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Latest version of solver with additions to initialize with modulated states to bias the solver.

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Karthik 2025-03-20 16:06:41 +01:00
parent 3594e8f2b1
commit 10ed5472af
6 changed files with 221 additions and 244 deletions
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79
Dipolar-Gas-Simulator/+Scripts/analyzeGSWavefunction_constrained_optimal_system_size.m Normal file
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@ -0,0 +1,79 @@
function MinEnergyDataArray = analyzeGSWavefunction_constrained_optimal_system_size(folder_path, LatticeSpacing)
% Initialize matrix to store [Lx, Ly, minEnergy]
MinEnergyDataArray = [];
% Get a list of all subfolders in the parent folder
subfolders = dir(fullfile(folder_path, 'Run_*'));
% Loop through each subfolder
for i = 1:length(subfolders)
% Get the full path of the current subfolder
subfolder_path = fullfile(subfolders(i).folder, subfolders(i).name);
% Check if the current item is a folder
if subfolders(i).isdir
% Load the data file from the current folder
data_file = fullfile(subfolder_path, 'psi_gs.mat');
if isfile(data_file)
% Load required variables from the .mat file
Data = load(data_file, 'Params', 'VParams');
% Extract Lx and Ly from Params.Dimensions
Lx = Data.Params.Lx;
Ly = Data.Params.Ly;
% Extract the minimum energy from VParams.E_vs_iter
try
minEnergy = min(gather(Data.VParams.E_vs_iter));
catch
minEnergy = NaN;
end
% Append [Lx, Ly, minEnergy] to the results array
MinEnergyDataArray(end + 1, :) = [Lx, Ly, minEnergy];
else
fprintf('Warning: File psi_gs.mat not found in %s\n', subfolder_path);
end
end
end
% Initialize arrays to store values
Lx_Range = zeros(1, length(LatticeSpacing));
Ly_Range = zeros(1, length(LatticeSpacing));
MinEnergyDataValues = zeros(1, length(LatticeSpacing));
% Loop through the values of LatticeSpacing
for i = 1:length(LatticeSpacing)
a = LatticeSpacing(i);
% Calculate Lx and Ly based on the given conditions
lx = a;
ly = sqrt(3) * a;
for idx = 1:size(MinEnergyDataArray, 1)
Lx = MinEnergyDataArray(idx, 1);
Ly = MinEnergyDataArray(idx, 2);
energy = MinEnergyDataArray(idx, 3);
tolerance = 1e-10; % Define a small tolerance
if (abs(Lx - lx) < tolerance) && (abs(Ly - ly) < tolerance)
Lx_Range(i) = Lx;
Ly_Range(i) = Ly;
MinEnergyDataValues(i) = energy;
elseif MinEnergyDataValues(i)==0 || isnan(MinEnergyDataValues(i))
Lx_Range(i) = NaN;
Ly_Range(i) = NaN;
MinEnergyDataValues(i) = NaN;
end
end
end
figure
clf
set(gcf,'Position',[50 50 950 750])
set(gca,'FontSize',16,'Box','On','Linewidth',2);
plot(LatticeSpacing, MinEnergyDataValues, Marker = "o", LineWidth=2.0);
xlim([min(LatticeSpacing) max(LatticeSpacing)])
xlabel('$a$','fontsize',16,'interpreter','latex');
ylabel('$E_{var}$','fontsize',16,'interpreter','latex');
title('Minimum variational energy for different (constrained) unit cell sizes', 'FontSize', 16);
grid on
end

32
Dipolar-Gas-Simulator/+Scripts/run_locally.m
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@ -337,8 +337,36 @@ SaveDirectory = './Results/Data_TiltingOfDipoles/TransitionAngle/OptimalSys
% Define the desired range % Define the desired range
LatticeSpacing = 1.0:0.05:4.0; LatticeSpacing = 1.0:0.05:4.0;
