Included BdG solver in to the Simulator, added plotting routines for the 2D solver, fixed bugs so that the 2D solver runs to completion.
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81
Dipolar-Gas-Simulator/+Plotter/visualizeGSWavefunction2D.m
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81
Dipolar-Gas-Simulator/+Plotter/visualizeGSWavefunction2D.m
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@ -0,0 +1,81 @@
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function visualizeGSWavefunction2D(run_index)
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set(0,'defaulttextInterpreter','latex')
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set(groot, 'defaultAxesTickLabelInterpreter','latex'); set(groot, 'defaultLegendInterpreter','latex');
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folder_path = './Data';
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% Load data
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Data = load(sprintf(horzcat(folder_path, '/Run_%03i/psi_gs.mat'),run_index),'psi','Params','Transf','Observ');
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Params = Data.Params;
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Transf = Data.Transf;
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Observ = Data.Observ;
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if isgpuarray(Data.psi)
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psi = gather(Data.psi);
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else
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psi = Data.psi;
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end
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if isgpuarray(Data.Observ.residual)
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Observ.residual = gather(Data.Observ.residual);
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else
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Observ.residual = Data.Observ.residual;
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end
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% Set long format for output
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format long
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% Coordinates in micrometers
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x = Transf.x * Params.l0 * 1e6;
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y = Transf.y * Params.l0 * 1e6;
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% Plotting
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figure('Position', [100, 100, 1600, 900]);
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clf
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% Compute probability density |psi|^2
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n = abs(psi).^2;
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% Plot |psi(x,y)|^2 (density in x and y plane)
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subplot('Position', [0.05, 0.55, 0.28, 0.4])
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pcolor(x, y, n');
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shading interp;
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colorbar;
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xlabel('$x$ [$\mu$m]', 'FontSize', 14); ylabel('$y$ [$\mu$m]', 'FontSize', 14);
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title('$|\Psi_{xy}|^2$', 'FontSize', 14);
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% Plot real part of psi in the x-y plane
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subplot('Position', [0.36, 0.55, 0.28, 0.4])
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pcolor(x, y, real(psi)');
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shading interp;
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colorbar;
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xlabel('$x$ [$\mu$m]', 'FontSize', 14); ylabel('$y$ [$\mu$m]', 'FontSize', 14);
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title('Re$\{\Psi_{xy}\}$', 'FontSize', 14);
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% Plot imaginary part of psi in the x-y plane
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subplot('Position', [0.67, 0.55, 0.28, 0.4])
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pcolor(x, y, imag(psi)');
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shading interp;
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colorbar;
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xlabel('$x$ [$\mu$m]', 'FontSize', 14); ylabel('$y$ [$\mu$m]', 'FontSize', 14);
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title('Im$\{\Psi_{xy}\}$', 'FontSize', 14);
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% Plot residual (time steps vs -log10(residual))
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subplot('Position', [0.05, 0.05, 0.26, 0.4]);
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plot(-log10(Observ.residual), '-b')
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ylabel('$-\mathrm{log}_{10}(r)$', 'FontSize', 14); xlabel('Time steps', 'FontSize', 14);
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title('Residual', 'FontSize', 14);
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% Plot total energy over time
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subplot('Position', [0.36, 0.05, 0.26, 0.4]);
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plot(Observ.EVec, '-b')
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ylabel('$E$', 'FontSize', 14); xlabel('Time steps', 'FontSize', 14);
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title('Total Energy', 'FontSize', 14);
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% Plot chemical potential over time
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subplot('Position', [0.67, 0.05, 0.26, 0.4]);
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plot(Observ.mucVec, '-b')
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ylabel('$\mu$', 'FontSize', 14); xlabel('Time steps', 'FontSize', 14);
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title('Chemical Potential', 'FontSize', 14);
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end
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@ -23,19 +23,19 @@ function visualizeSpace(Transf)
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end
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% set the axes labels' properties
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xlabel(gca, {'$x / l_o ~ (m)$'}, ...
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xlabel(gca, {'$x / l_o$'}, ...
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'Interpreter', 'latex', ...
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'FontName', 'Times New Roman', ...
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'FontSize', 14, ...
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'FontWeight', 'normal', ...
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'FontAngle', 'normal')
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ylabel(gca, {'$y / l_o ~ (m)$'}, ...
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ylabel(gca, {'$y / l_o$'}, ...
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'Interpreter', 'latex', ...
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'FontName', 'Times New Roman', ...
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'FontSize', 14, ...
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'FontWeight', 'normal', ...
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'FontAngle', 'normal')
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zlabel(gca, {'$z / l_o ~ (m)$'}, ...
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zlabel(gca, {'$z / l_o$'}, ...
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'Interpreter', 'latex', ...
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'FontName', 'Times New Roman', ...
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'FontSize', 14, ...
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@ -63,19 +63,19 @@ function visualizeSpace(Transf)
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end
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% set the axes labels' properties
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xlabel(gca, {'$k_x / l_o ~ (m^{-1})$'}, ...
