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Latest scripts - included energy minimization function with associated changes and additional functionality.

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Karthik 2025-03-30 16:27:09 +02:00
parent 0f3eca6791
commit 0acacc2362
8 changed files with 212 additions and 40 deletions
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1
Dipolar-Gas-Simulator/+Plotter/visualizeGSWavefunction.m
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@ -5,7 +5,6 @@ function visualizeGSWavefunction(folder_path, run_index)
format long
% Load data
Data = load(sprintf(horzcat(folder_path, '/Run_%03i/psi_gs.mat'),run_index),'psi','Params','Transf','Observ');

39
Dipolar-Gas-Simulator/+Scripts/run_locally.m
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@ -17,17 +17,17 @@ VerticalTrapFrequency = AspectRatio * HorizontalTrapFrequency;
OptionsStruct.TrapFrequencies = [HorizontalTrapFrequency, HorizontalTrapFrequency, VerticalTrapFrequency];
OptionsStruct.TrapPotentialType = 'Harmonic';
OptionsStruct.NumberOfGridPoints = [64, 64, 32];
OptionsStruct.NumberOfGridPoints = [128, 128, 64];
OptionsStruct.Dimensions = [18, 18, 18];
OptionsStruct.UseApproximationForLHY = true;
OptionsStruct.IncludeDDICutOff = true;
OptionsStruct.CutoffType = 'Cylindrical';
OptionsStruct.SimulationMode = 'ImaginaryTimeEvolution'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution'
OptionsStruct.TimeStepSize = 0.002; % in s
OptionsStruct.MinimumTimeStepSize = 1E-6; % in s
OptionsStruct.SimulationMode = 'EnergyMinimization'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution' | 'EnergyMinimization'
OptionsStruct.TimeStepSize = 1E-4; % in s
OptionsStruct.MinimumTimeStepSize = 2E-10; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.ResidualTolerance = 1E-08;
OptionsStruct.NoiseScaleFactor = 0.01;
OptionsStruct.PlotLive = true;
@ -51,19 +51,34 @@ sim.Potential = pot.trap(); % + pot.repulsive_chopstick(
Plotter.visualizeTrapPotential(sim.Potential,Params,Transf)
%% - Plot initial wavefunction
Plotter.visualizeWavefunction(psi,Params,Transf)
%%
SaveDirectory = './Results/Data_3D/AspectRatio2';
JobNumber = 0;
Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
%% - Plot GS wavefunction
% SaveDirectory = './Results/Data_3D/AspectRatio2_8';
SaveDirectory = './Results/Data_3D/AspectRatio3_7';
% SaveDirectory = './Results/Data_3D/AspectRatio3_8';
% SaveDirectory = './Results/Data_3D/CompleteLHY/AspectRatio2_8';
% SaveDirectory = './Results/Data_3D/CompleteLHY/AspectRatio3_7';
SaveDirectory = './Results/Data_3D/CompleteLHY/AspectRatio3_8';
JobNumber = 0;
Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
%%
% SaveDirectory = './Results/Data_3D/BeyondSSD_SSD';
SaveDirectory = './Results/Data_3D/BeyondSSD_Labyrinth';
% SaveDirectory = './Results/Data_3D/BeyondSSD_Honeycomb';
% SaveDirectory = './Results/Data_3D/CompleteLHY/BeyondSSD_SSD';
% SaveDirectory = './Results/Data_3D/CompleteLHY/BeyondSSD_Labyrinth';
SaveDirectory = './Results/Data_3D/CompleteLHY/BeyondSSD_Honeycomb';
JobNumber = 0;
Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
%% - Plot GS wavefunction
% SaveDirectory = './Results/Data_3D/ApproximateLHY/AspectRatio2_8';
% SaveDirectory = './Results/Data_3D/ApproximateLHY/AspectRatio3_7';
SaveDirectory = './Results/Data_3D/ApproximateLHY/AspectRatio3_8';
JobNumber = 0;
Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
%%
% SaveDirectory = './Results/Data_3D/ApproximateLHY/BeyondSSD_SSD';
SaveDirectory = './Results/Data_3D/ApproximateLHY/BeyondSSD_Labyrinth';
% SaveDirectory = './Results/Data_3D/ApproximateLHY/BeyondSSD_Honeycomb';
JobNumber = 0;
Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
%%
% To reproduce results from the Blair Blakie paper:

11
Dipolar-Gas-Simulator/+Scripts/run_on_cluster.m
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@ -5,7 +5,7 @@ OptionsStruct = struct;
OptionsStruct.NumberOfAtoms = 4E5;
OptionsStruct.DipolarPolarAngle = deg2rad(0);
OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 87;
OptionsStruct.ScatteringLength = 85;
AspectRatio = 2.0;
HorizontalTrapFrequency = 125;
@ -13,21 +13,22 @@ VerticalTrapFrequency = AspectRatio * HorizontalTrapFrequency;
OptionsStruct.TrapFrequencies = [HorizontalTrapFrequency, HorizontalTrapFrequency, VerticalTrapFrequency];
OptionsStruct.TrapPotentialType = 'Harmonic';
OptionsStruct.NumberOfGridPoints = [256, 256, 128];
OptionsStruct.NumberOfGridPoints = [128, 128, 64];
OptionsStruct.Dimensions = [18, 18, 18];
OptionsStruct.UseApproximationForLHY = true;
OptionsStruct.IncludeDDICutOff = true;
OptionsStruct.CutoffType = 'Cylindrical';
OptionsStruct.SimulationMode = 'ImaginaryTimeEvolution'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution'
OptionsStruct.TimeStepSize = 2E-3; % in s
OptionsStruct.TimeStepSize = 1E-3; % in s
OptionsStruct.MinimumTimeStepSize = 1E-6; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.01;
OptionsStruct.PlotLive = false;
OptionsStruct.PlotLive = true;
OptionsStruct.JobNumber = 0;
OptionsStruct.RunOnGPU = true;
OptionsStruct.RunOnGPU = false;
OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Results/Data_3D/BeyondSSD_Labyrinth';
options = Helper.convertstruct2cell(OptionsStruct);

27
Dipolar-Gas-Simulator/+Scripts/run_on_cluster_beyondSSD.m
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@ -13,16 +13,17 @@ VerticalTrapFrequency = AspectRatio * HorizontalTrapFrequency;
OptionsStruct.TrapFrequencies = [HorizontalTrapFrequency, HorizontalTrapFrequency, VerticalTrapFrequency];
OptionsStruct.TrapPotentialType = 'Harmonic';
OptionsStruct.NumberOfGridPoints = [256, 256, 128];
OptionsStruct.NumberOfGridPoints = [128, 128, 64];
OptionsStruct.Dimensions = [18, 18, 18];
OptionsStruct.UseApproximationForLHY = true;
OptionsStruct.IncludeDDICutOff = true;
OptionsStruct.CutoffType = 'Cylindrical';
OptionsStruct.SimulationMode = 'ImaginaryTimeEvolution'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution'
OptionsStruct.TimeStepSize = 2E-3; % in s
OptionsStruct.MinimumTimeStepSize = 1E-6; % in s
OptionsStruct.TimeStepSize = 1E-4; % in s
OptionsStruct.MinimumTimeStepSize = 2E-10; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.ResidualTolerance = 1E-08;
