mirror of
https://github.com/dmallubhotla/nam_paper.git
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68 lines
2.3 KiB
Plaintext
68 lines
2.3 KiB
Plaintext
Needs["namConductivity`"];
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Needs["namAsymptoticLowKConductivity`"];
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(* Defines lindhard functions *)
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epsL[qP_?NumericQ, omegaP_?NumericQ, vfP_?NumericQ, omegapP_?NumericQ,
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tauP_?NumericQ] :=
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With[{u = (vfP*qP)/omegaP, s = 1/(tauP*omegaP),
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prefactor = 3*(omegapP^2)/(omegaP^2)},
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1 + ((prefactor)/(u^2))*(1 + ((1 + I*s)/(2*u))*
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Log[(1 - u + I*s)/(1 + u + I*s)])/(1 + ((I*s)/(2*u))*
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Log[(1 - u + I*s)/(1 + u + I*s)])];
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epsSeries[qP_?NumericQ, omegaP_?NumericQ, vfP_?NumericQ,
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omegapP_?NumericQ, tauP_?NumericQ] :=
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With[{u = (vfP*qP)/omegaP, s = 1/(tauP*omegaP),
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prefactor = 3*(omegapP^2)/(omegaP^2)},
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1 + ((prefactor)) ((I/(3*(s - I))) +
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u^2*(-9*I + 5*s)/(45*(-I + s)^3))];
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epsEf[q_?NumericQ, omega_?NumericQ, vf_?NumericQ, omegap_?NumericQ,
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tau_?NumericQ] :=
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epsEf[q, omega, vf, omegap, tau] =
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Piecewise[{{epsSeries[q, omega, vf, omegap, tau],
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q < .01 * omega / vf}, {epsL[q, omega, vf, omegap, tau],
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q >= .01 * omega / vf}}];
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(* Nam stuff *)
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makeDimensionlessParams[\[Omega]_, \[Sigma]n_, \[Tau]_, vf_, T_, Tc_] :=
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With[{\[CapitalDelta] =
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3.06*Sqrt[
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Tc*(Tc - T)]}, <|\[Xi] -> \[Omega]/\[CapitalDelta], \[Nu] ->
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1/(\[CapitalDelta]*\[Tau]), A -> \[Omega]*vf/(1*\[CapitalDelta]),
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t -> T/\[CapitalDelta], B -> \[Sigma]n/\[Omega],
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C -> vf/\[CapitalDelta]|>];
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omega = 1;
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tau := .5;
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omegaPlasma := 10;
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sigmaN := omegaPlasma^2 * tau / (4 * Pi);
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vf := 1
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tempCritical := 3
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temp := .9999 * tempCritical
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params := makeDimensionlessParams[omega, sigmaN, tau, vf, temp, tempCritical]
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Print[params];
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epsNam2[q_, ps_] := With[
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{k = ps[C] * q},
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1 + 4 * Pi * I *
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ps[B] * \[CapitalSigma][ps[\[Xi]], k, ps[\[Nu]], ps[t]]
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];
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(* Populates the figures directory as ../figures *)
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figuresDirectory = FileNameJoin[{
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ParentDirectory[
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DirectoryName[
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FileNameJoin[{
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Directory[],
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$ScriptCommandLine[[1]]
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}]
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]
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], "figures"
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}];
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figure[filename_] := FileNameJoin[{figuresDirectory, filename}];
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plot1 = LogLinearPlot[ {Re@epsEf[q, omega, vf, omegaPlasma, tau], Re@epsNam2[q, params]} , {q, 0, 10^2}, ImageSize -> Large, AxesLabel -> {"q", StringForm["Re[\[Epsilon](q, \[Omega] = 1)]"]}, PlotRange -> All, PlotLegends -> {Lindhard, Nam}, ImagePadding -> {{50, Automatic}, {Automatic, Automatic}}];
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Export[figure["Cond1Re.jpg"], plot1, ImageResolution -> 1200];
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