MinEnergyDataArray = Scripts.analyzeGSWavefunction_constrained_optimal_system_size(SaveDirectory, LatticeSpacing); MinEnergyDataArray = Scripts.analyzeGSWavefunction_constrained_optimal_system_size(SaveDirectory, LatticeSpacing);
% Plotter.visualizeGSWavefunction2D(SaveDirectory, 1) % Plotter.visualizeGSWavefunction2D(SaveDirectory, 17)
% [contrast, periodX, periodY] = Scripts.analyzeGSWavefunction(SaveDirectory, 17);
%%
SaveDirectory = './Results/Data_TiltingOfDipoles/TransitionAngle/OptimalSystemSize/Hz500/Degree5';
% Define the desired range
LatticeSpacing = 1.0:0.05:4.0;
% MinEnergyDataArray = Scripts.analyzeGSWavefunction_constrained_optimal_system_size(SaveDirectory, LatticeSpacing);
% Plotter.visualizeGSWavefunction2D(SaveDirectory, 17)
[contrast, periodX, periodY] = Scripts.analyzeGSWavefunction(SaveDirectory, 17);
%%
SaveDirectory = './Results/Data_TiltingOfDipoles/TransitionAngle/OptimalSystemSize/Hz500/Degree7_5';
% Define the desired range
LatticeSpacing = 1.0:0.05:4.0;
% MinEnergyDataArray = Scripts.analyzeGSWavefunction_constrained_optimal_system_size(SaveDirectory, LatticeSpacing);
% Plotter.visualizeGSWavefunction2D(SaveDirectory, 17)
[contrast, periodX, periodY] = Scripts.analyzeGSWavefunction(SaveDirectory, 17);
%%
SaveDirectory = './Results/Data_TiltingOfDipoles/TransitionAngle/OptimalSystemSize/Hz500/Degree10';
% Define the desired range
LatticeSpacing = 1.0:0.05:4.0;
MinEnergyDataArray = Scripts.analyzeGSWavefunction_constrained_optimal_system_size(SaveDirectory, LatticeSpacing);
% Plotter.visualizeGSWavefunction2D(SaveDirectory, 17)
[contrast, periodX, periodY] = Scripts.analyzeGSWavefunction(SaveDirectory, 22);
%%
SaveDirectory = './Results/Data_TiltingOfDipoles/TransitionAngle/OptimalSystemSize/Hz500/Degree15';
% Define the desired range
LatticeSpacing = 1.0:0.05:4.0;
MinEnergyDataArray = Scripts.analyzeGSWavefunction_constrained_optimal_system_size(SaveDirectory, LatticeSpacing);
% Plotter.visualizeGSWavefunction2D(SaveDirectory, 17)
% [contrast, periodX, periodY] = Scripts.analyzeGSWavefunction(SaveDirectory, 22);
%% - Analysis %% - Analysis
SaveDirectory = './Results/Data_TiltingOfDipoles/HarmonicTrap/AspectRatio/AR2_8'; SaveDirectory = './Results/Data_TiltingOfDipoles/HarmonicTrap/AspectRatio/AR2_8';
JobNumber = 0; % 79 JobNumber = 0; % 79

2
Dipolar-Gas-Simulator/+Scripts/run_on_cluster.m
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@ -48,6 +48,8 @@ parfor (k = 1:totalIterations, cluster)
OptionsStruct.EnergyTolerance = 5E-10; OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05; OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05; OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.BiasWithAnsatz = true;
OptionsStruct.Ansatz = 'triangular';
OptionsStruct.IncludeDDICutOff = false; OptionsStruct.IncludeDDICutOff = false;
OptionsStruct.MaxIterations = 10; OptionsStruct.MaxIterations = 10;

299
Dipolar-Gas-Simulator/+Scripts/run_on_cluster_adjusted_system_size.m
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@ -1,39 +1,49 @@
%% Tilting of the dipoles %% Tilting of the dipoles
% Atom Number = 1250 ppum % Atom Number = 1250 ppum
% System size = [5 * l_rot, 5 * l_rot] % System size = [sf * unitcell_x, sf * unitcell_x]
%% v_z = 500, theta = 0: a_s = 76.41 ppum = 1250; % Atom Number Density in per micrometers
OptionsStruct = struct; %% v_z = 500, theta = 0: a_s = 76.00
OptionsStruct.NumberOfAtoms = 101250; a = 1.8;