OptionsStruct.NoiseScaleFactor = 0.01;
OptionsStruct.PlotLive = false;
@ -55,16 +56,17 @@ VerticalTrapFrequency = AspectRatio * HorizontalTrapFrequency;
OptionsStruct.TrapFrequencies = [HorizontalTrapFrequency, HorizontalTrapFrequency, VerticalTrapFrequency];
OptionsStruct.TrapPotentialType = 'Harmonic';
OptionsStruct.NumberOfGridPoints = [256, 256, 128];
OptionsStruct.NumberOfGridPoints = [128, 128, 64];
OptionsStruct.Dimensions = [18, 18, 18];
OptionsStruct.UseApproximationForLHY = true;
OptionsStruct.IncludeDDICutOff = true;
OptionsStruct.CutoffType = 'Cylindrical';
OptionsStruct.SimulationMode = 'ImaginaryTimeEvolution'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution'
OptionsStruct.TimeStepSize = 2E-3; % in s
OptionsStruct.MinimumTimeStepSize = 1E-6; % in s
OptionsStruct.TimeStepSize = 1E-4; % in s
OptionsStruct.MinimumTimeStepSize = 2E-10; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.ResidualTolerance = 1E-08;
OptionsStruct.NoiseScaleFactor = 0.01;
OptionsStruct.PlotLive = false;
@ -97,16 +99,17 @@ VerticalTrapFrequency = AspectRatio * HorizontalTrapFrequency;
OptionsStruct.TrapFrequencies = [HorizontalTrapFrequency, HorizontalTrapFrequency, VerticalTrapFrequency];
OptionsStruct.TrapPotentialType = 'Harmonic';
OptionsStruct.NumberOfGridPoints = [256, 256, 128];
OptionsStruct.NumberOfGridPoints = [128, 128, 64];
OptionsStruct.Dimensions = [18, 18, 18];
OptionsStruct.UseApproximationForLHY = true;
OptionsStruct.IncludeDDICutOff = true;
OptionsStruct.CutoffType = 'Cylindrical';
OptionsStruct.SimulationMode = 'ImaginaryTimeEvolution'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution'
OptionsStruct.TimeStepSize = 2E-3; % in s
OptionsStruct.MinimumTimeStepSize = 1E-6; % in s
OptionsStruct.TimeStepSize = 1E-4; % in s
OptionsStruct.MinimumTimeStepSize = 2E-10; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.ResidualTolerance = 1E-08;
OptionsStruct.NoiseScaleFactor = 0.01;
OptionsStruct.PlotLive = false;

61
Dipolar-Gas-Simulator/+Scripts/run_on_cluster_vary_aspect_ratio.m
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@ -13,16 +13,17 @@ VerticalTrapFrequency = AspectRatio * HorizontalTrapFrequency;
OptionsStruct.TrapFrequencies = [HorizontalTrapFrequency, HorizontalTrapFrequency, VerticalTrapFrequency];
OptionsStruct.TrapPotentialType = 'Harmonic';
OptionsStruct.NumberOfGridPoints = [256, 256, 128];
OptionsStruct.NumberOfGridPoints = [128, 128, 64];
OptionsStruct.Dimensions = [18, 18, 18];
OptionsStruct.UseApproximationForLHY = true;
OptionsStruct.IncludeDDICutOff = true;
OptionsStruct.CutoffType = 'Cylindrical';
OptionsStruct.SimulationMode = 'ImaginaryTimeEvolution'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution'
OptionsStruct.TimeStepSize = 2E-3; % in s
OptionsStruct.MinimumTimeStepSize = 1E-6; % in s
OptionsStruct.TimeStepSize = 1E-4; % in s
OptionsStruct.MinimumTimeStepSize = 2E-10; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.ResidualTolerance = 1E-08;
OptionsStruct.NoiseScaleFactor = 0.01;
OptionsStruct.PlotLive = false;
