File:Anderson Localization- modes vs disorder.gif
Summary
| Description |
English: In a periodic potential all eigenmodes will be extended. But if disorder is introduced the eigenmodes are first deformed and then become exponentially confined in a small region of the sample. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1226819009967878144 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
blu[z_] := {RGBColor[1 - z^0.2, 1 - z^0.2, 1], Opacity[z]};
dim = 30;
randomness = 1;
disorder = DiagonalMatrix[RandomReal[{-randomness, randomness}, dim^2]];
structdis = Table[RandomReal[{-randomness/5, randomness/5}], {i, 1, dim}, {j, 1, dim}];
moden = 4;
p1 = Table[
chain2dd = Normal[-KirchhoffMatrix[GridGraph[{dim, dim}]]] + \[Alpha] disorder;
\[Zeta] = Eigenvectors[chain2dd, moden];
GraphicsGrid@Partition[Table[
Show[
Graphics[{Table[{Disk[{i, j}, 0.3 + \[Alpha] structdis[[i, j]]]}, {i, 1, dim}, {j, 1, dim}], {Text[Style[StringForm["Mode #``", k], Bold, FontSize -> 15], {15, 32}]}}], ListContourPlot[Partition[Abs[\[Zeta][[k]]], dim], PlotRange -> All, ColorFunction -> blu, InterpolationOrder -> 3, Frame -> False, DataRange -> {{0.5, 30.5}, {0.5, 30.5}}], ImageSize -> Medium
]
, {k, 1, moden}], 2], {\[Alpha], 0, 1, 0.05}];
ListAnimate[p1]
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