{
"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 +29.20760409403 -1.43 6.22s\n",
" 2 +20.85388814959 0.92 -0.86 11.4ms\n",
" 3 +14.93833287626 0.77 -0.52 11.2ms\n",
" 4 +11.01211468653 0.59 -0.44 11.1ms\n",
" 5 +9.534266722378 0.17 -0.67 11.2ms\n",
" 6 +9.041315024736 -0.31 -0.89 9.57ms\n",
" 7 +8.710800478470 -0.48 -0.92 10.2ms\n",
" 8 +8.421140116681 -0.54 -1.00 10.1ms\n",
" 9 +8.234080023630 -0.73 -1.02 10.2ms\n",
" 10 +8.172481879351 -1.21 -1.09 7.73ms\n",
" 11 +8.131652234647 -1.39 -1.14 45.6ms\n",
" 12 +8.093818476651 -1.42 -1.16 7.37ms\n",
" 13 +8.027729285184 -1.18 -1.04 9.35ms\n",
" 14 +7.953979241651 -1.13 -1.05 9.20ms\n",
" 15 +7.915593895989 -1.42 -1.08 7.02ms\n",
" 16 +7.906921605710 -2.06 -1.13 6.96ms\n",
" 17 +7.896221681600 -1.97 -1.11 6.91ms\n",
" 18 +7.874466708388 -1.66 -1.14 6.87ms\n",
" 19 +7.838639633744 -1.45 -1.18 6.82ms\n",
" 20 +7.812228826917 -1.58 -1.20 6.85ms\n",
" 21 +7.785212413950 -1.57 -1.15 6.96ms\n",
" 22 +7.781577871459 -2.44 -1.18 6.85ms\n",
" 23 +7.760042527541 -1.67 -1.25 6.89ms\n",
" 24 +7.742122200708 -1.75 -1.24 6.85ms\n",
" 25 +7.729996266371 -1.92 -1.24 9.06ms\n",
" 26 +7.728124501589 -2.73 -1.15 6.87ms\n",
" 27 +7.715051035541 -1.88 -1.15 9.04ms\n",
" 28 +7.704761845941 -1.99 -1.17 9.04ms\n",
" 29 +7.695518197068 -2.03 -1.30 6.98ms\n",
" 30 +7.687449713278 -2.09 -1.29 6.98ms\n",
" 31 +7.686597649441 -3.07 -1.26 6.88ms\n",
" 32 +7.678761744468 -2.11 -1.39 6.84ms\n",
" 33 +7.669901643741 -2.05 -1.12 9.00ms\n",
" 34 +7.662138996798 -2.11 -1.46 6.84ms\n",
" 35 +7.659470500387 -2.57 -1.41 6.87ms\n",
" 36 +7.656552017184 -2.53 -1.51 9.02ms\n",
" 37 +7.650822335362 -2.24 -1.14 9.02ms\n",
" 38 +7.646928432303 -2.41 -1.64 6.85ms\n",
" 39 +7.646126286382 -3.10 -1.71 6.85ms\n",
" 40 +7.643949905197 -2.66 -1.60 6.88ms\n",
" 41 +7.642405574595 -2.81 -1.56 9.01ms\n",
" 42 +7.640439569586 -2.71 -1.41 8.99ms\n",
" 43 +7.638875079524 -2.81 -1.69 7.00ms\n",
" 44 +7.637826776546 -2.98 -1.72 9.01ms\n",
" 45 +7.636018108122 -2.74 -1.75 6.87ms\n",
" 46 +7.635383919676 -3.20 -1.50 6.88ms\n",
" 47 +7.634251345602 -2.95 -1.66 6.86ms\n",
" 48 +7.633381461756 -3.06 -1.67 6.93ms\n",
" 49 +7.632734036503 -3.19 -1.63 6.86ms\n",
" 50 +7.631992464845 -3.13 -1.50 6.88ms\n",
" 51 +7.631214669225 -3.11 -1.67 6.87ms\n",
" 52 +7.628966877377 -2.65 -1.71 6.93ms\n",