@ -55,16 +56,60 @@ VerticalTrapFrequency = AspectRatio * HorizontalTrapFrequency;
OptionsStruct.TrapFrequencies = [HorizontalTrapFrequency, HorizontalTrapFrequency, VerticalTrapFrequency];
OptionsStruct.TrapPotentialType = 'Harmonic';
OptionsStruct.NumberOfGridPoints = [256, 256, 128];
OptionsStruct.NumberOfGridPoints = [128, 128, 64];
OptionsStruct.Dimensions = [18, 18, 18];
OptionsStruct.UseApproximationForLHY = true;
OptionsStruct.IncludeDDICutOff = true;
OptionsStruct.CutoffType = 'Cylindrical';
OptionsStruct.SimulationMode = 'ImaginaryTimeEvolution'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution'
OptionsStruct.TimeStepSize = 2E-3; % in s
OptionsStruct.MinimumTimeStepSize = 1E-6; % in s
OptionsStruct.TimeStepSize = 1E-4; % in s
OptionsStruct.MinimumTimeStepSize = 2E-10; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.ResidualTolerance = 1E-08;
OptionsStruct.NoiseScaleFactor = 0.01;
OptionsStruct.PlotLive = false;
OptionsStruct.JobNumber = 0;
OptionsStruct.RunOnGPU = true;
OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = sprintf('./Results/Data_3D/AspectRatio%s', strrep(num2str(AspectRatio), '.', '_'));
options = Helper.convertstruct2cell(OptionsStruct);
clear OptionsStruct
sim = Simulator.DipolarGas(options{:});
pot = Simulator.Potentials(options{:});
sim.Potential = pot.trap();
%-% Run Simulation %-%
[Params, Transf, psi, V, VDk] = sim.run();
%% - Aspect Ratio: 3.8
OptionsStruct = struct;
OptionsStruct.NumberOfAtoms = 5E5;
OptionsStruct.DipolarPolarAngle = deg2rad(0);
OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 85;
AspectRatio = 3.8;
HorizontalTrapFrequency = 125;
VerticalTrapFrequency = AspectRatio * HorizontalTrapFrequency;
OptionsStruct.TrapFrequencies = [HorizontalTrapFrequency, HorizontalTrapFrequency, VerticalTrapFrequency];
OptionsStruct.TrapPotentialType = 'Harmonic';
OptionsStruct.NumberOfGridPoints = [128, 128, 64];
OptionsStruct.Dimensions = [18, 18, 18];
OptionsStruct.UseApproximationForLHY = true;
OptionsStruct.IncludeDDICutOff = true;
OptionsStruct.CutoffType = 'Cylindrical';
OptionsStruct.SimulationMode = 'ImaginaryTimeEvolution'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution'
OptionsStruct.TimeStepSize = 1E-4; % in s
OptionsStruct.MinimumTimeStepSize = 2E-10; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-08;
OptionsStruct.NoiseScaleFactor = 0.01;
OptionsStruct.PlotLive = false;

2
Dipolar-Gas-Simulator/+Simulator/@DipolarGas/DipolarGas.m
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@ -54,7 +54,7 @@ classdef DipolarGas < handle & matlab.mixin.Copyable
addParameter(p, 'Dimensions', 10 * ones(1,3),...
@(x) assert(isnumeric(x) && isvector(x) && all(x > 0)));
addParameter(p, 'SimulationMode', 'ImaginaryTimeEvolution',...
@(x) assert(any(strcmpi(x,{'ImaginaryTimeEvolution','RealTimeEvolution'}))));
@(x) assert(any(strcmpi(x,{'ImaginaryTimeEvolution','RealTimeEvolution', 'EnergyMinimization'}))));
addParameter(p, 'CutOffType', 'Cylindrical',...
@(x) assert(any(strcmpi(x,{'None', 'Cylindrical','CylindricalInfiniteZ', 'Spherical', 'CustomCylindrical'}))));
addParameter(p, 'TimeStepSize', 5E-4,...

