{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Gross-Pitaevskii equation with external magnetic field"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "We solve the 2D Gross-Pitaevskii equation with a magnetic field.\n",
    "This is similar to the\n",
    "previous example (Gross-Pitaevskii equation in one dimension),\n",
    "but with an extra term for the magnetic field.\n",
    "We reproduce here the results of https://arxiv.org/pdf/1611.02045.pdf Fig. 10"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n     Energy            log10(ΔE)   log10(Δρ)   Δtime\n",
      "---   ---------------   ---------   ---------   ------\n",
      "  1   +30.40743520513                   -1.42    5.13s\n",
      "  2   +23.95051791622        0.81       -0.77   10.6ms\n",
      "  3   +21.65829285710        0.36       -0.37   10.4ms\n",
      "  4   +19.79805467132        0.27       -0.28   10.5ms\n",
      "  5   +18.34725768879        0.16       -0.49   10.4ms\n",
      "  6   +13.44183896546        0.69       -0.45   10.4ms\n",
      "  7   +10.03875646258        0.53       -0.45   10.4ms\n",
      "  8   +9.224587654307       -0.09       -0.71   8.44ms\n",
      "  9   +8.915536203565       -0.51       -0.95   8.51ms\n",
      " 10   +8.748496019147       -0.78       -1.01   8.41ms\n",
      " 11   +8.624414735914       -0.91       -0.98   8.36ms\n",
      " 12   +8.496505081782       -0.89       -0.98   8.36ms\n",
      " 13   +8.403619841622       -1.03       -1.06   6.37ms\n",
      " 14   +8.318072596839       -1.07       -1.07   6.37ms\n",
      " 15   +8.220172203342       -1.01       -1.01   6.49ms\n",
      " 16   +8.174244157943       -1.34       -1.06   6.54ms\n",
      " 17   +8.122124893775       -1.28       -1.05   6.39ms\n",
      " 18   +8.057408145205       -1.19       -0.78   49.5ms\n",
      " 19   +8.016103387287       -1.38       -1.00   6.91ms\n",
      " 20   +7.976589050989       -1.40       -1.14   6.66ms\n",
      " 21   +7.942160965503       -1.46       -1.22   6.51ms\n",
      " 22   +7.912519223739       -1.53       -1.09   8.39ms\n",
      " 23   +7.885169958563       -1.56       -1.19   6.38ms\n",
      " 24   +7.857929374049       -1.56       -1.18   6.41ms\n",
      " 25   +7.838054375681       -1.70       -1.18   6.45ms\n",
      " 26   +7.813489391633       -1.61       -1.27   6.36ms\n",
      " 27   +7.807638907214       -2.23       -1.26   6.36ms\n",
      " 28   +7.794523541314       -1.88       -1.35   6.37ms\n",
      " 29   +7.786136511033       -2.08       -1.36   6.35ms\n",
      " 30   +7.770365002571       -1.80       -1.12   8.48ms\n",
      " 31   +7.763995631407       -2.20       -1.24   6.40ms\n",
      " 32   +7.749705060282       -1.84       -1.31   6.39ms\n",
      " 33   +7.742339367976       -2.13       -1.34   6.43ms\n",
      " 34   +7.731506958657       -1.97       -1.14   8.37ms\n",
      " 35   +7.722796413393       -2.06       -1.40   6.37ms\n",
      " 36   +7.720441219131       -2.63       -1.28   33.1ms\n",
      " 37   +7.710635638641       -2.01       -1.42   6.79ms\n",
      " 38   +7.707967460885       -2.57       -1.27   6.41ms\n",
      " 39   +7.699905369066       -2.09       -1.48   6.39ms\n",
      " 40   +7.699751183325       -3.81       -1.34   6.40ms\n",
      " 41   +7.692279641004       -2.13       -1.47   6.36ms\n",
      " 42   +7.686639013682       -2.25       -1.34   8.35ms\n",
      " 43   +7.683328563494       -2.48       -1.43   6.37ms\n",
      " 44   +7.681589036952       -2.76       -1.46   6.40ms\n",
      " 45   +7.679111709509       -2.61       -1.46   6.35ms\n",
