') as handle:\n",
    "#     phys_params = pickle.load(handle)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extract expectations from data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # get expectations\n",
    "# el_dens = np.zeros([len(Q_array), len(k), len(k)])\n",
    "# hole_dens = np.zeros([len(Q_array), len(k), len(k)])\n",
    "# coherence = np.zeros([len(Q_array), len(k), len(k)])\n",
    "# gap = np.zeros([len(Q_array), len(k), len(k)])\n",
    "# ne_minus_nh = np.zeros([len(Q_array)])\n",
    "# ne_plus_nh = np.zeros([len(Q_array)])\n",
    "# phot_tot = np.zeros([len(Q_array)])\n",
    "# anisotr = np.zeros([len(Q_array)])\n",
    "\n",
    "# for i in range(len(Q_array)):\n",
    "\n",
    "#     q = Q_array[i]\n",
    "\n",
    "#     aux = el_hole_dens_and_coherence(Solution[i,:], phys_params, q)\n",
    "    \n",
    "#     el_dens[i,:,:] = aux['electron density']\n",
    "#     hole_dens[i,:,:] = aux['hole density']\n",
    "#     coherence[i,:,:] = aux['coherence']\n",
    "#     gap[i,:,:] = aux['gap function']\n",
    "#     ne_minus_nh[i] = aux['eh real space density difference']\n",
    "#     ne_plus_nh[i] = aux['Ne plus Nh']\n",
    "#     phot_tot[i] = aux['phi squared']\n",
    "#     anisotr[i] = aux['anisotropy parameter']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Free energy vs Q\n",
    "### Red star highlights a local minimum corresponding to an FF state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ft = 22\n",
    "fff = 68\n",
    "\n",
    "fig, ax1 = plt.subplots(figsize=(4, 4))\n",
    "\n",
    "fff = 68\n",
    "ggg = 23\n",
    "\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "\n",
    "ax1.semilogx(q_array/2, (Energy + 16.2)*2, marker = '.', label = '$F(Q)$', color = 'k')\n",
    "ax1.plot(q_array[fff]/2, (Energy[fff]+16.2)*2, marker = '*', color = 'r', markersize = 8)\n",
    "ax1.plot(q_array[ggg]/2, (Energy[ggg]+16.2)*2, marker = '*', color = 'r', markersize = 8)\n",
    "\n",
    "#import matplotlib.ticker as mtick\n",
    "#ax1.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.2e'))\n",
    "\n",
    "from pylab import MaxNLocator\n",
    "ax1.yaxis.set_major_locator(MaxNLocator(integer=True))\n",
    "#ax1.set_yticks([-18, -15, -12, -9, -6, -3, 0])\n",
    "\n",
    "\n",
    "#ax2.plot(n_0_array[:last_bright], phot_fraction_B[:last_bright], marker = '.', color = 'dodgerblue')\n",
    "ax2.loglog(q_array, phot_tot, marker = '.', label = '$\\phi^2$', color = 'dodgerblue')\n",
    "ax2.set_ylim(1e-10, 2e+1)\n",
    "\n",
    "\n",
    "import matplotlib\n",
    "ft = 22\n",
    "matplotlib.rcParams['font.size']=ft\n",
    "# plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n",
    "# plt.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
    "\n",
    "\n",
    "\n",
    "plt.xlim(1e-6, 5.0)\n",
    "plt.xticks([1e-6, 1e-4, 1e-2, 1e-0]  )\n",
    "\n",
    "\n",
    "ax1.set_xlabel('$a_B Q$', fontsize = ft)\n",
    "#ax1.set_ylabel('$10^2$ $(32.4 + F/E_B )$', fontsize = ft)\n",
    "ax2.set_ylabel('$\\\\langle \\phi \\\\rangle^2 $', color = 'dodgerblue', fontsize = ft)\n",
    "plt.yticks((1e-9, 1e-6, 1e-3, 1e-0, ), color = 'dodgerblue', fontsize = ft)\n",
    "\n",
    "        \n",
    "\n",