OptionsStruct.DipolarPolarAngle = 0; scalingfactor = 5;
lx = scalingfactor*a;
ly = scalingfactor*sqrt(3)*a;
% Initialize OptionsStruct
OptionsStruct = struct;
% Assign values to OptionsStruct
OptionsStruct.NumberOfAtoms = ppum * (lx*ly);
OptionsStruct.DipolarPolarAngle = deg2rad(0);
OptionsStruct.DipolarAzimuthAngle = 0; OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 76.41; OptionsStruct.ScatteringLength = 76.00;
OptionsStruct.TrapFrequencies = [0, 0, 500]; OptionsStruct.TrapFrequencies = [0, 0, 500];
OptionsStruct.TrapPotentialType = 'None'; OptionsStruct.TrapPotentialType = 'None';
OptionsStruct.NumberOfGridPoints = [128, 128]; OptionsStruct.NumberOfGridPoints = [128, 128];
OptionsStruct.Dimensions = [9, 9]; OptionsStruct.Dimensions = [lx, ly];
OptionsStruct.TimeStepSize = 0.005; % in s OptionsStruct.TimeStepSize = 1E-3; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 2E6; % in s OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10; OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05; OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05; OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.IncludeDDICutOff = false;
OptionsStruct.MaxIterations = 10; OptionsStruct.MaxIterations = 10;
OptionsStruct.VariationalWidth = 1.2; OptionsStruct.VariationalWidth = 1.15;
OptionsStruct.WidthLowerBound = 0.01; OptionsStruct.WidthLowerBound = 0.01;
OptionsStruct.WidthUpperBound = 12; OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 5e-3; OptionsStruct.WidthCutoff = 1e-2;
OptionsStruct.PlotLive = false; OptionsStruct.PlotLive = false;
OptionsStruct.JobNumber = 0; OptionsStruct.JobNumber = 0;
OptionsStruct.RunOnGPU = true; OptionsStruct.RunOnGPU = true;
OptionsStruct.SaveData = true; OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Results/Data_TiltingOfDipoles/AdjustedSystemSize/Hz500'; OptionsStruct.SaveDirectory = './Results/Data_TiltingOfDipoles/SystemSize100squm/Hz500';
options = Helper.convertstruct2cell(OptionsStruct); options = Helper.convertstruct2cell(OptionsStruct);
clear OptionsStruct clear OptionsStruct
@ -44,38 +54,46 @@ solver.Potential = pot.trap();
%-% Run Solver %-% %-% Run Solver %-%
[Params, Transf, psi, V, VDk] = solver.run(); [Params, Transf, psi, V, VDk] = solver.run();
%% v_z = 500, theta = 15: a_s = 77.45 %% v_z = 500, theta = 7.5: a_s = 76.00
OptionsStruct = struct; a = 1.5;
scalingfactor = 5;
lx = scalingfactor*a;
ly = scalingfactor*sqrt(3)*a;
OptionsStruct.NumberOfAtoms = 101250; % Initialize OptionsStruct
OptionsStruct.DipolarPolarAngle = deg2rad(15); OptionsStruct = struct;
% Assign values to OptionsStruct
OptionsStruct.NumberOfAtoms = ppum * (lx*ly);
OptionsStruct.DipolarPolarAngle = deg2rad(7.5);
OptionsStruct.DipolarAzimuthAngle = 0; OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 77.45; OptionsStruct.ScatteringLength = 76.00;
OptionsStruct.TrapFrequencies = [0, 0, 500]; OptionsStruct.TrapFrequencies = [0, 0, 500];
OptionsStruct.TrapPotentialType = 'None'; OptionsStruct.TrapPotentialType = 'None';
OptionsStruct.NumberOfGridPoints = [128, 128]; OptionsStruct.NumberOfGridPoints = [128, 128];
OptionsStruct.Dimensions = [9, 9]; OptionsStruct.Dimensions = [lx, ly];
OptionsStruct.TimeStepSize = 0.005; % in s OptionsStruct.TimeStepSize = 1E-3; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 2E6; % in s OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10; OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05; OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05; OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.IncludeDDICutOff = false;
