File:Many Interacting Worlds-Tunneling.gif

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Many_Interacting_Worlds-Tunneling.gif (360 × 293 pixels, file size: 1.53 MB, MIME type: image/gif, looped, 200 frames)

Captions

Captions

Tunneling in the Many Interacting World interpretation

Summary

[edit]
Description
English: In the Many Interacting World interpretation of QM particle behave classically, apart from interacting with their own copies in other worlds. As this interaction is repulsive, it can give one of the copies enough energy to jump over a barrier (tunneling).
Date
Source https://twitter.com/j_bertolotti/status/1118519904330821632
Author Jacopo Bertolotti
Permission
(Reusing this file)
https://twitter.com/j_bertolotti/status/1030470604418428929

Mathematica 11.0 code

[edit]
Clear[pos, posold, posoldold, acc];
np = 30;
m = 1;
k = 10;
dt = 0.002;
b = 0.1;
pos = Table[RandomReal[{-1, -0.2}], np];
v0 = Table[0, np];
nstep = 2000;
V = x^2 + 1. E^(-(x^2/(2 0.01^2)));
dV = D[V, x];
posold = pos;
posoldold = pos;
evoq = Reap[Do[
      P = (Exp[-Sqrt[(x - #)^2]/b] &) /@ pos;
      acc = Table[
        -k (dV /. {x -> pos[[j]]}) - (Evaluate[D[0.01 (Total@Drop[D[P, x], {j}]/Total@Drop[P, {j}])^2, x]] /. {x -> pos[[j]]})
        , {j, 1, np}];
      posoldold = posold;
      posold = pos;
      pos = 2 posold - posoldold + acc dt^2;
      Sow[{pos, m/2 ((pos - posold)/dt)^2 + k/2 pos^2}];
      (*Print[posoldold,posold,pos,acc];*)
      , nstep];][[2, 1]];
p1q = Table[
   Show[
    Plot[V, {x, -1, 1}, PlotStyle -> {Red, Thick, Dashed}, Ticks -> None, AxesLabel -> {"x", "E"}, LabelStyle -> {Black, Bold}, PlotLabel -> 
      "Quantum case:\n copies do interact (U=|\!\(\*FractionBox[\(\\[Del]\[Rho]\), \(\[Rho]\)]\)\!\(\*SuperscriptBox[\(|\), \(2\)]\))"],    Graphics[{Table[{Opacity[0.3], Disk[{evoq[[j, 1, n]], 0}, 0.05]}, {n, 1, np}]}, PlotRange -> {{-1., 1.}, {-1, 1}}]
    ]
   , {j, 1, nstep, 10}];
ListAnimate[p1q]

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
current11:54, 18 April 2019Thumbnail for version as of 11:54, 18 April 2019360 × 293 (1.53 MB)Berto (talk | contribs)User created page with UploadWizard

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