      " 46   +7.675881512906       -2.49       -1.56   6.34ms\n",
      " 47   +7.671921382044       -2.40       -1.32   8.30ms\n",
      " 48   +7.669112597370       -2.55       -1.68   6.32ms\n",
      " 49   +7.668966744259       -3.84       -1.45   6.38ms\n",
      " 50   +7.666071357831       -2.54       -1.77   6.37ms\n",
      " 51   +7.662929783659       -2.50       -1.36   8.33ms\n",
      " 52   +7.660899070272       -2.69       -1.59   6.42ms\n",
      " 53   +7.658443827569       -2.61       -1.73   6.38ms\n",
      " 54   +7.656117400000       -2.63       -1.60   6.37ms\n",
      " 55   +7.654093412043       -2.69       -1.36   8.37ms\n",
      " 56   +7.652194642305       -2.72       -1.50    110ms\n",
      " 57   +7.652008351222       -3.73       -1.49   8.56ms\n",
      " 58   +7.650008522980       -2.70       -1.62   8.11ms\n",
      " 59   +7.648742068357       -2.90       -1.57   8.22ms\n",
      " 60   +7.646056039246       -2.57       -1.17   10.6ms\n",
      " 61   +7.644011513007       -2.69       -1.67   8.26ms\n",
      " 62   +7.643283208520       -3.14       -1.64   8.36ms\n",
      " 63   +7.640607721221       -2.57       -1.42   8.26ms\n",
      " 64   +7.638793894247       -2.74       -1.52   10.8ms\n",
      " 65   +7.637288344953       -2.82       -1.68   8.28ms\n",
      " 66   +7.635702379870       -2.80       -1.56   10.6ms\n",
      " 67   +7.635635896940       -4.18       -1.71   8.31ms\n",
      " 68   +7.635506725063       -3.89       -1.54   8.11ms\n",
      " 69   +7.634244756424       -2.90       -1.58   10.9ms\n",
      " 70   +7.632347478761       -2.72       -1.80   8.37ms\n",
      " 71   +7.630822064931       -2.82       -1.64    551ms\n",
      " 72   +7.629498567770       -2.88       -1.89   6.59ms\n",
      " 73   +7.628177859889       -2.88       -1.46   8.70ms\n",
      " 74   +7.627243957282       -3.03       -1.77   6.52ms\n",
      " 75   +7.626306735581       -3.03       -1.88   6.41ms\n",
      " 76   +7.625576061958       -3.14       -2.04   6.42ms\n",
      " 77   +7.625056631662       -3.28       -1.92   6.51ms\n",
      " 78   +7.624463816544       -3.23       -1.47   8.58ms\n",
      " 79   +7.623792793674       -3.17       -1.49   8.51ms\n",
      " 80   +7.623104801284       -3.16       -2.03   7.46ms\n",
      " 81   +7.622682516599       -3.37       -1.78   8.59ms\n",
      " 82   +7.622354999403       -3.48       -1.78   8.00ms\n",
      " 83   +7.622139013520       -3.67       -2.04   7.96ms\n",
      " 84   +7.621749301055       -3.41       -2.09   7.95ms\n",
      " 85   +7.621549590557       -3.70       -2.02   7.91ms\n",
      " 86   +7.621384635449       -3.78       -2.06   8.03ms\n",
      " 87   +7.621052695397       -3.48       -2.09   8.10ms\n",
      " 88   +7.620835760113       -3.66       -1.91   8.07ms\n",
      " 89   +7.620682807220       -3.82       -1.81   8.14ms\n",
      " 90   +7.620619929810       -4.20       -2.19   8.09ms\n",
      " 91   +7.620223192538       -3.40       -2.11   8.24ms\n",
      " 92   +7.620096760435       -3.90       -2.18   8.03ms\n",
      " 93   +7.619835935341       -3.58       -1.90   10.6ms\n",
      " 94   +7.619748661897       -4.06       -1.93   6.99ms\n",
      " 95   +7.619590529046       -3.80       -2.29   6.94ms\n",
      " 96   +7.619471623799       -3.92       -2.09   7.00ms\n",
      " 97   +7.619262466071       -3.68       -1.92   9.29ms\n",
      " 98   +7.619157128193       -3.98       -2.08   7.04ms\n",
      " 99   +7.619016316774       -3.85       -2.06   7.01ms\n",