" 53 +7.627769889617 -2.92 -1.57 9.52ms\n",
" 54 +7.626493495055 -2.89 -1.67 7.74ms\n",
" 55 +7.625362880083 -2.95 -1.93 7.69ms\n",
" 56 +7.624719771948 -3.19 -1.79 7.72ms\n",
" 57 +7.624065432201 -3.18 -1.84 10.1ms\n",
" 58 +7.623627131627 -3.36 -1.80 7.74ms\n",
" 59 +7.623063325217 -3.25 -1.77 10.1ms\n",
" 60 +7.622513571968 -3.26 -1.67 10.1ms\n",
" 61 +7.622304232555 -3.68 -1.62 7.67ms\n",
" 62 +7.622144507543 -3.80 -1.64 7.67ms\n",
" 63 +7.621366277558 -3.11 -1.80 7.66ms\n",
" 64 +7.620865506767 -3.30 -1.83 10.1ms\n",
" 65 +7.620390415967 -3.32 -1.69 7.66ms\n",
" 66 +7.619555774826 -3.08 -1.89 34.1ms\n",
" 67 +7.618806973614 -3.13 -1.72 10.7ms\n",
" 68 +7.618342113496 -3.33 -1.86 14.1ms\n",
" 69 +7.617921113585 -3.38 -1.76 10.5ms\n",
" 70 +7.617472932331 -3.35 -1.91 10.4ms\n",
" 71 +7.616656545146 -3.09 -1.98 10.0ms\n",
" 72 +7.615995037878 -3.18 -1.61 9.10ms\n",
" 73 +7.615433494626 -3.25 -1.62 9.04ms\n",
" 74 +7.615296991708 -3.86 -1.88 6.87ms\n",
" 75 +7.614934965217 -3.44 -2.01 6.87ms\n",
" 76 +7.614553545761 -3.42 -1.70 8.96ms\n",
" 77 +7.614351526492 -3.69 -1.90 6.86ms\n",
" 78 +7.614034422786 -3.50 -2.02 6.86ms\n",
" 79 +7.613932579643 -3.99 -1.96 6.85ms\n",
" 80 +7.613855770699 -4.11 -1.95 6.94ms\n",
" 81 +7.613551057470 -3.52 -1.80 6.88ms\n",
" 82 +7.613307451406 -3.61 -2.10 6.85ms\n",
" 83 +7.612962782429 -3.46 -2.06 6.89ms\n",
" 84 +7.612603967210 -3.45 -1.92 6.90ms\n",
" 85 +7.612074668409 -3.28 -1.89 6.89ms\n",
" 86 +7.611955758084 -3.92 -1.86 6.94ms\n",
" 87 +7.611513536152 -3.35 -2.11 6.84ms\n",
" 88 +7.611298540227 -3.67 -1.89 6.90ms\n",
" 89 +7.611159598830 -3.86 -1.94 6.95ms\n",
" 90 +7.610971271236 -3.73 -1.79 6.95ms\n",
" 91 +7.610495806947 -3.32 -1.77 9.01ms\n",
" 92 +7.610006811646 -3.31 -1.82 9.03ms\n",
" 93 +7.609681656177 -3.49 -1.95 6.86ms\n",
" 94 +7.609555914283 -3.90 -1.99 6.92ms\n",
" 95 +7.609108483111 -3.35 -1.76 9.00ms\n",
" 96 +7.608883899260 -3.65 -2.01 6.90ms\n",
" 97 +7.608616711585 -3.57 -1.88 6.84ms\n",
" 98 +7.608343081069 -3.56 -2.17 6.89ms\n",
" 99 +7.608075675107 -3.57 -1.95 6.89ms\n",
" 100 +7.608062108717 -4.87 -1.86 6.86ms\n",
" 101 +7.607642902001 -3.38 -1.71 9.01ms\n",
" 102 +7.607221432483 -3.38 -2.08 6.87ms\n",
" 103 +7.606890632365 -3.48 -2.15 6.88ms\n",
" 104 +7.606662167275 -3.64 -1.97 6.91ms\n",