OptionsStruct.MaxIterations = 10; OptionsStruct.MaxIterations = 10;
OptionsStruct.VariationalWidth = 1.2; OptionsStruct.VariationalWidth = 1.15;
OptionsStruct.WidthLowerBound = 0.01; OptionsStruct.WidthLowerBound = 0.01;
OptionsStruct.WidthUpperBound = 12; OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 5e-3; OptionsStruct.WidthCutoff = 1e-2;
OptionsStruct.PlotLive = false; OptionsStruct.PlotLive = false;
OptionsStruct.JobNumber = 1; OptionsStruct.JobNumber = 2;
OptionsStruct.RunOnGPU = true; OptionsStruct.RunOnGPU = true;
OptionsStruct.SaveData = true; OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Results/Data_TiltingOfDipoles/AdjustedSystemSize/Hz500'; OptionsStruct.SaveDirectory = './Results/Data_TiltingOfDipoles/SystemSize100squm/Hz500';
options = Helper.convertstruct2cell(OptionsStruct); options = Helper.convertstruct2cell(OptionsStruct);
clear OptionsStruct clear OptionsStruct
@ -86,80 +104,46 @@ solver.Potential = pot.trap();
%-% Run Solver %-% %-% Run Solver %-%
[Params, Transf, psi, V, VDk] = solver.run(); [Params, Transf, psi, V, VDk] = solver.run();
%% v_z = 750, theta = 0: a_s = 70.5 %% v_z = 500, theta = 15: a_s = 76.00
OptionsStruct = struct; a = 1.05;
scalingfactor = 5;
lx = scalingfactor*a;
ly = scalingfactor*sqrt(3)*a;
OptionsStruct.NumberOfAtoms = 61250; % Initialize OptionsStruct
OptionsStruct.DipolarPolarAngle = 0; OptionsStruct = struct;
OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 70.5;
OptionsStruct.TrapFrequencies = [0, 0, 750]; % Assign values to OptionsStruct
OptionsStruct.TrapPotentialType = 'None'; OptionsStruct.NumberOfAtoms = ppum * (lx*ly);
OptionsStruct.NumberOfGridPoints = [128, 128];
OptionsStruct.Dimensions = [7, 7];
OptionsStruct.TimeStepSize = 0.005; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.MaxIterations = 10;
OptionsStruct.VariationalWidth = 0.85;
OptionsStruct.WidthLowerBound = 0.01;
OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 5e-3;
OptionsStruct.PlotLive = false;
OptionsStruct.JobNumber = 0;
OptionsStruct.RunOnGPU = true;
OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Results/Data_TiltingOfDipoles/AdjustedSystemSize/Hz750';
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();
%% v_z = 750, theta = 15: a_s = 72.5
OptionsStruct = struct;
OptionsStruct.NumberOfAtoms = 61250;
OptionsStruct.DipolarPolarAngle = deg2rad(15); OptionsStruct.DipolarPolarAngle = deg2rad(15);
OptionsStruct.DipolarAzimuthAngle = 0; OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 72.5; OptionsStruct.ScatteringLength = 76.00;
OptionsStruct.TrapFrequencies = [0, 0, 750]; OptionsStruct.TrapFrequencies = [0, 0, 500];
OptionsStruct.TrapPotentialType = 'None'; OptionsStruct.TrapPotentialType = 'None';
OptionsStruct.NumberOfGridPoints = [128, 128]; OptionsStruct.NumberOfGridPoints = [128, 128];
OptionsStruct.Dimensions = [7, 7]; OptionsStruct.Dimensions = [lx, ly];
OptionsStruct.TimeStepSize = 0.005; % in s OptionsStruct.TimeStepSize = 1E-3; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 2E6; % in s OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10; OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05; OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05; OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.IncludeDDICutOff = false;
