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

Dipolar-Gas-Simulator/+Plotter/visualizeGSWavefunction.m

@@ -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');
     

Dipolar-Gas-Simulator/+Scripts/run_locally.m

@@ -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.SimulationMode          = 'EnergyMinimization'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution' | 'EnergyMinimization'
-OptionsStruct.TimeStepSize            = 0.002;           % in s
+OptionsStruct.TimeStepSize            = 1E-4;            % in s
-OptionsStruct.MinimumTimeStepSize     = 1E-6;            % 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/CompleteLHY/AspectRatio2_8';
-SaveDirectory = './Results/Data_3D/AspectRatio3_7';
+% SaveDirectory = './Results/Data_3D/CompleteLHY/AspectRatio3_7';
-% SaveDirectory = './Results/Data_3D/AspectRatio3_8';
+SaveDirectory = './Results/Data_3D/CompleteLHY/AspectRatio3_8';
 JobNumber     = 0;
 Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
 %%
-% SaveDirectory = './Results/Data_3D/BeyondSSD_SSD';
+% SaveDirectory = './Results/Data_3D/CompleteLHY/BeyondSSD_SSD';
-SaveDirectory = './Results/Data_3D/BeyondSSD_Labyrinth';
+% SaveDirectory = './Results/Data_3D/CompleteLHY/BeyondSSD_Labyrinth';
-% SaveDirectory = './Results/Data_3D/BeyondSSD_Honeycomb';
+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:

Dipolar-Gas-Simulator/+Scripts/run_on_cluster.m

@@ -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);

Dipolar-Gas-Simulator/+Scripts/run_on_cluster_beyondSSD.m

@@ -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.TimeStepSize            = 1E-4;            % in s
-OptionsStruct.MinimumTimeStepSize     = 1E-6;            % 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.TimeStepSize            = 1E-4;            % in s
-OptionsStruct.MinimumTimeStepSize     = 1E-6;            % 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.TimeStepSize            = 1E-4;            % in s
-OptionsStruct.MinimumTimeStepSize     = 1E-6;            % 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;

Dipolar-Gas-Simulator/+Scripts/run_on_cluster_vary_aspect_ratio.m

@@ -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.TimeStepSize            = 1E-4;            % in s
-OptionsStruct.MinimumTimeStepSize     = 1E-6;            % 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.TimeStepSize            = 1E-4;            % in s
-OptionsStruct.MinimumTimeStepSize     = 1E-6;            % 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;

Dipolar-Gas-Simulator/+Simulator/@DipolarGas/DipolarGas.m

@@ -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,...

Dipolar-Gas-Simulator/+Simulator/@DipolarGas/minimizeEnergyFunctional.m

@@ -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

Dipolar-Gas-Simulator/+Simulator/@DipolarGas/run.m

@@ -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))
+    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