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Solver for the 2-D BdG equations.

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Karthik 2024-11-12 18:50:42 +01:00
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Bogoliubov-deGennes-Solver/solveBogoliubovdeGennesIn2D.m Normal file
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function [evals, modes] = solveBogoliubovdeGennesIn2D(psi, Params, VDk, VParams, muchem)
wz_tilde = Params.wz / Params.w0;
gs = Params.gs;
gdd = Params.gdd;
gammaQF = Params.gammaQF;
KEop = 0.5*kx.^2 + 0.5*ky.^2;
Ez = (0.25*VParams.sigma^2) + (0.25*wz_tilde^2*VParams.sigma^2);
muchem_tilde = muchem - Ez;
gs_pf_2D = 1/(sqrt(2*pi)*VParams.sigma);
gdd_pf_2D = sqrt(2/5)/(pi^(3/4)*VParams.sigma^(3/2));
% eigs only works with column vectors
psi = psi.';
KEop = KEop.';
VDk = VDk.';
% Interaction Potential
frho = fftn(abs(psi).^2);
Phi = real(ifftn(frho.*VDk));
H = @(w) real(ifft(KEop.*fft(w)));
C = @(w) (((gs_pf_2D*gs*abs(psi).^2) + (gdd_pf_2D*gdd*Phi)).*w) + (gammaQF.* abs(psi).^3 .*w);
muHC = @(w) (-muchem_tilde .* w) + H(w) + C(w);
X = @(w,psi) (psi.*real(ifft(VDk.*fft(psi.*w)))) + (3/2)*(gammaQF.* abs(psi).^3).*w;
BdG = @(g) muHC(muHC(g) + (2.*X(g)));
syssize = size(psi);
opts.v0 = psi(:);
opts.tol = 1e-16;
opts.disp = 1;
opts.issym = 0;
opts.isreal = 1;
opts.maxit = 1e4;
Neigs = syssize;
[g,D] = eigs(BdG,syssize,Neigs,'sr',opts);
evals = diag(D);
clear D;
% Eigenvalues
evals = sqrt(evals);
end