105
Dipolar-Gas-Simulator/+Simulator/@DipolarGas/minimizeEnergyFunctional.m Normal file
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@ -0,0 +1,105 @@
function [psi] = minimizeEnergyFunctional(this,psi,Params,Transf,VDk,V)
format long;
% Define the function handle
f = @(X) this.Calculator.calculateTotalEnergy(X, Params, Transf, VDk, V)/Params.N;
% Convergence Criteria:
Epsilon = 1E-5;
% Gradient Calculation
J = compute_gradient(psi, Params, Transf, VDk, V); % Gradient at initial point
S = -J; % Initial search direction
% Iteration Counter:
i = 1;
% Minimization
while norm(S(:)) > Epsilon % Halting Criterion
% Step Size Optimization (Line Search)
alpha = optimize_step_size(f, psi, S, Params, Transf, VDk, V);
% Update the solution
x_o_new = psi + alpha * S;
% Update the gradient and search direction
J_old = J;
J = compute_gradient(x_o_new, Params, Transf, VDk, V);
S = update_search_direction(S, J, J_old);
% Update for next iteration
psi = x_o_new;
Norm = sum(abs(psi(:)).^2)*Transf.dx*Transf.dy*Transf.dz;
psi = sqrt(Params.N)*psi/sqrt(Norm);
i = i + 1;
end
disp('Minimum found!');
fprintf('Number of Iterations for Convergence: %d\n\n', i);
muchem = this.Calculator.calculateChemicalPotential(psi,Params,Transf,VDk,V);
disp('Saving data...');
save(sprintf(strcat(this.SaveDirectory, '/Run_%03i/psi_gs.mat'),Params.njob),'psi','muchem','Transf','Params','VDk','V');
disp('Save complete!');
end
%% Helper functions
% Numerical Gradient Calculation using the finite differences method
function J = compute_gradient(psi, Params, Transf, VDk, V)
% Kinetic energy
KEop = 0.5*(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
H_o = KEop + V;
%Contact interactions
Hint = Params.gs*abs(psi).^2;
% DDIs
frho = fftn(abs(psi).^2);
Phi = real(ifftn(frho.*VDk));
Hddi = Params.gdd*Phi;
%Quantum fluctuations
Hqf = Params.gammaQF*abs(psi).^3;
H = H_o + Hint + Hddi + Hqf;
J = H.*psi;
end
% Line Search (Step Size Optimization)
function alpha = optimize_step_size(f, X, S, Params, Transf, VDk, V)
alpha = 1; % Initial step size
rho = 0.5; % Step size reduction factor
c = 1E-4; % Armijo condition constant
max_iter = 100; % Max iterations for backtracking
tol = 1E-8; % Tolerance for stopping
grad = compute_gradient(X, Params, Transf, VDk, V); % Compute gradient once
f_X = f(X); % Evaluate f(X) once
for k = 1:max_iter
% Evaluate Armijo condition with precomputed f(X) and grad
if f(X + alpha * S) <= f_X + c * alpha * (S(:)' * grad(:))
break;
else
alpha = rho * alpha; % Reduce the step size
end
% Early stopping if step size becomes too small
if alpha < tol
break;
end
end
end
% Update Search Direction (Polak-Ribiere method)
function S_new = update_search_direction(S, J_new, J_old)
beta = (norm(J_new(:))^2) / (norm(J_old(:))^2);
S_new = -J_new + beta * S;
end

6
Dipolar-Gas-Simulator/+Simulator/@DipolarGas/run.m
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@ -19,5 +19,9 @@ function [Params, Transf, psi,V,VDk] = run(this)
% --- Run Simulation ---
mkdir(sprintf(this.SaveDirectory))
mkdir(sprintf(strcat(this.SaveDirectory, '/Run_%03i'),Params.njob))
[psi] = this.propagateWavefunction(psi,Params,Transf,VDk,V,t_idx,Observ);
if strcmp(this.SimulationMode, 'EnergyMinimization')
[psi] = this.minimizeEnergyFunctional(psi,Params,Transf,VDk,V);
else
[psi] = this.propagateWavefunction(psi,Params,Transf,VDk,V,t_idx,Observ);
end
end