diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/AnalyzeResults.m b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/AnalyzeResults.m index d46dc76..95703ba 100644 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/AnalyzeResults.m +++ b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/AnalyzeResults.m @@ -1,4 +1,8 @@ -load('ExtractingKRoton_Result.mat') +%% Across range of a_s, n + +% load('.\Results\ExtractingKRoton_Result_Below1000.mat') +% load('.\Results\ExtractingKRoton_Result_Above1000.mat') +load('.\Results\ExtractingKRoton_Result_Above10000.mat') PlanckConstantReduced = 6.62607015E-34/(2*pi); AtomicMassUnit = 1.660539066E-27; @@ -10,6 +14,293 @@ DyMagneticMoment = 9.93*BohrMagneton; add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length +% Create a tiled layout with tighter spacing +figure(17) +clf +set(gcf,'Position',[50 50 1800 500]) +t = tiledlayout(1, 3, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid + +% First subplot +nexttile; % Equivalent to subplot(2, 2, 1) +for idx = 1:length(data_struct) + theta_values = data_struct(idx).theta_values; + eps_dd_values = data_struct(idx).eps_dd_values; + plot(theta_values, eps_dd_values, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); + hold on +end +xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); +ylabel('$\epsilon_{dd}$', 'fontsize', 16, 'interpreter', 'latex'); +grid on +legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size + +% Second subplot +nexttile; % Equivalent to subplot(2, 2, 2) +for idx = 1:length(data_struct) + theta_values = data_struct(idx).theta_values; + n_values = data_struct(idx).n_values; + plot(theta_values, n_values * 1E-15, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); + hold on +end +xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); +ylabel('$n (\times 10^{3} \mu m^{-2})$', 'fontsize', 16, 'interpreter', 'latex'); +grid on +legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size + +% Third subplot +nexttile; % Equivalent to subplot(2, 2, 3) +for idx = 1:length(data_struct) + theta_values = data_struct(idx).theta_values; + k_roton_values = data_struct(idx).k_roton_values; + plot(theta_values, k_roton_values * 1E-6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); + hold on +end +xlabel('$\theta$','fontsize',16,'interpreter','latex'); +ylabel('$k_{roton} (\mu m^{-1})$','fontsize',16,'interpreter','latex'); +grid on +legend('location', 'northeast','fontsize', 10, 'Interpreter','latex') + +% Adjust layout to minimize space +t.TileSpacing = 'compact'; % Minimize space between tiles +t.Padding = 'compact'; % Minimize padding around the layout + +% Convert to units relevant to experiment + +% Create a tiled layout with tighter spacing +figure(18) +clf +set(gcf,'Position',[50 50 1800 500]) +t = tiledlayout(1, 3, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid + +% First subplot +nexttile; % Equivalent to subplot(2, 2, 1) +for idx = 1:length(data_struct) + theta_values = data_struct(idx).theta_values; + eps_dd_values = data_struct(idx).eps_dd_values; + plot(theta_values, (1 ./ eps_dd_values) * (add / BohrRadius), '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); + hold on +end +xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); +ylabel('$a_s (\times a_o)$', 'fontsize', 16, 'interpreter', 'latex'); +grid on +legend('location', 'southeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size + +% Second subplot +nexttile; % Equivalent to subplot(2, 2, 2) +for idx = 1:length(data_struct) + theta_values = data_struct(idx).theta_values; + n_values = data_struct(idx).n_values; + Lx = 10e-6; + Ly = 10e-6; + AtomNumber = n_values .