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xlabel(gca, {'$k_x / l_o$'}, ...
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'Interpreter', 'latex', ...
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'FontName', 'Times New Roman', ...
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'FontSize', 14, ...
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'FontWeight', 'normal', ...
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'FontAngle', 'normal')
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ylabel(gca, {'$k_y / l_o ~ (m^{-1})$'}, ...
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ylabel(gca, {'$k_y / l_o$'}, ...
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'Interpreter', 'latex', ...
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'FontName', 'Times New Roman', ...
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'FontSize', 14, ...
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'FontWeight', 'normal', ...
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'FontAngle', 'normal')
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zlabel(gca, {'$k_z / l_o ~ (m^{-1})$'}, ...
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zlabel(gca, {'$k_z / l_o$'}, ...
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'Interpreter', 'latex', ...
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'FontName', 'Times New Roman', ...
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'FontSize', 14, ...
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@ -26,13 +26,13 @@ function visualizeSpace2D(Transf)
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axis equal % Ensures equal scaling for both axes
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% Set axes labels
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xlabel(gca, {'$x / l_o ~ (m)$'}, ...
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xlabel(gca, {'$x / l_o$'}, ...
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'Interpreter', 'latex', ...
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'FontName', 'Times New Roman', ...
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'FontSize', 14, ...
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'FontWeight', 'normal', ...
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'FontAngle', 'normal')
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ylabel(gca, {'$y / l_o ~ (m)$'}, ...
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ylabel(gca, {'$y / l_o$'}, ...
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'Interpreter', 'latex', ...
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'FontName', 'Times New Roman', ...
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'FontSize', 14, ...
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@ -62,13 +62,13 @@ function visualizeSpace2D(Transf)
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axis equal % Ensure equal scaling for both axes
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% Set axes labels
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xlabel(gca, {'$k_x / l_o ~ (m^{-1})$'}, ...
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xlabel(gca, {'$k_x / l_o$'}, ...
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'Interpreter', 'latex', ...
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'FontName', 'Times New Roman', ...
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'FontSize', 14, ...
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'FontWeight', 'normal', ...
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'FontAngle', 'normal')
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ylabel(gca, {'$k_y / l_o ~ (m^{-1})$'}, ...
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ylabel(gca, {'$k_y / l_o$'}, ...
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'Interpreter', 'latex', ...
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'FontName', 'Times New Roman', ...
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'FontSize', 14, ...
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41
Dipolar-Gas-Simulator/+Plotter/visualizeWavefunction2D.m
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41
Dipolar-Gas-Simulator/+Plotter/visualizeWavefunction2D.m
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@ -0,0 +1,41 @@
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function visualizeWavefunction2D(psi, Params, Transf)
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set(0,'defaulttextInterpreter','latex')
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set(groot, 'defaultAxesTickLabelInterpreter','latex'); set(groot, 'defaultLegendInterpreter','latex');
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format long
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height = 10;
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width = 30;
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figure(1)
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clf
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set(gcf, 'Units', 'centimeters')
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set(gcf, 'Position', [2 8 width height])
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set(gcf, 'PaperPositionMode', 'auto')
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% Axes scaling and coordinates in micrometers
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x = Transf.x * Params.l0 * 1e6;
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y = Transf.y * Params.l0 * 1e6;
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% Compute probability density |psi|^2
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n = abs(psi).^2;
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% Plot |psi(x,y)|^2
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subplot(1, 2, 1)
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pcolor(x, y, n')
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shading interp; % Smooth shading
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colorbar; % Show color bar
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xlabel('$x$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
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ylabel('$y$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
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title('$|\Psi(x,y)|^2$', 'Interpreter', 'latex', 'FontSize', 14)
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% Plot real part of psi
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subplot(1, 2, 2)
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pcolor(x, y, real(psi)')
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shading interp;
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colorbar;
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xlabel('$x$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
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ylabel('$y$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
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title('Re$\{\Psi(x,y)\}$', 'Interpreter', 'latex', 'FontSize', 14)
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end
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@ -14,8 +14,8 @@ function [psi,V,VDk] = initialize(this,Params,VParams,Transf)
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else
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VDk = this.Calculator.calculateVDkWithCutoff(rcut, Transf, Params, VParams);
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save(sprintf(strcat(this.SaveDirectory, '/VDk_M.mat')),'VDk');
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end
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fprintf('Computed and saved DDI potential in Fourier space with cutoff.\n')
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end
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% == Setting up the initial wavefunction == %