OptionsStruct.MaxIterations = 10; OptionsStruct.MaxIterations = 10;
OptionsStruct.VariationalWidth = 0.85; OptionsStruct.VariationalWidth = 1.15;
OptionsStruct.WidthLowerBound = 0.01; OptionsStruct.WidthLowerBound = 0.01;
OptionsStruct.WidthUpperBound = 12; OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 5e-3; OptionsStruct.WidthCutoff = 1e-2;
OptionsStruct.PlotLive = false; OptionsStruct.PlotLive = false;
OptionsStruct.JobNumber = 1; OptionsStruct.JobNumber = 2;
OptionsStruct.RunOnGPU = true; OptionsStruct.RunOnGPU = true;
OptionsStruct.SaveData = true; OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Results/Data_TiltingOfDipoles/AdjustedSystemSize/Hz750'; OptionsStruct.SaveDirectory = './Results/Data_TiltingOfDipoles/SystemSize100squm/Hz500';
options = Helper.convertstruct2cell(OptionsStruct); options = Helper.convertstruct2cell(OptionsStruct);
clear OptionsStruct clear OptionsStruct
@ -170,170 +154,3 @@ solver.Potential = pot.trap();
%-% Run Solver %-% %-% Run Solver %-%
[Params, Transf, psi, V, VDk] = solver.run(); [Params, Transf, psi, V, VDk] = solver.run();
%% v_z = 1000, theta = 0: a_s = 65.95
OptionsStruct = struct;
OptionsStruct.NumberOfAtoms = 45000;
OptionsStruct.DipolarPolarAngle = 0;
OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 65.95;
OptionsStruct.TrapFrequencies = [0, 0, 1000];
OptionsStruct.TrapPotentialType = 'None';
OptionsStruct.NumberOfGridPoints = [128, 128];
OptionsStruct.Dimensions = [6, 6];
OptionsStruct.TimeStepSize = 0.005; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.MaxIterations = 10;
OptionsStruct.VariationalWidth = 0.7;
OptionsStruct.WidthLowerBound = 0.01;
OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 5e-3;
OptionsStruct.PlotLive = false;
OptionsStruct.JobNumber = 0;
OptionsStruct.RunOnGPU = true;
OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Results/Data_TiltingOfDipoles/AdjustedSystemSize/Hz1000';
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();
%% v_z = 1000, theta = 15: a_s = 67.25
OptionsStruct = struct;
OptionsStruct.NumberOfAtoms = 45000;
OptionsStruct.DipolarPolarAngle = deg2rad(15);
OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 67.25;
OptionsStruct.TrapFrequencies = [0, 0, 1000];
OptionsStruct.TrapPotentialType = 'None';
OptionsStruct.NumberOfGridPoints = [128, 128];
OptionsStruct.Dimensions = [6, 6];
OptionsStruct.TimeStepSize = 0.005; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.MaxIterations = 10;
OptionsStruct.VariationalWidth = 0.7;
OptionsStruct.WidthLowerBound = 0.01;
OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 5e-3;
OptionsStruct.PlotLive = false;
OptionsStruct.JobNumber = 1;
OptionsStruct.RunOnGPU = true;
OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Results/Data_TiltingOfDipoles/AdjustedSystemSize/Hz1000';
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();
%% v_z = 2000, theta = 0: a_s = 54.90
OptionsStruct = struct;
OptionsStruct.NumberOfAtoms = 31250;
OptionsStruct.DipolarPolarAngle = 0;
OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 54.90;
OptionsStruct.TrapFrequencies = [0, 0, 2000];
OptionsStruct.TrapPotentialType = 'None';
OptionsStruct.NumberOfGridPoints = [128, 128];
OptionsStruct.Dimensions = [5, 5];