* Lx * Ly; + plot(theta_values, AtomNumber * 1e-5, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); + hold on +end +xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); +ylabel('Atom number in a trap of area 100 $\mu m^2 (\times 10^{5})$', 'fontsize', 16, 'interpreter', 'latex'); +grid on +legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size + +% Third subplot +nexttile; % Equivalent to subplot(2, 2, 3) +for idx = 1:length(data_struct) + theta_values = data_struct(idx).theta_values; + lambda_roton_values = (2 * pi) ./ data_struct(idx).k_roton_values; + plot(theta_values, lambda_roton_values * 1E6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); + hold on +end +xlabel('$\theta$','fontsize',16,'interpreter','latex'); +ylabel('$\lambda_{roton} (\mu m)$','fontsize',16,'interpreter','latex'); +grid on +legend('location', 'northeast','fontsize', 10, 'Interpreter','latex') + +% Adjust layout to minimize space +t.TileSpacing = 'compact'; % Minimize space between tiles +t.Padding = 'compact'; % Minimize padding around the layout + +%% Fixed Density results + +load('.\Results\ExtractingKRoton_Result_FixedDensity_phi0.mat') + +PlanckConstantReduced = 6.62607015E-34/(2*pi); +AtomicMassUnit = 1.660539066E-27; +Dy164Mass = 163.929174751*AtomicMassUnit; +VacuumPermeability = 1.25663706212E-6; +BohrMagneton = 9.274009994E-24; +BohrRadius = 5.2917721067E-11; +DyMagneticMoment = 9.93*BohrMagneton; + +add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length + +% Create a tiled layout with tighter spacing +figure(19) +clf +set(gcf,'Position',[50 50 1200 500]) +t = tiledlayout(1, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid + +% First subplot +nexttile; +for idx = 1:length(data_struct) + theta_values = data_struct(idx).theta_values; + eps_dd_values = data_struct(idx).eps_dd_values; + plot(theta_values, eps_dd_values, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); + hold on +end +xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); +ylabel('$\epsilon_{dd}$', 'fontsize', 16, 'interpreter', 'latex'); +grid on +legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size + +% Second subplot +nexttile; +for idx = 1:length(data_struct) + theta_values = data_struct(idx).theta_values; + k_roton_values = data_struct(idx).k_roton_values; + plot(theta_values, k_roton_values * 1E-6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); + hold on +end +xlabel('$\theta$','fontsize',16,'interpreter','latex'); +ylabel('$k_{roton} (\mu m^{-1})$','fontsize',16,'interpreter','latex'); +grid on +legend('location', 'northeast','fontsize', 10, 'Interpreter','latex') + +% Adjust layout to minimize space +t.TileSpacing = 'compact'; % Minimize space between tiles +t.Padding = 'compact'; % Minimize padding around the layout + +% Create a tiled layout with tighter spacing +figure(20) +clf +set(gcf,'Position',[50 50 1200 500]) +t = tiledlayout(1, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid + +% First subplot +nexttile; +for idx = 1:length(data_struct) + theta_values = data_struct(idx).theta_values; + eps_dd_values = data_struct(idx).eps_dd_values; + plot(theta_values, (1 ./ eps_dd_values) * (add / BohrRadius), '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); + hold on +end +xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); +ylabel('$a_s (\times a_o)$', 'fontsize', 16, 'interpreter', 'latex'); +grid on +legend('location', 'northwest', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size + +% Second subplot +nexttile; +for idx = 1:length(data_struct) + theta_values = data_struct(idx).theta_values; + lambda_roton_values = (2 * pi) ./ data_struct(idx).k_roton_values; + semilogy(theta_values, lambda_roton_values * 1E6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); + hold on +end +% ylim([0 2]) +xlabel('$\theta$','fontsize',16,'interpreter','latex'); +ylabel('$\lambda_{roton} (\mu m)$','fontsize',16,'interpreter','latex'); +grid on +legend('location', 'southeast','fontsize', 10, 'Interpreter','latex') + +% Adjust layout to minimize space +t.TileSpacing = 'compact'; % Minimize space between tiles +t.Padding = 'compact'; % Minimize padding around the layout + +%% Fixed Density results - compare two orthogonal directions + +data0 = load('.\Results\ExtractingKRoton_Result_FixedDensity_phi0.mat'); +data90 = load('.