" 105 +7.606335212744 -3.49 -1.69 9.04ms\n",
" 106 +7.606172571411 -3.79 -2.08 6.86ms\n",
" 107 +7.605953573795 -3.66 -1.87 9.02ms\n",
" 108 +7.605816540524 -3.86 -1.99 9.05ms\n",
" 109 +7.605706131556 -3.96 -2.21 7.71ms\n",
" 110 +7.605574831823 -3.88 -2.11 7.66ms\n",
" 111 +7.605395912571 -3.75 -1.69 10.1ms\n",
" 112 +7.605292445624 -3.99 -2.10 10.1ms\n",
" 113 +7.605152728412 -3.85 -2.18 7.74ms\n",
" 114 +7.605054857443 -4.01 -2.18 7.70ms\n",
" 115 +7.604966014114 -4.05 -2.00 7.74ms\n",
" 116 +7.604849930579 -3.94 -2.40 7.72ms\n",
" 117 +7.604747088523 -3.99 -2.14 7.65ms\n",
" 118 +7.604667149368 -4.10 -2.31 7.69ms\n",
" 119 +7.604626355562 -4.39 -2.26 7.67ms\n",
" 120 +7.604548143952 -4.11 -2.19 10.1ms\n",
" 121 +7.604484428593 -4.20 -2.27 10.1ms\n",
" 122 +7.604418177852 -4.18 -2.43 20.0ms\n",
" 123 +7.604366564215 -4.29 -2.50 6.92ms\n",
" 124 +7.604317236376 -4.31 -2.35 9.05ms\n",
" 125 +7.604283188828 -4.47 -2.32 6.88ms\n",
" 126 +7.604257456314 -4.59 -2.41 6.88ms\n",
" 127 +7.604249547980 -5.10 -2.36 6.90ms\n",
" 128 +7.604210654808 -4.41 -2.38 6.91ms\n",
" 129 +7.604204920247 -5.24 -2.27 6.86ms\n",
" 130 +7.604204315242 -6.22 -2.17 6.90ms\n",
" 131 +7.604142342776 -4.21 -2.57 6.84ms\n",
" 132 +7.604074618361 -4.17 -2.55 6.87ms\n",
" 133 +7.604068741935 -5.23 -2.40 6.88ms\n",
" 134 +7.604044516795 -4.62 -2.47 6.92ms\n",
" 135 +7.604028472558 -4.79 -2.60 6.86ms\n",
" 136 +7.604021721120 -5.17 -2.35 6.85ms\n",
" 137 +7.604015390104 -5.20 -2.40 6.88ms\n",
" 138 +7.603979691104 -4.45 -2.35 9.06ms\n",
" 139 +7.603970535853 -5.04 -2.41 6.89ms\n",
" 140 +7.603970444967 -7.04 -2.19 7.03ms\n",
" 141 +7.603912051361 -4.23 -2.04 9.15ms\n",
" 142 +7.603886594053 -4.59 -2.47 9.05ms\n",
" 143 +7.603849505724 -4.43 -2.58 6.91ms\n",
" 144 +7.603801478355 -4.32 -2.38 6.90ms\n",
" 145 +7.603788549395 -4.89 -2.39 6.95ms\n",
" 146 +7.603760625900 -4.55 -2.42 9.10ms\n",
" 147 +7.603721537221 -4.41 -2.12 9.06ms\n",
" 148 +7.603720768963 -6.11 -2.14 6.88ms\n",
" 149 +7.603683256937 -4.43 -2.67 6.91ms\n",
" 150 +7.603668770158 -4.84 -1.99 6.87ms\n",
" 151 +7.603541835717 -3.90 -1.45 9.07ms\n",
" 152 +7.603459550282 -4.08 -2.21 6.98ms\n",
" 153 +7.603408618089 -4.29 -2.11 6.99ms\n",
" 154 +7.603362726792 -4.34 -2.20 6.90ms\n",
" 155 +7.603286145309 -4.12 -1.90 9.04ms\n",