      " 100   +7.618741575751       -3.56       -2.02   7.11ms\n",
      " 101   +7.618538029263       -3.69       -1.90   9.34ms\n",
      " 102   +7.618387688675       -3.82       -2.16   6.90ms\n",
      " 103   +7.618312103968       -4.12       -2.03   6.85ms\n",
      " 104   +7.618124879712       -3.73       -2.27   6.87ms\n",
      " 105   +7.617851225696       -3.56       -1.64   8.65ms\n",
      " 106   +7.617639407998       -3.67       -1.89   6.45ms\n",
      " 107   +7.617459118068       -3.74       -1.76   6.35ms\n",
      " 108   +7.617161560088       -3.53       -2.10   6.41ms\n",
      " 109   +7.616775347856       -3.41       -1.56   8.35ms\n",
      " 110   +7.616596136718       -3.75       -1.73   6.39ms\n",
      " 111   +7.616187590718       -3.39       -1.87   6.48ms\n",
      " 112   +7.615872640753       -3.50       -2.05   6.50ms\n",
      " 113   +7.615407741996       -3.33       -1.50   9.26ms\n",
      " 114   +7.614931825532       -3.32       -1.54   9.32ms\n",
      " 115   +7.614920210061       -4.93       -1.84   7.11ms\n",
      " 116   +7.614803369590       -3.93       -1.95   7.37ms\n",
      " 117   +7.614572942469       -3.64       -1.72   6.99ms\n",
      " 118   +7.614449504529       -3.91       -1.87   6.74ms\n",
      " 119   +7.614103057224       -3.46       -1.87   7.69ms\n",
      " 120   +7.613940183063       -3.79       -2.02   6.50ms\n",
      " 121   +7.613501569257       -3.36       -1.79   6.45ms\n",
      " 122   +7.613434390333       -4.17       -1.79   6.67ms\n",
      " 123   +7.612945672758       -3.31       -1.98   6.49ms\n",
      " 124   +7.612546821629       -3.40       -1.70   8.63ms\n",
      " 125   +7.611997559739       -3.26       -2.05   23.2ms\n",
      " 126   +7.611333048058       -3.18       -1.64   8.87ms\n",
      " 127   +7.610942149066       -3.41       -1.75   8.46ms\n",
      " 128   +7.610788638182       -3.81       -1.99   6.51ms\n",
      " 129   +7.610477920726       -3.51       -1.81   8.45ms\n",
      " 130   +7.610284001260       -3.71       -1.93   8.40ms\n",
      " 131   +7.610263135250       -4.68       -1.78   6.47ms\n",
      " 132   +7.609959375595       -3.52       -2.14   6.43ms\n",
      " 133   +7.609915086966       -4.35       -1.48   6.45ms\n",
      " 134   +7.609599466041       -3.50       -1.78   6.37ms\n",
      " 135   +7.609174677972       -3.37       -1.84   8.36ms\n",
      " 136   +7.608677873783       -3.30       -1.93   6.52ms\n",
      " 137   +7.608437035874       -3.62       -1.98   6.58ms\n",
      " 138   +7.608298119723       -3.86       -2.01   6.48ms\n",
      " 139   +7.607990735010       -3.51       -1.76   8.44ms\n",
      " 140   +7.607660477391       -3.48       -2.03   6.47ms\n",
      " 141   +7.607445773850       -3.67       -2.09   8.54ms\n",
      " 142   +7.607270337122       -3.76       -1.87   6.47ms\n",
      " 143   +7.607186400597       -4.08       -2.12   6.43ms\n",
      " 144   +7.606946753872       -3.62       -1.80   9.01ms\n",
      " 145   +7.606722581589       -3.65       -1.88   8.59ms\n",
      " 146   +7.606624294590       -4.01       -2.04   6.48ms\n",
      " 147   +7.606394872724       -3.64       -1.90   8.42ms\n",
      " 148   +7.606334516054       -4.22       -2.08   6.76ms\n",
      " 149   +7.606243060616       -4.04       -1.95   6.47ms\n",
      " 150   +7.606209479334       -4.47       -2.20   6.43ms\n",
      " 151   +7.606017073368       -3.72       -2.09   6.41ms\n",
      " 152   +7.605956753803       -4.22       -2.24   6.43ms\n",
      " 153   +7.605849161817       -3.97       -2.07   6.51ms\n",