    "#plt.savefig('anis_phot_vs_n0__alpha_100.svg', bbox_inches='tight', transparent=True)\n",
    "\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Global minimum corresponding to a crescent state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(4, 4))\n",
    "\n",
    "\n",
    "plt.plot(q_array/2, (Energy + 16.28346)*2*1e+5, marker = '.', label = '$F(Q)$', color = 'k')\n",
    "plt.plot(q_array[ggg]/2, (Energy[ggg]+ 16.28346)*2*1e+5, marker = '*', color = 'r', markersize = 8)\n",
    "\n",
    "plt.xlim(-5e-5, 2e-5)\n",
    "plt.ylim(-1.5, 0)\n",
    "\n",
    "plt.xticks(fontsize=ft, rotation=0)\n",
    "plt.yticks(fontsize=ft, rotation=0)\n",
    "\n",
    "matplotlib.rcParams['font.size']=ft\n",
    "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n",
    "plt.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
    "\n",
    "\n",
    "#x = [0, 0.6]\n",
    "#y = [-10, 0]\n",
    "#plt.xticks(np.arange(0.0, 0.51e-4, 1e-5)  )\n",
    "#plt.yticks( [-1.5, -1.0, -0.5, 0.0]   )\n",
    "#plt.grid()\n",
    "\n",
    "#plt.text(0.015, -1.5045, '$n_0 = $' + str(str(np.round(phys_params['target particle real space density n_0'],4))), \n",
    "#                     color = 'k', fontsize = ft)\n",
    "\n",
    "\n",
    "\n",
    "#plt.xlabel('$10^5$ $a_B Q$', fontsize = ft)\n",
    "plt.ylabel('$10^5$ (' + str(16.28346*2) + '$ + F / E_B )$', fontsize = ft)\n",
    "#plt.savefig('Eq_crescent.svg', bbox_inches='tight', transparent=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CS state expectations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ft = 22\n",
    "\n",
    "y, x = np.meshgrid(k/2, k/2)\n",
    "\n",
    "\n",
    "plt.figure( figsize=(4.0, 4.0) ) \n",
    "plt.pcolormesh(y, x, el_dens[ggg,:,:], vmin = 0.0, vmax = 1 ,  rasterized = True)#, cmap=plt.cm.jet)\n",
    "#plt.colorbar()\n",
    "plt.xlim(-2.5, 2.5)\n",
    "plt.ylim(-2.5, 2.5)\n",
    "plt.xlabel('$a_B k_x$', size=ft)\n",
    "plt.ylabel('$a_B k_y$', size=ft)\n",
    "plt.xticks(fontsize=ft, rotation=0)\n",
    "plt.yticks(fontsize=ft, rotation=0)\n",
    "\n",
    "x = [-2.5, 2.5]\n",
    "y = [-2.5, 2.5]\n",
    "plt.xticks(np.arange(-2, 2.1, 1)   )\n",
    "plt.yticks(np.arange(-2, 2.1, 1)   )\n",
    "\n",
    "plt.text(-1.9, -0.8, \n",
    "         '$\\langle \\hat{e}^{\\dagger}_{\\mathbf{k} + \\mathbf{Q}/2}'\n",
    "          '\\hat{e}^{}_{\\mathbf{k} + \\mathbf{Q}/2}\\\\rangle $ \\n CS',\n",
    "         color = 'k', fontsize = 22)\n",
    "\n",
    "#plt.savefig('el_dens.svg', bbox_inches='tight', transparent=True)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(4.0, 4))\n",
    "\n",
    "ft = 24\n",
    "\n",
    "plt.plot(k/2, el_dens[ggg, zero_ind, :], marker = '.', \n",
    "         label = '$\\langle \\hat{e}^{\\dagger}_{\\mathbf{Q}/2 + \\mathbf{k}}'\n",
    "                 ' \\hat{e}^{}_{\\mathbf{Q}/2 + \\mathbf{k}} \\\\rangle$')\n",
    "plt.plot(k/2, hole_dens[ggg, zero_ind, :], marker = '.', \n",
    "         label = '$\\langle \\hat{h}^{\\dagger}_{\\mathbf{Q}/2 -\\mathbf{k}}'\n",
    "                 ' \\hat{h}^{}_{\\mathbf{Q}/2 -\\mathbf{k}} \\\\rangle$')\n",
    "plt.plot(k/2, abs(coherence[ggg, zero_ind, :]), marker = '.', \n",
    "         label = '$|\\langle \\hat{h}^{}_{\\mathbf{Q}/2 -\\mathbf{k}}'\n",
