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Added and tested 2D BdG solver - works until Matlab starts solving for the eigen-values and vectors.

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Karthik 2024-11-22 16:18:27 +01:00
parent fd59a6199e
commit 196663e367
4 changed files with 141 additions and 38 deletions
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35
Dipolar-Gas-Simulator/+BdGSolver2D/BdGMatrix.m Normal file
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@ -0,0 +1,35 @@
function BdGVec = BdGMatrix(gVec, psi, Params, VDk, VParams, Transf, muchem)
gs = Params.gs;
gdd = Params.gdd;
gammaQF = Params.gammaQF;
KEop = 0.5*(Transf.KX.^2+Transf.KY.^2);
g_pf_2D = 1/(sqrt(2*pi)*VParams.ell);
gQF_pf_2D = sqrt(2/5)/(pi^(3/4)*VParams.ell^(3/2));
Ez = (0.25/VParams.ell^2) + (0.25*Params.gz*VParams.ell^2);
muchem_tilde = muchem - Ez;
% eigs only works with column vectors
psi = psi.';
KEop = KEop.';
VDk = VDk.';
% Interaction Potential
frho = fftn(abs(psi).^2);
Phi = real(ifftn(frho.*VDk));
% Operators
H = @(w) real(ifft(KEop.*fft(w)));
C = @(w) (((g_pf_2D*gs*abs(psi).^2) + (g_pf_2D*gdd*Phi)).*w) + (gQF_pf_2D*gammaQF*abs(psi).^3.*w);
muHC = @(w) (-muchem_tilde * w) + H(w) + C(w);
X = @(w) (psi.*real(ifft(VDk.*fft(psi.*w)))) + (3/2)*(gQF_pf_2D*gammaQF*abs(psi).^3).*w;
g = reshape(gVec, size(psi));
% Operate in order on g
BdG = muHC(muHC(g) + (2.*X(g)));
BdGVec = reshape(BdG, [], 1);
end

38
Dipolar-Gas-Simulator/+BdGSolver2D/solveBogoliubovdeGennesIn2D.m
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@ -1,44 +1,16 @@
function [evals, modes] = solveBogoliubovdeGennesIn2D(psi, Params, VDk, VParams, Transf, muchem)
gs = Params.gs;
gdd = Params.gdd;
gammaQF = Params.gammaQF;
KEop = 0.5*(Transf.KX.^2+Transf.KY.^2);
g_pf_2D = 1/(sqrt(2*pi)*VParams.ell);
gQF_pf_2D = sqrt(2/5)/(pi^(3/4)*VParams.ell^(3/2));
Ez = (0.25/VParams.ell^2) + (0.25*Params.gz*VParams.ell^2);
muchem_tilde = muchem - Ez;
% eigs only works with column vectors
psi = psi.';
KEop = KEop.';
VDk = VDk.';
% Interaction Potential
frho = fftn(abs(psi).^2);
Phi = real(ifftn(frho.*VDk));
% Operators
H = @(w) real(ifft(KEop.*fft(w)));
C = @(w) (((g_pf_2D*gs*abs(psi).^2) + (g_pf_2D*gdd*Phi)).*w) + (gQF_pf_2D*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)*(gQF_pf_2D*gammaQF*abs(psi).^3).*w;
% Operate in order on g
BdG = @(g) muHC(muHC(g) + (2.*X(g)));
syssize = size(psi);
opts.v0 = psi(:);
Size = length(psi(:));
Neigs = length(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);
BdGVec = @(g) BdGSolver2D.BdGMatrix(g, psi, Params, VDk, VParams, Transf, muchem);
[g,D] = eigs(BdGVec,Size,Neigs,'sr',opts);
evals = diag(D);
clear D;