      " 154   +7.605732581268       -3.93       -2.04   6.38ms\n",
      " 155   +7.605616680147       -3.94       -2.14   8.45ms\n",
      " 156   +7.605533361457       -4.08       -2.32   6.43ms\n",
      " 157   +7.605405414760       -3.89       -2.06   8.40ms\n",
      " 158   +7.605357463386       -4.32       -2.32   6.46ms\n",
      " 159   +7.605273662135       -4.08       -2.23   8.36ms\n",
      " 160   +7.605254958895       -4.73       -2.33   6.35ms\n",
      " 161   +7.605219392203       -4.45       -2.19   35.6ms\n",
      " 162   +7.605169221727       -4.30       -2.40   9.13ms\n",
      " 163   +7.605118997533       -4.30       -2.29   6.58ms\n",
      " 164   +7.605058881814       -4.22       -2.25   8.52ms\n",
      " 165   +7.604978183226       -4.09       -2.05   8.41ms\n",
      " 166   +7.604956030375       -4.65       -2.47   6.39ms\n",
      " 167   +7.604935142828       -4.68       -2.34   6.39ms\n",
      " 168   +7.604905768199       -4.53       -2.58   6.40ms\n",
      " 169   +7.604879814290       -4.59       -2.20   6.40ms\n",
      " 170   +7.604824251203       -4.26       -2.56   6.40ms\n",
      " 171   +7.604776894693       -4.32       -2.20   6.50ms\n",
      " 172   +7.604692221918       -4.07       -2.13   8.37ms\n",
      " 173   +7.604630748127       -4.21       -2.25   6.45ms\n",
      " 174   +7.604560924221       -4.16       -2.00   8.35ms\n",
      " 175   +7.604472760627       -4.05       -2.50   6.46ms\n",
      " 176   +7.604411805435       -4.21       -2.23   6.40ms\n",
      " 177   +7.604327627764       -4.07       -2.05   8.38ms\n",
      " 178   +7.604249904082       -4.11       -1.81   8.51ms\n",
      " 179   +7.604190588420       -4.23       -2.05   8.40ms\n",
      " 180   +7.604085709147       -3.98       -1.61   8.36ms\n",
      " 181   +7.604065857909       -4.70       -2.15   6.35ms\n",
      " 182   +7.603960120423       -3.98       -1.57   8.40ms\n",
      " 183   +7.603908442865       -4.29       -2.20   6.35ms\n",
      " 184   +7.603826087998       -4.08       -2.23   6.47ms\n",
      " 185   +7.603800245040       -4.59       -2.32   6.36ms\n",
      " 186   +7.603712066841       -4.05       -2.33   6.37ms\n",
      " 187   +7.603651682821       -4.22       -2.07   8.41ms\n",
      " 188   +7.603604458943       -4.33       -2.34   6.40ms\n",
      " 189   +7.603553427850       -4.29       -2.32   20.2ms\n",
      " 190   +7.603493610866       -4.22       -2.19   6.53ms\n",
      " 191   +7.603454734658       -4.41       -2.26   6.45ms\n",
      " 192   +7.603401976902       -4.28       -2.12   6.43ms\n",
      " 193   +7.603347386849       -4.26       -2.33   8.40ms\n",
      " 194   +7.603309883062       -4.43       -2.05   6.40ms\n",
      " 195   +7.603262659122       -4.33       -2.17   6.39ms\n",
      " 196   +7.603258057164       -5.34       -2.11   6.41ms\n",
      " 197   +7.603186603127       -4.15       -2.50   6.43ms\n",
      " 198   +7.603176662550       -5.00       -2.44   6.41ms\n",
      " 199   +7.603108292370       -4.17       -2.14   6.42ms\n",
      " 200   +7.603080127346       -4.55       -2.33   6.35ms\n",
      " 201   +7.603023836162       -4.25       -2.42   6.37ms\n",
      " 202   +7.602952786680       -4.15       -2.16   8.35ms\n",
      " 203   +7.602892316555       -4.22       -2.09   8.39ms\n",
      " 204   +7.602869888511       -4.65       -2.48   6.40ms\n",
      " 205   +7.602798119397       -4.14       -1.91   8.41ms\n",
      " 206   +7.602757954926       -4.40       -2.10   8.37ms\n",
      " 207   +7.602702504457       -4.26       -1.88   8.36ms\n",