    "                 ' \\hat{e}^{}_{\\mathbf{Q}/2 + \\mathbf{k}} \\\\rangle|$', color = 'g')\n",
    "\n",
    "\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(0, 1.02)\n",
    "\n",
    "plt.legend(fontsize = ft-2, loc = (1.1, 0.3), framealpha = 0.95, handlelength = 1)\n",
    "plt.xticks(fontsize=ft, rotation=0)\n",
    "plt.yticks(fontsize=ft, rotation=0)\n",
    "\n",
    "\n",
    "x = [-5, 5]\n",
    "y = [-0.0, 1.01]\n",
    "plt.xticks(np.arange(min(x), max(x)+0.1, 2)    )\n",
    "plt.yticks(np.arange(min(y), max(y), 0.2)     )\n",
    "plt.grid()\n",
    "\n",
    "plt.xlabel('$a_B k_x$', fontsize = ft)\n",
    "#plt.savefig('dens.svg', bbox_inches='tight', transparent=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FF state expectations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ft = 22\n",
    "\n",
    "y, x = np.meshgrid(k/2, k/2)\n",
    "\n",
    "\n",
    "plt.figure( figsize=(4.0, 4.0) ) \n",
    "plt.pcolormesh(y, x, el_dens[fff,:,:], vmin = 0.0, vmax = 1 ,  rasterized = True)\n",
    "#plt.colorbar()\n",
    "plt.xlim(-2.5, 2.5)\n",
    "plt.ylim(-2.5, 2.5)\n",
    "plt.xlabel('$a_B k_x$', size=ft)\n",
    "plt.ylabel('$a_B k_y$', size=ft)\n",
    "plt.xticks(fontsize=ft, rotation=0)\n",
    "plt.yticks(fontsize=ft, rotation=0)\n",
    "\n",
    "x = [-2.5, 2.5]\n",
    "y = [-2.5, 2.5]\n",
    "plt.xticks(np.arange(-2, 2.1, 1)   )\n",
    "plt.yticks(np.arange(-2, 2.1, 1)   )\n",
    "\n",
    "plt.text(-1.9, -0.8, \n",
    "         '$\\langle \\hat{e}^{\\dagger}_{\\mathbf{k} + \\mathbf{Q}/2}'\n",
    "          '\\hat{e}^{}_{\\mathbf{k} + \\mathbf{Q}/2}\\\\rangle $ \\n FF',\n",
    "         color = 'k', fontsize = 22)\n",
    "\n",
    "#plt.savefig('el_dens.svg', bbox_inches='tight', transparent=True)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(4.0, 4))\n",
    "\n",
    "ft = 24\n",
    "\n",
    "plt.plot(k/2, el_dens[fff, zero_ind, :], marker = '.', \n",
    "         label = '$\\langle \\hat{e}^{\\dagger}_{\\mathbf{Q}/2 + \\mathbf{k}}'\n",
    "                 ' \\hat{e}^{}_{\\mathbf{Q}/2 + \\mathbf{k}} \\\\rangle$')\n",
    "plt.plot(k/2, hole_dens[fff, zero_ind, :], marker = '.', \n",
    "         label = '$\\langle \\hat{h}^{\\dagger}_{\\mathbf{Q}/2 -\\mathbf{k}}'\n",
    "                 ' \\hat{h}^{}_{\\mathbf{Q}/2 -\\mathbf{k}} \\\\rangle$')\n",
    "plt.plot(k/2, abs(coherence[fff, zero_ind, :]), marker = '.', \n",
    "         label = '$|\\langle \\hat{h}^{}_{\\mathbf{Q}/2 -\\mathbf{k}}'\n",
    "                 ' \\hat{e}^{}_{\\mathbf{Q}/2 + \\mathbf{k}} \\\\rangle|$', color = 'g')\n",
    "\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(0, 1.02)\n",
    "\n",
    "plt.legend(fontsize = ft-2, loc = (1.1, 0.3), framealpha = 0.95, handlelength = 1)\n",
    "plt.xticks(fontsize=ft, rotation=0)\n",
    "plt.yticks(fontsize=ft, rotation=0)\n",
    "\n",
    "x = [-5, 5]\n",
    "y = [-0.0, 1.01]\n",
    "plt.xticks(np.arange(min(x), max(x)+0.1, 2)    )\n",
    "plt.yticks(np.arange(min(y), max(y), 0.2)     )\n",
    "plt.grid()\n",
    "\n",
    "plt.xlabel('$a_B k_x$', fontsize = ft)\n",
    "#plt.savefig('dens.svg', bbox_inches='tight', transparent=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "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": 2
}