" 156 +7.603181132907 -3.98 -1.44 9.11ms\n",
" 157 +7.603105468758 -4.12 -1.98 9.12ms\n",
" 158 +7.603047004272 -4.23 -1.96 9.04ms\n",
" 159 +7.603027387699 -4.71 -1.98 6.91ms\n",
" 160 +7.603001761116 -4.59 -1.96 6.84ms\n",
" 161 +7.602943262500 -4.23 -1.75 9.03ms\n",
" 162 +7.602854643797 -4.05 -2.14 9.01ms\n",
" 163 +7.602752766689 -3.99 -2.34 6.93ms\n",
" 164 +7.602666806725 -4.07 -1.82 7.70ms\n",
" 165 +7.602551788745 -3.94 -2.10 7.71ms\n",
" 166 +7.602476077413 -4.12 -2.19 7.76ms\n",
" 167 +7.602335792425 -3.85 -2.01 10.1ms\n",
" 168 +7.602282241846 -4.27 -1.89 7.66ms\n",
" 169 +7.602157464825 -3.90 -1.92 10.1ms\n",
" 170 +7.601985290778 -3.76 -1.96 7.82ms\n",
" 171 +7.601793481432 -3.72 -1.81 10.2ms\n",
" 172 +7.601617485561 -3.75 -1.98 10.1ms\n",
" 173 +7.601519680375 -4.01 -2.17 10.1ms\n",
" 174 +7.601393074673 -3.90 -1.92 10.1ms\n",
" 175 +7.601292208395 -4.00 -1.85 10.2ms\n",
" 176 +7.601143115679 -3.83 -2.18 20.5ms\n",
" 177 +7.601003075816 -3.85 -1.61 9.13ms\n",
" 178 +7.600910725953 -4.03 -1.88 9.03ms\n",
" 179 +7.600778845428 -3.88 -1.91 6.86ms\n",
" 180 +7.600729225817 -4.30 -2.03 6.88ms\n",
" 181 +7.600666952534 -4.21 -2.07 6.85ms\n",
" 182 +7.600544929342 -3.91 -1.84 6.85ms\n",
" 183 +7.600417651815 -3.90 -1.80 9.06ms\n",
" 184 +7.600368345418 -4.31 -1.97 6.95ms\n",
" 185 +7.600341045753 -4.56 -2.12 6.84ms\n",
" 186 +7.600219429306 -3.92 -2.16 6.84ms\n",
" 187 +7.600089275551 -3.89 -2.26 6.82ms\n",
" 188 +7.599969650745 -3.92 -2.25 6.96ms\n",
" 189 +7.599864002721 -3.98 -2.30 6.89ms\n",
" 190 +7.599859359149 -5.33 -2.22 6.84ms\n",
" 191 +7.599848946386 -4.98 -1.93 6.84ms\n",
" 192 +7.599747278263 -3.99 -1.91 9.09ms\n",
" 193 +7.599662651939 -4.07 -2.22 6.88ms\n",
" 194 +7.599548057453 -3.94 -2.28 6.92ms\n",
" 195 +7.599414828392 -3.88 -1.88 9.19ms\n",
" 196 +7.599269255408 -3.84 -1.72 9.07ms\n",
" 197 +7.599254089144 -4.82 -2.05 10.1ms\n",
" 198 +7.599168756777 -4.07 -2.14 10.7ms\n",
" 199 +7.599054158887 -3.94 -2.31 10.7ms\n",
" 200 +7.598891230708 -3.79 -2.12 10.5ms\n",
" 201 +7.598698974128 -3.72 -1.33 13.7ms\n",
" 202 +7.598644292117 -4.26 -1.81 7.13ms\n",
" 203 +7.598447466993 -3.71 -1.91 6.94ms\n",
" 204 +7.598259522533 -3.73 -2.25 6.87ms\n",
" 205 +7.597993104548 -3.57 -1.84 6.85ms\n",
" 206 +7.597844638631 -3.83 -2.01 6.84ms\n",
" 207 +7.597570334924 -3.56 -1.94 9.51ms\n",
