File:Quantum Zeno effect animation.gif
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Quantum_Zeno_effect_animation.gif (700 × 350 pixels, file size: 2.8 MB, MIME type: image/gif, looped, 130 frames, 13 s)
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Summary
| Description |
English: Schematic depiction of quantum Zeno effect. A wave function smoothly "melts" as a result of its free time evolution, see the left part. A quantum measurement localizes the wave function in one of the nine sectors, where the choice of a sector depends on its overlap with the wave function, see the middle part. If one performs a series of successive measurements, the overlap of the wave function with border sectors is negligible and the function is localized every time in the central sector, see the right part. This last case corresponds to the quantum Zeno effect. Čeština: Schématické znázornění kvantového Zenónova jevu. Vlnová funkce se v rámci svého volného časového vývoje "rozlévá" do stran, viz levá část. Kvantové měření lokalizuje vlnovou funkci v jednom z devíti sektorů, přičemž volba sektoru závisí na jeho překryvu s vlnovou funkcí, viz střední část. Pokud provádíme sérii těsně po sobě jdoucích měření, je překryv funkce s okrajovými sektory zanedbatelný a funkce je tak lokalizována neustále v prostředním sektoru, viz pravá část. Tento poslední případ odpovídá kvantovému Zenónově jevu. |
| Date | |
| Source | Own work |
| Author | JozumBjada |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Source code
This animation was created using Wolfram language 12.0.0 for Microsoft Windows (64-bit) (April 6, 2019). The source code follows.
(* ::Package:: *)
(* ::Chapter:: *)
(*Routines*)
(* ::Input::Initialization:: *)
indicatorMeas[t_,num_:7]:=Module[{tloc,measpos,m=1.9,h=1,line},
line=Line;
tloc=Rescale[t,{0,1},{-m,m}];
measpos=Round[tloc,2m/num]-Boole[OddQ[num]]m/num;
{
{Thickness[0.01],Translate[line[{{0,0,0},{0,0,h}}],{{0,-m,0},{0,m,0}}]},
Translate[line[{{0,0,0},{0,0,h}}],{0,#,0}&/@Subdivide[-m,m,num]],
line[{{0,-m,h/2},{0,m,h/2}}],
{Gray,Thickness[.012],line[{{0,tloc,0},{0,tloc,h}}]},
If[Abs[tloc-measpos]<.05,{Red,Thickness[.015],line[{{0,measpos,0},{0,measpos,h}}]},{}]
}
]
(* ::Input::Initialization:: *)
measAxes=Module[{list,polFun},
polFun[y_]:=With[{x=2,z=.8},Polygon[{{-x,y,0},{x,y,0},{x,y,z},{-x,y,z}}]];
list=polFun/@(2{1,1/3,-1/3,-1});
{EdgeForm[],Red,list,Rotate[#,\[Pi]/2,{0,0,1}]&/@list}
];
(* ::Input::Initialization:: *)
zrange={-.1,1.01/(2\[Pi] (0.2)^2)};
(* ::Input::Initialization:: *)
ClearAll[plot]
plot[t_,evollist_]:=Module[{m=2,plot,\[Sigma],tloc,meas=measAxes,x0,y0,num=Length[evollist],idx,corrfac=.95,meshlist,fac,max\[Sigma]=.6,min\[Sigma]=.2},
fac=2m/3;
{idx,tloc}=QuotientRemainder[t,1/num];
\[Sigma]=Rescale[tloc,{0,1},{corrfac min\[Sigma],max\[Sigma]}];
\[Sigma]=Clip[\[Sigma],{min\[Sigma],max\[Sigma]}];
{x0,y0}=evollist[[Clip[idx+1,{1,Length[evollist]}]]];
meshlist={{Automatic,Automatic,Automatic},{Automatic,Automatic,Automatic},{Automatic,Automatic,Automatic}};
If[tloc<0.03,meshlist=ReplacePart[meshlist,{y0+2,x0+2}->Red]];
plot=Plot3D[1/(2\[Pi] \[Sigma]^2)Exp[-((x-fac x0)^2+(y-fac y0)^2)/(2\[Sigma]^2)],{x,-m,m},{y,-m,m},
Filling->If[\[Sigma]>1,Bottom,None],PlotRange->{{-m,m},{-m,m},zrange},Axes->False,Boxed->False,
Mesh->2,MeshFunctions->{#1&,#2&},MeshShading->meshlist,
PlotPoints->30,ViewCenter->{{0.5,.5,.5},{0.5,0.6}}];
plot=First@Cases[plot,_GraphicsComplex,Infinity,1];
plot={plot,Translate[indicatorMeas[t,num],{-m-.3,0,0}]};
If[tloc<0.03&&idx!=0,{plot,meas},{plot}]
]
(* ::Input::Initialization:: *)
animation[ti_]:=Module[{elist1,elist2,elist3,t=Clip[ti,{0,0.99}],grid},
elist1={{0,0}};
elist2={{0,0},{0,1},{0,1},{1,1},{1,0}};
elist3=Table[{0,0},21];
grid=Show[
Graphics3D[plot[t,elist1]],
Graphics3D[Translate[plot[t,elist2],{5,0,0}]],
Graphics3D[Translate[plot[t,elist3],{10,0,0}]],
Boxed->False,PlotRange->{{-2.3,12},{-2,2},zrange},BoxRatios->{3,1,.5}
];
Graphics[{Inset[grid,ImageScaled[{0.5,0.62}],ImageScaled[{0.5,0.5}],2]},PlotRange->{{-1,1},.5{-1,1}},ImageSize->800]
];
(* ::Chapter:: *)
(*Generation and export*)
(* ::Input:: *)
(*(*Manipulate[animation[t],{{t,0.808},0,1}]*)*)
(* ::Input:: *)
(*numOfFrames=130;*)
(*rasterSize=700;*)
(*{time,frames}=AbsoluteTiming[ParallelMap[Rasterize[#,RasterSize->rasterSize]&,Table[animation[t],{t,Subdivide[numOfFrames-1]}]]];*)
(*Print["The calculation took ",time/60.," minutes."];*)
(* ::Input:: *)
(*(*Echo[numOfFrames Times@@ImageDimensions[frames[[1]]]]\[LessEqual]100*^6*)*)
(* ::Input:: *)
(*(*ListAnimate[frames,AnimationRate\[Rule]5]*)*)
(* ::Input:: *)
(*SetDirectory[NotebookDirectory[]]*)
(*Export["zeno_anim.gif",frames,AnimationRepetitions->Infinity]*)
(*FileSize[%]*)
(* ::Input:: *)
(*(*SystemOpen[%%]*)*)
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:27, 18 November 2021 | | 700 × 350 (2.8 MB) | JozumBjada | Cross-wiki upload from cs.wikipedia.org |
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