OptionsStruct.TimeStepSize = 0.005; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.MaxIterations = 10;
OptionsStruct.VariationalWidth = 0.5;
OptionsStruct.WidthLowerBound = 0.01;
OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 5e-3;
OptionsStruct.PlotLive = false;
OptionsStruct.JobNumber = 0;
OptionsStruct.RunOnGPU = true;
OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Results/Data_TiltingOfDipoles/AdjustedSystemSize/Hz2000';
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();
%% v_z = 2000, theta = 15: a_s = 55.5
OptionsStruct = struct;
OptionsStruct.NumberOfAtoms = 31250;
OptionsStruct.DipolarPolarAngle = deg2rad(15);
OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 55.5;
OptionsStruct.TrapFrequencies = [0, 0, 2000];
OptionsStruct.TrapPotentialType = 'None';
OptionsStruct.NumberOfGridPoints = [128, 128];
OptionsStruct.Dimensions = [5, 5];
OptionsStruct.TimeStepSize = 0.005; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.MaxIterations = 10;
OptionsStruct.VariationalWidth = 0.5;
OptionsStruct.WidthLowerBound = 0.01;
OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 5e-3;
OptionsStruct.PlotLive = false;
OptionsStruct.JobNumber = 1;
OptionsStruct.RunOnGPU = true;
OptionsStruct.SaveData = true;
OptionsStruct.SaveDirectory = './Results/Data_TiltingOfDipoles/AdjustedSystemSize/Hz2000';
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();

2
Dipolar-Gas-Simulator/+Scripts/run_on_cluster_optimal_system_size.m
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@ -52,6 +52,8 @@ parfor (k = 1:totalIterations, cluster)
OptionsStruct.EnergyTolerance = 5E-10; OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05; OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05; OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.BiasWithAnsatz = true;
OptionsStruct.Ansatz = 'triangular';
OptionsStruct.IncludeDDICutOff = false; OptionsStruct.IncludeDDICutOff = false;
OptionsStruct.MaxIterations = 10; OptionsStruct.MaxIterations = 10;

49
Dipolar-Gas-Simulator/+VariationalSolver2D/@DipolarGas/setupCosineModulatedAnsatz.m Normal file
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@ -0,0 +1,49 @@
function [psi] = setupCosineModulatedAnsatz(this, Params, Transf)
format long
% Extract transformation coordinates
X = Transf.X;
Y = Transf.Y;
% Check the BiasAnsatz and apply the corresponding function
if strcmp(this.Ansatz, 'stripe')
% STRIPES 2-D
% Parameters
c = 1; % Fourier coefficient
k = 2 * pi / Params.Lx; % Wavenumber
n = 2; % Order
% Define the 2D function for stripes
psi = (1 + (c * cos(n * k * Y))) / (1 + (0.5 * c^2));
elseif strcmp(this.Ansatz, 'triangular')
% TRIANGULAR LATTICE 2-D
% Parameters
c1 = 0.2;
c2 = 0.2;
k = 2 * pi / Params.Lx; % Wavenumber
n = 1;
% Define the 2D function for a triangular lattice
psi = 1 + (c1 * cos(n * k * (2/sqrt(3)) * Y)) + ...
(2 * c2 * cos(n * k * (1/sqrt(3)) * Y) .* cos(n * k * X));
elseif strcmp(this.Ansatz, 'honeycomb')
% HONEYCOMB LATTICE 2-D
% Parameters
c1 = 0.2;
c2 = 0.2;
k = 2 * pi / Params.Lx; % Wavenumber
n = 1;
% Define the 2D function for a honeycomb lattice
psi = 1 - (c1 * cos(n * k * (2/sqrt(3)) * X)) - ...
(2 * c2 * cos(n * k * (1/sqrt(3)) * X) .* cos(n * k * Y));
else
error('Unknown Ansatz type');
end
% Normalize the result
Norm = sum(abs(psi(:)).^2) * Transf.dx * Transf.dy;
psi = sqrt(Params.N) * psi / sqrt(Norm);
end