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psi = this.setupWavefunction(Params,Transf);
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@ -27,7 +27,7 @@ function [psi] = propagateWavefunction(this, psi, Params, VParams, Transf, VDk,
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EVar = VParams.nu^2*gamma(2-1/VParams.nu)/(8*VParams.ell^2*gamma(1/VParams.nu)) + 0.5*Params.gz*VParams.ell^2*gamma(3/VParams.nu)/gamma(1/VParams.nu);
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pb = Helper.ProgressBar();
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pb.run('Running simulation in imaginary time: ');
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pb.run('Propagating in imaginary time: ');
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while t_idx < Params.sim_time_cut_off
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@ -69,15 +69,12 @@ function [psi] = propagateWavefunction(this, psi, Params, VParams, Transf, VDk,
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Observ.residual = [Observ.residual res];
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Observ.res_idx = Observ.res_idx + 1;
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save(sprintf('./Data/Run_%03i/psi_gs.mat',Params.njob),'psi','muchem','Observ','t_idx','Transf','Params','VDk','V');
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%Adaptive time step -- Careful, this can quickly get out of control
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relres = abs(Observ.residual(Observ.res_idx)-Observ.residual(Observ.res_idx-1))/Observ.residual(Observ.res_idx);
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if relres <1e-4
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if AdaptIdx > 3 && abs(dt) > Params.mindt
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dt = dt / 2;
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fprintf('Time step changed to '); disp(dt);
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AdaptIdx = 0;
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elseif AdaptIdx > 3 && abs(dt) < Params.mindt
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break
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@ -95,6 +92,7 @@ function [psi] = propagateWavefunction(this, psi, Params, VParams, Transf, VDk,
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break
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end
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t_idx=t_idx+1;
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pb.run(100*t_idx/Params.sim_time_cut_off);
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end
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% Change in Energy
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@ -110,8 +108,5 @@ function [psi] = propagateWavefunction(this, psi, Params, VParams, Transf, VDk,
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% Chemical potential
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Observ.mucVec = [Observ.mucVec muchem];
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pb.run(' - Job Completed!');
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disp('Saving data...');
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save(sprintf('./Data/Run_%03i/psi_gs.mat',Params.njob),'psi','muchem','Observ','t_idx','Transf','Params','VDk','V');
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disp('Save complete!');
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pb.run(' - Done!');
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end
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@ -23,13 +23,13 @@ function [Params, Transf, psi, V, VDk] = run(this)
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[psi,V,VDk] = this.initialize(Params,VParams,Transf);
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ells(1) = VarArray(1);
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nus(1) = VarArray(2);
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E_Var = @(x) this.Calculator.calculateVariationalEnergy(psi,Params,x,Transf,VDk,V)/Params.N;
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E_Var = @(x) this.Calculator.calculateVariationalEnergy(psi, Params, x, Transf, VDk, V)/Params.N;
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E_vs_iter(1) = E_Var([ells(1) nus(1)]);
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t_idx = 1; % Start at t = 0;
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for nn = 1:Params.SelfConIter
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Observ.EVec = []; Observ.NormVec = []; Observ.PCVec = []; Observ.tVecPlot = []; Observ.mucVec = [];
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Observ.EVec = []; Observ.NormVec = []; Observ.PCVec = []; Observ.tVecPlot = []; Observ.mucVec = []; Observ.residual = [];
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Observ.res_idx = 1;
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VParams.ell = VarArray(1);
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@ -47,11 +47,11 @@ function [Params, Transf, psi, V, VDk] = run(this)
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psi = psi + 4*noise;
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% --- Run ---
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[psi,Observ] = this.propagateWavefunction(psi,Params,Transf,VDk,V,t_idx,Observ);
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[psi] = this.propagateWavefunction(psi, Params, VParams, Transf, VDk, V, t_idx, Observ);
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psi = gather(psi);
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% --- Constrained minimization ---
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E_Var = @(x) this.Calculator.calculateVariationalEnergy(psi,Params,x,Transf,V)/Params.N;
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E_Var = @(x) this.Calculator.calculateVariationalEnergy(psi, Params, x, Transf, VDk, V)/Params.N;
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VarArray = fmincon(E_Var,VarArray,[],[],[],[],[Params.ell_lower, Params.nu_lower],[Params.ell_upper, Params.nu_upper],[],fminconoptions);
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% --- Convergence check ---
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@ -61,13 +61,16 @@ function [Params, Transf, psi, V, VDk] = run(this)
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relnudiff = abs(nus(nn+1)-nus(nn))/nus(nn);
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E_vs_iter = [E_vs_iter E_Var(VarArray)];
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save(sprintf('./Data/Run_%03i/psi_gs_%i.mat',runIdx,nn),'psi','Observ','Transf','Params','VDk','V','VarArray');
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save(sprintf('./Data/Run_%03i/psi_gs_%i.mat',Params.njob),'psi','Observ','Transf','Params','VDk','V','VarArray');
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if relelldiff < Params.ellcutoff && relnudiff < Params.nucutoff
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break
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end
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end
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save(sprintf('./Data/Run_%03i/psi_gs.mat',runIdx),'psi','Observ','Transf','Params','VDk','V','VarArray');
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delete(sprintf('./Data/Run_%03i/psi_gs_*.mat',runIdx))
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disp('Saving data...');
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save(sprintf('./Data/Run_%03i/psi_gs.mat',Params.njob),'psi','Observ','Transf','Params','VDk','V','VarArray');
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disp('Save complete!');
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delete(sprintf('./Data/Run_%03i/psi_gs_*.mat',Params.njob))
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end
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