      " 208   +7.602680883115       -4.67       -2.60   6.40ms\n",
      " 209   +7.602641580782       -4.41       -1.90   8.42ms\n",
      " 210   +7.602636048556       -5.26       -2.16   6.36ms\n",
      " 211   +7.602593017411       -4.37       -1.88   8.36ms\n",
      " 212   +7.602568702238       -4.61       -2.38   16.8ms\n",
      " 213   +7.602545915393       -4.64       -2.50   6.50ms\n",
      " 214   +7.602531577161       -4.84       -2.59   6.50ms\n",
      " 215   +7.602507699482       -4.62       -2.16   8.37ms\n",
      " 216   +7.602481657301       -4.58       -2.53   6.41ms\n",
      " 217   +7.602467523383       -4.85       -2.62   8.35ms\n",
      " 218   +7.602455183466       -4.91       -2.77   6.38ms\n",
      " 219   +7.602443143956       -4.92       -2.58   6.37ms\n",
      " 220   +7.602435066949       -5.09       -2.70   6.40ms\n",
      " 221   +7.602421769265       -4.88       -2.31   8.36ms\n",
      " 222   +7.602409128020       -4.90       -2.51   6.36ms\n",
      " 223   +7.602400843571       -5.08       -2.55   6.40ms\n",
      " 224   +7.602389229286       -4.94       -2.49   6.37ms\n",
      " 225   +7.602387043233       -5.66       -2.32   6.36ms\n",
      " 226   +7.602368903040       -4.74       -2.73   6.40ms\n",
      " 227   +7.602363952066       -5.31       -2.52   6.37ms\n",
      " 228   +7.602347700196       -4.79       -2.68   6.36ms\n",
      " 229   +7.602347647311       -7.28       -2.67   6.40ms\n",
      " 230   +7.602340583817       -5.15       -2.61   6.37ms\n",
      " 231   +7.602335299557       -5.28       -2.37   6.43ms\n",
      " 232   +7.602325884138       -5.03       -2.73   15.4ms\n",
      " 233   +7.602312260251       -4.87       -2.54   6.47ms\n",
      " 234   +7.602284879580       -4.56       -2.32   8.46ms\n",
      " 235   +7.602273325539       -4.94       -2.49   6.40ms\n",
      " 236   +7.602256291123       -4.77       -2.42   8.37ms\n",
      " 237   +7.602244110998       -4.91       -2.57   6.50ms\n",
      " 238   +7.602241928492       -5.66       -2.40   6.41ms\n",
      " 239   +7.602231087326       -4.96       -2.59   6.44ms\n",
      " 240   +7.602216406811       -4.83       -2.40   8.41ms\n",
      " 241   +7.602211965176       -5.35       -2.32   6.37ms\n",
      " 242   +7.602183452543       -4.54       -2.06   8.41ms\n",
      " 243   +7.602163667876       -4.70       -2.44   6.38ms\n",
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      " 745   +7.600932113661       -8.10       -4.23   6.35ms\n",
      " 746   +7.600932110473       -8.50       -3.75   6.38ms\n",
      " 747   +7.600932106494       -8.40       -3.84   6.38ms\n",
      " 748   +7.600932094354       -7.92       -4.05   6.38ms\n",
      " 749   +7.600932087210       -8.15       -4.25   6.43ms\n",
      " 750   +7.600932085808       -8.85       -4.26   12.3ms\n",
      " 751   +7.600932082496       -8.48       -4.31   6.52ms\n",
      " 752   +7.600932072053       -7.98       -4.17   8.41ms\n",
      " 753   +7.600932071061       -9.00       -4.08   6.39ms\n",
      " 754   +7.600932064537       -8.19       -4.38   6.34ms\n",
      " 755   +7.600932063237       -8.89       -4.08   6.35ms\n",
      " 756   +7.600932058523       -8.33       -4.16   8.37ms\n",
      " 757   +7.600932053526       -8.30       -4.31   8.36ms\n",
      " 758   +7.600932049182       -8.36       -4.28   8.46ms\n",
      " 759   +7.600932046892       -8.64       -4.60   13.0ms\n",
      " 760   +7.600932045948       -9.02       -4.37   6.52ms\n",
      " 761   +7.600932040740       -8.28       -4.05   8.40ms\n",
