File:Fermi Gas.gif
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Fermi_Gas.gif (480 × 297 pixels, file size: 2.29 MB, MIME type: image/gif, looped, 303 frames, 15 s)
Captions
Captions
Fermi function as a function of the temperature
Summary[edit]
| Description |
English: Fermions can't occupy the same energy state, so (at zero temperature) they just pile up until the last one has an energy known as the "Fermi energy". At nonzero temperature the lower energy fermions can't do anything because there is no free state to excite them too, but the ones close to the Fermi energy can be excited, and thus (e.g.) contribute to conductivity. |
| Date | |
| Source | https://mathstodon.xyz/@j_bertolotti/112365117189864463 |
| Author | Berto |
| Permission (Reusing this file) |
https://mathstodon.xyz/@j_bertolotti/111363365323269417 |
Mathematica 14.0 code[edit]
pfd[\[CapitalEpsilon]_, \[Mu]_, T_] := 1/(Exp[(\[CapitalEpsilon] - \[Mu])/(T)] + 1);
nparticles = 100;
plot[T_] := Module[{occupation, excited, j, n},
occupation = Boole[RandomReal[] <= #] & /@ Table[pfd[en, nparticles, T], {en, 1, nparticles}];
dim = Dimensions[occupation][[1]];
excited = {};
If[Dimensions[Position[occupation, 0]][[1]] > 0,
For[i = 1, i <= Dimensions[Position[occupation, 0]][[1]], i++,
j = 0;
Until[n == 1 && (Not@MemberQ[excited, j]),
j++;
If[j > 3*T, Break[];];
n = Boole[RandomReal[] <= Exp[-(nparticles + j - Position[occupation, 0][[i, 1]])/T] ];
];
AppendTo[excited, j];
];
occupation =
Join[occupation, Table[If[MemberQ[excited, j], 1, 0], {j, 1, Max[excited]}]];
];
Plot[pfd[e, nparticles, T], {e, 0, 1.7*nparticles}, PlotStyle -> Directive[Thickness[0.01], Purple], Axes -> False, PlotRange -> {{-10, 1.9*nparticles}, {-0.1, 1.1}},
Prolog -> {Orange, Rectangle[{nparticles - T, 0}, {nparticles + T, 1}], Black, Arrow[{{0, 0}, {1.9*nparticles, 0}}], Arrow[{{0, 0}, {0, 1.1}}], Text[Style["Fermi Energy", Medium, Bold], {nparticles, 1.05}], Text[Style["\!\(\*SubscriptBox[\(k\), \(B\)]\)T", Medium, Bold, Orange], {nparticles + T + 10, 0.8}]},
Epilog -> {Table[ Disk[{j, 0}, 1*occupation[[j]]*{1, 1/nparticles}], {j, 1, Dimensions[occupation][[1]]}], Thick, Dashed, Line[{{nparticles, 0}, {nparticles, 1}}], Rotate[Text[Style["Fermi Function", Medium, Bold], {-5, 0.5}], \[Pi]/2], Text[Style["Energy", Medium, Bold], {0.8*nparticles, -0.06}]}]
]
sinstep[t_] := Sin[\[Pi]/2 t]^2;
frames = Flatten@Table[Table[plot[20*sinstep[t] + 0.001], {3}], {t, 0, 1, 0.01}];
ListAnimate[frames]
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
 
|
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/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:13, 2 May 2024 | | 480 × 297 (2.29 MB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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