" 208 +7.597255514048 -3.50 -1.66 9.07ms\n",
" 209 +7.596868922299 -3.41 -1.97 6.92ms\n",
" 210 +7.596775061661 -4.03 -1.97 6.84ms\n",
" 211 +7.596522036633 -3.60 -2.10 6.98ms\n",
" 212 +7.596257743664 -3.58 -1.83 9.15ms\n",
" 213 +7.595991671535 -3.58 -2.14 6.89ms\n",
" 214 +7.595950571043 -4.39 -2.01 6.96ms\n",
" 215 +7.595866139991 -4.07 -1.99 6.91ms\n",
" 216 +7.595657526756 -3.68 -2.35 6.90ms\n",
" 217 +7.595512237214 -3.84 -2.06 6.87ms\n",
" 218 +7.595412727029 -4.00 -2.24 6.89ms\n",
" 219 +7.595320665328 -4.04 -2.24 7.69ms\n",
" 220 +7.595183851206 -3.86 -2.30 7.72ms\n",
" 221 +7.595079114185 -3.98 -2.28 10.1ms\n",
" 222 +7.595051974584 -4.57 -2.28 7.67ms\n",
" 223 +7.595017429397 -4.46 -2.37 7.68ms\n",
" 224 +7.594950793859 -4.18 -2.40 7.66ms\n",
" 225 +7.594891059419 -4.22 -2.38 7.69ms\n",
" 226 +7.594814288704 -4.11 -2.18 10.2ms\n",
" 227 +7.594772258032 -4.38 -2.38 10.1ms\n",
" 228 +7.594735887918 -4.44 -2.46 7.64ms\n",
" 229 +7.594735388002 -6.30 -2.37 7.68ms\n",
" 230 +7.594696139905 -4.41 -2.41 10.1ms\n",
" 231 +7.594662716381 -4.48 -2.45 7.68ms\n",
" 232 +7.594634790781 -4.55 -2.68 20.1ms\n",
" 233 +7.594612520835 -4.65 -2.27 6.94ms\n",
" 234 +7.594610061760 -5.61 -2.19 6.92ms\n",
" 235 +7.594566692420 -4.36 -2.46 6.82ms\n",
" 236 +7.594524003110 -4.37 -2.28 6.83ms\n",
" 237 +7.594447487481 -4.12 -2.50 6.90ms\n",
" 238 +7.594419841305 -4.56 -2.30 6.87ms\n",
" 239 +7.594342357897 -4.11 -2.23 6.86ms\n",
" 240 +7.594218789678 -3.91 -1.98 9.03ms\n",
" 241 +7.594142958325 -4.12 -2.63 6.84ms\n",
" 242 +7.594082449264 -4.22 -2.25 8.98ms\n",
" 243 +7.594068370484 -4.85 -2.32 6.88ms\n",
" 244 +7.594012486600 -4.25 -1.99 9.10ms\n",
" 245 +7.593936940549 -4.12 -1.92 9.01ms\n",
" 246 +7.593902625613 -4.46 -2.19 6.87ms\n",
" 247 +7.593884856311 -4.75 -2.39 6.90ms\n",
" 248 +7.593858165746 -4.57 -2.32 6.90ms\n",
" 249 +7.593791362418 -4.18 -1.68 9.10ms\n",
" 250 +7.593743460555 -4.32 -2.16 6.93ms\n",
" 251 +7.593728181606 -4.82 -2.41 6.92ms\n",
" 252 +7.593692465239 -4.45 -2.56 6.92ms\n",
" 253 +7.593652384893 -4.40 -2.50 6.91ms\n",
" 254 +7.593639810369 -4.90 -2.36 6.90ms\n",
" 255 +7.593610390181 -4.53 -2.46 6.88ms\n",
" 256 +7.593577708757 -4.49 -2.38 9.17ms\n",
" 257 +7.593557412118 -4.69 -2.52 6.87ms\n",
" 258 +7.593534549621 -4.64 -2.57 6.90ms\n",