      " 762   +7.600932037239       -8.46       -4.00   8.39ms\n",
      " 763   +7.600932035184       -8.69       -4.63   6.35ms\n",
      " 764   +7.600932031763       -8.47       -3.96   8.36ms\n",
      " 765   +7.600932031270       -9.31       -4.53   6.46ms\n",
      " 766   +7.600932029858       -8.85       -4.01   6.36ms\n",
      " 767   +7.600932028204       -8.78       -4.76   6.38ms\n",
      " 768   +7.600932027684       -9.28       -4.52   6.37ms\n",
      " 769   +7.600932026022       -8.78       -4.79   12.6ms\n",
      " 770   +7.600932025874       -9.83       -4.78   6.48ms\n",
      " 771   +7.600932023603       -8.64       -4.23   6.51ms\n",
      " 772   +7.600932022389       -8.92       -4.51   6.41ms\n",
      " 773   +7.600932020039       -8.63       -4.90   6.36ms\n",
      " 774   +7.600932019838       -9.70       -4.87   6.39ms\n",
      " 775   +7.600932018664       -8.93       -4.80   6.35ms\n",
      " 776   +7.600932016945       -8.76       -4.18   8.34ms\n",
      " 777   +7.600932015286       -8.78       -4.06   8.44ms\n",
      " 778   +7.600932013471       -8.74       -4.15   6.40ms\n",
      " 779   +7.600932011296       -8.66       -3.77   14.6ms\n",
      " 780   +7.600932010275       -8.99       -4.16   8.51ms\n",
      " 781   +7.600932008331       -8.71       -3.71   8.41ms\n",
      " 782   +7.600932007722       -9.22       -4.08   6.35ms\n",
      " 783   +7.600932006704       -8.99       -4.06   6.35ms\n",
      " 784   +7.600932005486       -8.91       -4.48   6.38ms\n",
      " 785   +7.600932004445       -8.98       -4.07   6.36ms\n",
      " 786   +7.600932001545       -8.54       -4.54   6.34ms\n",
      " 787   +7.600932000896       -9.19       -4.25   6.38ms\n",
      " 788   +7.600931998974       -8.72       -4.33   6.34ms\n",
      " 789   +7.600931997446       -8.82       -4.57   14.4ms\n",
      " 790   +7.600931996302       -8.94       -4.62   6.40ms\n",
      " 791   +7.600931994773       -8.82       -4.40   6.41ms\n",
      " 792   +7.600931994205       -9.25       -4.44   6.37ms\n",
      " 793   +7.600931993326       -9.06       -4.21   8.32ms\n",
      " 794   +7.600931992552       -9.11       -4.26   6.35ms\n",
      " 795   +7.600931992203       -9.46       -4.46   6.34ms\n",
      " 796   +7.600931991973       -9.64       -4.34   6.39ms\n",
      " 797   +7.600931990993       -9.01       -4.69   6.36ms\n",
      " 798   +7.600931990704       -9.54       -4.27   6.37ms\n",
      " 799   +7.600931990091       -9.21       -4.78   12.8ms\n",
      " 800   +7.600931988897       -8.92       -4.51   6.52ms\n",
      " 801   +7.600931988102       -9.10       -4.50   6.48ms\n",
      " 802   +7.600931987292       -9.09       -4.53   6.41ms\n",
      " 803   +7.600931987197      -10.02       -4.71   6.37ms\n",
      " 804   +7.600931986434       -9.12       -4.84   6.44ms\n",
      " 805   +7.600931985434       -9.00       -4.76   8.37ms\n",
      " 806   +7.600931984407       -8.99       -4.42   8.37ms\n",
      " 807   +7.600931983406       -9.00       -4.46   8.37ms\n",
      " 808   +7.600931982887       -9.28       -4.38   6.36ms\n",
      " 809   +7.600931981222       -8.78       -4.22   14.6ms\n",
      " 810   +7.600931980641       -9.24       -4.43   8.43ms\n",
      " 811   +7.600931980050       -9.23       -4.63   6.40ms\n",
      " 812   +7.600931979126       -9.03       -4.37   8.33ms\n",
      " 813   +7.600931978363       -9.12       -4.47   6.35ms\n",
      " 814   +7.600931977822       -9.27       -4.02   6.36ms\n",
      " 815   +7.600931976871       -9.02       -4.52   6.35ms\n",