37
Dipolar-Gas-Simulator/+Scripts/run_locally.m
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@ -88,7 +88,7 @@ OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 1e-2;
OptionsStruct.PlotLive = true;
OptionsStruct.JobNumber = 2;
OptionsStruct.JobNumber = 1;
OptionsStruct.RunOnGPU = false;
OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Data_TriangularPhase';
@ -100,7 +100,33 @@ pot = VariationalSolver2D.Potentials(options{:
solver.Potential = pot.trap();
%-% Run Solver %-%
[Params, Transf, psi, V, VDk] = solver.run();
% [Params, Transf, psi, V, VDk] = solver.run();
% Solve BdG equations
% Load data
Data = load(sprintf(horzcat(solver.SaveDirectory, '/Run_%03i/psi_gs.mat'),solver.JobNumber),'psi','Params','Transf');
Params = Data.Params;
Transf = Data.Transf;
if isgpuarray(Data.psi)
psi = gather(Data.psi);
else
psi = Data.psi;
end
VParams.ell = Params.ell;
% == DDI potential == %
VDk = solver.Calculator.calculateVDkWithCutoff(Transf, Params, VParams.ell);
% == Trap potential == %
X = Transf.X; Y = Transf.Y;
V = 0.0*(Params.gx.*X.^2+Params.gy.*Y.^2);
% == Chemical potential == %
muchem = solver.Calculator.calculateChemicalPotential(psi,Params,VParams,Transf,VDk,V);
[evals, modes] = BdGSolver2D.solveBogoliubovdeGennesIn2D(psi, Params, VDk, VParams, Transf, muchem);
%% - Create Variational2D and Calculator object with specified options
@ -130,7 +156,7 @@ OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 1e-2;
OptionsStruct.PlotLive = true;
OptionsStruct.JobNumber = 2;
OptionsStruct.JobNumber = 1;
OptionsStruct.RunOnGPU = false;
OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Data_StripePhase';
@ -172,7 +198,7 @@ OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 1e-2;
OptionsStruct.PlotLive = true;
OptionsStruct.JobNumber = 2;
OptionsStruct.JobNumber = 1;
OptionsStruct.RunOnGPU = false;
OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Data_HoneycombPhase';
@ -211,4 +237,5 @@ Scripts.analyzeRun2D(SaveDirectory, JobNumber)
SaveDirectory = './Data_HoneycombPhase';
JobNumber = 3;
% Plotter.visualizeGSWavefunction2D(SaveDirectory, JobNumber)
Scripts.analyzeRun2D(SaveDirectory, JobNumber)
Scripts.analyzeRun2D(SaveDirectory, JobNumber)

69
Dipolar-Gas-Simulator/+Scripts/run_on_cluster.m
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@ -10,6 +10,7 @@
% as = ((as/add)*Params.add)/Params.a0
% Critical point: 102.5133; Triangular phase: 98.0676; Stripe phase: 100.0289; Honeycomb phase: 101.9903
%{
%% - Create Variational2D and Calculator object with specified options
OptionsStruct = struct;
@ -135,3 +136,71 @@ solver.Potential = pot.trap();
%-% Run Solver %-%
[Params, Transf, psi, V, VDk] = solver.run();
%}
%% - Create Variational2D and Calculator object with specified options
OptionsStruct = struct;
OptionsStruct.NumberOfAtoms = 2.0030e+07;
OptionsStruct.DipolarPolarAngle = 0;
OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 98.0676;
OptionsStruct.TrapFrequencies = [10, 10, 72.4];
OptionsStruct.TrapPotentialType = 'None';
OptionsStruct.NumberOfGridPoints = [128, 128];
OptionsStruct.Dimensions = [100, 100];
OptionsStruct.TimeStepSize = 500E-6; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 1E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-04;
OptionsStruct.NoiseScaleFactor = 4;
OptionsStruct.MaxIterations = 1;
OptionsStruct.VariationalWidth = 5.0;
OptionsStruct.WidthLowerBound = 0.2;
OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 1e-2;
OptionsStruct.PlotLive = true;
OptionsStruct.JobNumber = 1;
OptionsStruct.RunOnGPU = false;
OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Data_TriangularPhase';
options = Helper.convertstruct2cell(OptionsStruct);
clear OptionsStruct
solver = VariationalSolver2D.DipolarGas(options{:});
pot = VariationalSolver2D.Potentials(options{:});
solver.Potential = pot.trap();
%-% Run Solver %-%
% [Params, Transf, psi, V, VDk] = solver.run();
% Solve BdG equations
% Load data
Data = load(sprintf(horzcat(solver.SaveDirectory, '/Run_%03i/psi_gs.mat'),solver.JobNumber),'psi','Params','Transf');
Params = Data.Params;
Transf = Data.Transf;
if isgpuarray(Data.psi)
psi = gather(Data.psi);
else
psi = Data.psi;
end
VParams.ell = Params.ell;
% == DDI potential == %
VDk = solver.Calculator.calculateVDkWithCutoff(Transf, Params, VParams.ell);
% == Trap potential == %
X = Transf.X; Y = Transf.Y;
V = 0.0*(Params.gx.*X.^2+Params.gy.*Y.^2);
% == Chemical potential == %
muchem = solver.Calculator.calculateChemicalPotential(psi,Params,VParams,Transf,VDk,V);
[evals, modes] = BdGSolver2D.solveBogoliubovdeGennesIn2D(psi, Params, VDk, VParams, Transf, muchem);