" 259 +7.593528482991 -5.22 -2.43 6.88ms\n",
" 260 +7.593516536549 -4.92 -2.49 6.89ms\n",
" 261 +7.593492913341 -4.63 -2.63 6.94ms\n",
" 262 +7.593469762821 -4.64 -2.40 9.06ms\n",
" 263 +7.593457264644 -4.90 -2.56 6.92ms\n",
" 264 +7.593454471361 -5.55 -2.70 6.92ms\n",
" 265 +7.593436761215 -4.75 -2.69 6.97ms\n",
" 266 +7.593420658964 -4.79 -2.52 9.08ms\n",
" 267 +7.593407240822 -4.87 -2.87 6.92ms\n",
" 268 +7.593393025468 -4.85 -2.52 9.15ms\n",
" 269 +7.593384800545 -5.08 -2.76 6.91ms\n",
" 270 +7.593369971618 -4.83 -2.34 9.00ms\n",
" 271 +7.593368953237 -5.99 -2.34 6.94ms\n",
" 272 +7.593359504168 -5.02 -2.81 6.90ms\n",
" 273 +7.593347728143 -4.93 -2.80 6.90ms\n",
" 274 +7.593343932065 -5.42 -2.43 6.87ms\n",
" 275 +7.593326319399 -4.75 -2.25 10.1ms\n",
" 276 +7.593317567877 -5.06 -2.76 7.84ms\n",
" 277 +7.593300234068 -4.76 -2.74 7.68ms\n",
" 278 +7.593287917154 -4.91 -2.60 7.66ms\n",
" 279 +7.593273703631 -4.85 -2.73 7.69ms\n",
" 280 +7.593263808691 -5.00 -2.63 7.70ms\n",
" 281 +7.593246074512 -4.75 -2.74 7.72ms\n",
" 282 +7.593226756396 -4.71 -2.32 10.2ms\n",
" 283 +7.593207967864 -4.73 -2.50 7.76ms\n",
" 284 +7.593191864798 -4.79 -2.42 7.69ms\n",
" 285 +7.593157051572 -4.46 -1.77 10.1ms\n",
" 286 +7.593144029784 -4.89 -2.48 10.1ms\n",
" 287 +7.593116813381 -4.57 -2.16 7.66ms\n",
" 288 +7.593105669887 -4.95 -2.20 19.8ms\n",
" 289 +7.593078036173 -4.56 -2.03 6.93ms\n",
" 290 +7.593071360167 -5.18 -2.33 6.88ms\n",
" 291 +7.593040910083 -4.52 -2.13 9.10ms\n",
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" 882 +7.592300189776 -7.87 -3.28 6.86ms\n",
" 883 +7.592300179182 -7.97 -3.18 6.99ms\n",
" 884 +7.592300161403 -7.75 -3.07 10.1ms\n",
" 885 +7.592300155872 -8.26 -3.67 7.69ms\n",
" 886 +7.592300150047 -8.23 -3.62 10.1ms\n",
" 887 +7.592300146514 -8.45 -4.37 7.66ms\n",
" 888 +7.592300144606 -8.72 -4.20 7.77ms\n",
" 889 +7.592300138961 -8.25 -4.12 10.2ms\n",
" 890 +7.592300133073 -8.23 -4.17 7.74ms\n",
" 891 +7.592300130456 -8.58 -3.71 7.75ms\n",
" 892 +7.592300123224 -8.14 -3.92 7.69ms\n",
" 893 +7.592300121602 -8.79 -4.39 7.68ms\n",
" 894 +7.592300118746 -8.54 -4.27 7.72ms\n",
" 895 +7.592300114699 -8.39 -4.58 7.63ms\n",
" 896 +7.592300110033 -8.33 -4.22 10.1ms\n",
" 897 +7.592300104981 -8.30 -4.58 20.1ms\n",
" 898 +7.592300103785 -8.92 -4.35 6.91ms\n",
