68 lines
2.3 KiB
Matlab
68 lines
2.3 KiB
Matlab
function [evals, modes] = solveBogoliubovdeGennesIn2D(psi, Params, VDk, VParams, Transf, muchem)
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gs = Params.gs;
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gdd = Params.gdd;
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gammaQF = Params.gammaQF;
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KEop = 0.5*(Transf.KX.^2+Transf.KY.^2);
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g_pf_2D = 1/(sqrt(2*pi)*VParams.ell);
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gQF_pf_2D = sqrt(2/5)/(pi^(3/4)*VParams.ell^(3/2));
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Ez = (0.25/VParams.ell^2) + (0.25*Params.gz*VParams.ell^2);
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muchem_tilde = muchem - Ez;
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% eigs only works with column vectors
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psi = psi.';
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KEop = KEop.';
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VDk = VDk.';
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% Interaction Potential
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frho = fftn(abs(psi).^2);
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Phi = real(ifftn(frho.*VDk));
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% Operators
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H = @(w) real(ifft(KEop.*fft(w)));
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C = @(w) (((g_pf_2D*gs*abs(psi).^2) + (g_pf_2D*gdd*Phi)).*w) + (gQF_pf_2D*gammaQF*abs(psi).^3.*w);
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muHC = @(w) (-muchem_tilde * w) + H(w) + C(w);
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X = @(w) (psi.*real(ifft(VDk.*fft(psi.*w)))) + (3/2)*(gQF_pf_2D*gammaQF*abs(psi).^3).*w;
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% 2-D matrix will be unravelled to a single column vector and the corresponding BdG matrix of (N^2)^2 elements solved for.
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Size = length(psi(:));
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Neigs = length(psi(:));
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opts.tol = 1e-16;
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opts.disp = 1;
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opts.issym = 0;
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opts.isreal = 1;
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opts.maxit = 1e4;
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BdGVec = @(g) BdGSolver2D.BdGMatrix(g, psi, Params, VDk, VParams, Transf, muchem); % This function takes a column vector as input and returns a
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% matrix-vector product which is also a column vector
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[g,D] = eigs(BdGVec,Size,Neigs,'sr',opts);
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evals = diag(D);
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clear D;
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% Eigenvalues
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evals = sqrt(evals);
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% Obtain f from g
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for ii = 1:Neigs
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gres = reshape(g(:,ii), size(psi));
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f(:,ii) = reshape((1/evals(ii)) * (muHC(gres) + (2.*X(gres))), [], 1);
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end
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% Obtain u and v from f and g
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u = (f + g)/2;
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v = (f - g)/2;
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% Renormalize to \int |u|^2 - |v|^2 = 1
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for ii=1:Neigs
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normalization = sum(abs(u(:,ii)).^2 - abs(v(:,ii)).^2);
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u(:,ii) = u(:,ii)/sqrt(normalization);
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v(:,ii) = v(:,ii)/sqrt(normalization);
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end
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modes.u = u'; modes.v = v';
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modes.g = g'; modes.f = f';
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end
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