      " 816   +7.600931975540       -8.88       -4.82   6.39ms\n",
      " 817   +7.600931973536       -8.70       -4.50   6.38ms\n",
      " 818   +7.600931972120       -8.85       -4.80   6.34ms\n",
      " 819   +7.600931970741       -8.86       -4.32   14.5ms\n",
      " 820   +7.600931969909       -9.08       -4.86   6.42ms\n",
      " 821   +7.600931969006       -9.04       -4.80   6.38ms\n",
      " 822   +7.600931968116       -9.05       -4.40   6.37ms\n",
      " 823   +7.600931967123       -9.00       -4.46   6.33ms\n",
      " 824   +7.600931966280       -9.07       -4.30   6.42ms\n",
      " 825   +7.600931964039       -8.65       -3.89   8.38ms\n",
      " 826   +7.600931963702       -9.47       -4.22   6.40ms\n",
      " 827   +7.600931963227       -9.32       -4.49   6.39ms\n",
      " 828   +7.600931962380       -9.07       -4.30   6.35ms\n",
      " 829   +7.600931961781       -9.22       -4.33   12.8ms\n",
      " 830   +7.600931960837       -9.02       -4.66   6.52ms\n",
      " 831   +7.600931959587       -8.90       -4.61   6.49ms\n",
      " 832   +7.600931958733       -9.07       -4.73   6.40ms\n",
      " 833   +7.600931957644       -8.96       -4.54   6.37ms\n",
      " 834   +7.600931956920       -9.14       -4.65   6.40ms\n",
      " 835   +7.600931955490       -8.84       -4.62   6.40ms\n",
      " 836   +7.600931954372       -8.95       -4.52   8.34ms\n",
      " 837   +7.600931952948       -8.85       -4.65   8.36ms\n",
      " 838   +7.600931952093       -9.07       -4.72   14.7ms\n",
      " 839   +7.600931950966       -8.95       -4.58   8.56ms\n",
      " 840   +7.600931950019       -9.02       -4.54   8.88ms\n",
      " 841   +7.600931949504       -9.29       -4.68   8.52ms\n",
      " 842   +7.600931949278       -9.65       -4.83   6.47ms\n",
      " 843   +7.600931949243      -10.45       -4.82   6.49ms\n",
      " 844   +7.600931948760       -9.32       -4.75   6.43ms\n",
      " 845   +7.600931948539       -9.66       -4.76   6.43ms\n",
      " 846   +7.600931948082       -9.34       -4.71   6.53ms\n",
      " 847   +7.600931947689       -9.41       -5.04   6.42ms\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=1}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 1
    }
   ],
   "cell_type": "code",
   "source": [
    "using DFTK\n",
    "using StaticArrays\n",
    "using Plots\n",
    "\n",
    "# Unit cell. Having one of the lattice vectors as zero means a 2D system\n",
    "a = 15\n",
    "lattice = a .* [[1 0 0.]; [0 1 0]; [0 0 0]];\n",
    "\n",
    "# Confining scalar potential, and magnetic vector potential\n",
    "pot(x, y, z) = ((x - a/2)^2 + (y - a/2)^2)/2\n",
    "ω = .6\n",
    "Apot(x, y, z) = ω * @SVector [y - a/2, -(x - a/2), 0]\n",
    "Apot(X) = Apot(X...);\n",
    "\n",
    "\n",
    "# Parameters\n",
    "Ecut = 20  # Increase this for production\n",
    "η = 500\n",
    "C = η/2\n",
    "α = 2\n",
    "n_electrons = 1;  # Increase this for fun\n",
    "\n",
    "# Collect all the terms, build and run the model\n",
    "terms = [Kinetic(),\n",
    "         ExternalFromReal(X -> pot(X...)),\n",
    "         LocalNonlinearity(ρ -> C * ρ^α),\n",
    "         Magnetic(Apot),\n",
    "]\n",
    "model = Model(lattice; n_electrons, terms, spin_polarization=:spinless)  # spinless electrons\n",
    "basis = PlaneWaveBasis(model; Ecut, kgrid=(1, 1, 1))\n",
    "scfres = direct_minimization(basis, tol=1e-5)  # Reduce tol for production\n",
    "heatmap(scfres.ρ[:, :, 1, 1], c=:blues)"
   ],
   "metadata": {},
   "execution_count": 1
  }
 ],
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