" 899 +7.592300100479 -8.48 -4.54 9.01ms\n",
" 900 +7.592300098679 -8.74 -4.54 6.99ms\n",
" 901 +7.592300096759 -8.72 -4.13 6.93ms\n",
" 902 +7.592300094138 -8.58 -4.23 9.01ms\n",
" 903 +7.592300091545 -8.59 -4.34 6.87ms\n",
" 904 +7.592300090769 -9.11 -4.08 6.84ms\n",
" 905 +7.592300087104 -8.44 -3.97 9.01ms\n",
" 906 +7.592300084898 -8.66 -4.18 6.83ms\n",
" 907 +7.592300082231 -8.57 -4.62 6.81ms\n",
" 908 +7.592300080300 -8.71 -4.60 6.85ms\n",
" 909 +7.592300075757 -8.34 -3.78 8.95ms\n",
" 910 +7.592300074073 -8.77 -4.37 9.01ms\n",
" 911 +7.592300073106 -9.01 -4.16 6.83ms\n",
" 912 +7.592300071367 -8.76 -4.10 8.99ms\n",
" 913 +7.592300069574 -8.75 -4.47 6.86ms\n",
" 914 +7.592300067037 -8.60 -4.45 6.91ms\n",
" 915 +7.592300064060 -8.53 -3.85 9.12ms\n",
" 916 +7.592300062853 -8.92 -4.56 9.01ms\n",
" 917 +7.592300060973 -8.73 -4.10 9.00ms\n",
" 918 +7.592300060037 -9.03 -4.93 6.88ms\n",
" 919 +7.592300059151 -9.05 -4.44 6.84ms\n",
" 920 +7.592300057877 -8.89 -4.88 6.84ms\n",
" 921 +7.592300056692 -8.93 -4.57 6.85ms\n",
" 922 +7.592300055995 -9.16 -4.34 6.98ms\n",
" 923 +7.592300053953 -8.69 -4.71 6.86ms\n",
" 924 +7.592300053509 -9.35 -4.64 6.83ms\n",
" 925 +7.592300052080 -8.85 -4.36 6.87ms\n",
" 926 +7.592300050870 -8.92 -4.28 8.99ms\n",
" 927 +7.592300049437 -8.84 -4.51 6.87ms\n",
" 928 +7.592300047679 -8.76 -4.55 6.88ms\n",
" 929 +7.592300046266 -8.85 -4.58 6.91ms\n",
" 930 +7.592300046200 -10.18 -4.48 6.84ms\n",
" 931 +7.592300045387 -9.09 -4.76 6.85ms\n",
" 932 +7.592300045272 -9.94 -4.44 6.88ms\n",
" 933 +7.592300043394 -8.73 -4.14 9.01ms\n",
" 934 +7.592300042487 -9.04 -4.42 8.99ms\n",
" 935 +7.592300041354 -8.95 -4.11 9.00ms\n",
" 936 +7.592300040525 -9.08 -4.29 9.02ms\n",
" 937 +7.592300040095 -9.37 -4.67 6.89ms\n",
" 938 +7.592300039986 -9.97 -4.48 7.34ms\n",
" 939 +7.592300039830 -9.80 -4.87 7.71ms\n",
" 940 +7.592300039200 -9.20 -5.06 7.80ms\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": 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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"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
}
],
"nbformat_minor": 3,
"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.10.2"
},
"kernelspec": {
"name": "julia-1.10",
"display_name": "Julia 1.10.2",
"language": "julia"
}
},
"nbformat": 4
}