File:Anderson Localization- modes vs disorder.gif

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Original file ‎(743 × 780 pixels, file size: 11.28 MB, MIME type: image/gif, looped, 52 frames)

Captions

Captions

Modes vs disorder

Summary

[edit]
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

[edit]
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]

Licensing

[edit]
I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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Date/TimeThumbnailDimensionsUserComment
current09:51, 12 February 2020Thumbnail for version as of 09:51, 12 February 2020743 × 780 (11.28 MB)Berto (talk | contribs)User created page with UploadWizard

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