\Results\ExtractingKRoton_Result_FixedDensity_phi90.mat'); + +PlanckConstantReduced = 6.62607015E-34/(2*pi); +AtomicMassUnit = 1.660539066E-27; +Dy164Mass = 163.929174751*AtomicMassUnit; +VacuumPermeability = 1.25663706212E-6; +BohrMagneton = 9.274009994E-24; +BohrRadius = 5.2917721067E-11; +DyMagneticMoment = 9.93*BohrMagneton; + +add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length + +% Create a tiled layout with tighter spacing +figure(21) +clf +set(gcf,'Position',[50 50 1200 500]) +t = tiledlayout(1, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid + +idx = 4; + +% First subplot +nexttile; +theta_values = data0.data_struct(idx).theta_values; +eps_dd_values = data0.data_struct(idx).eps_dd_values; +plot(theta_values, eps_dd_values, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data0.data_struct(idx).wz_value), ' Hz; $\phi = 0^\circ$']); +hold on +theta_values = data90.data_struct(idx).theta_values; +eps_dd_values = data90.data_struct(idx).eps_dd_values; +plot(theta_values, eps_dd_values, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data90.data_struct(idx).wz_value), ' Hz; $\phi = 90^\circ$']); +xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); +ylabel('$\epsilon_{dd}$', 'fontsize', 16, 'interpreter', 'latex'); +grid on +legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size + +% Second subplot +nexttile; +theta_values = data0.data_struct(idx).theta_values; +k_roton_values = data0.data_struct(idx).k_roton_values; +plot(theta_values, k_roton_values * 1E-6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data0.data_struct(idx).wz_value), ' Hz; $\phi = 0^\circ$']); +hold on +theta_values = data90.data_struct(idx).theta_values; +k_roton_values = data90.data_struct(idx).k_roton_values; +plot(theta_values, k_roton_values * 1E-6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data90.data_struct(idx).wz_value), ' Hz; $\phi = 90^\circ$']); +xlabel('$\theta$','fontsize',16,'interpreter','latex'); +ylabel('$k_{roton} (\mu m^{-1})$','fontsize',16,'interpreter','latex'); +grid on +legend('location', 'northeast','fontsize', 10, 'Interpreter','latex') + +% Adjust layout to minimize space +t.TileSpacing = 'compact'; % Minimize space between tiles +t.Padding = 'compact'; % Minimize padding around the layout + + +% Create a tiled layout with tighter spacing +figure(22) +clf +set(gcf,'Position',[50 50 1200 500]) +t = tiledlayout(1, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid + +% First subplot +nexttile; +theta_values = data0.data_struct(idx).theta_values; +eps_dd_values = data0.data_struct(idx).eps_dd_values; +plot(theta_values, (1 ./ eps_dd_values) * (add / BohrRadius), '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data0.data_struct(idx).wz_value), ' Hz; $\phi = 0^\circ$']); +hold on +theta_values = data90.data_struct(idx).theta_values; +eps_dd_values = data90.data_struct(idx).eps_dd_values; +plot(theta_values, (1 ./ eps_dd_values) * (add / BohrRadius), '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data90.data_struct(idx).wz_value), ' Hz; $\phi = 90^\circ$']); +xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); +ylabel('$a_s (\times a_o)$', 'fontsize', 16, 'interpreter', 'latex'); +grid on +legend('location', 'northwest', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size + +% Second subplot +nexttile; +theta_values = data0.data_struct(idx).theta_values; +k_roton_values = data0.data_struct(idx).k_roton_values; +lambda_roton_values = (2 * pi) ./ k_roton_values; +semilogy(theta_values, lambda_roton_values * 1E6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data0.data_struct(idx).wz_value), ' Hz; $\phi = 0^\circ$']); +hold on +theta_values = data90.data_struct(idx).theta_values; +k_roton_values = data90.data_struct(idx).k_roton_values; +lambda_roton_values = (2 * pi) ./ k_roton_values; +semilogy(theta_values, lambda_roton_values * 1E6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data90.data_struct(idx).wz_value), ' Hz; $\phi = 90^\circ$']); +xlabel('$\theta$','fontsize',16,'interpreter','latex'); +ylabel('$\lambda_{roton} (\mu m)$','fontsize',16,'interpreter','latex'); +grid on +legend('location', 'northwest','fontsize', 10, 'Interpreter','latex') + +% Adjust layout to minimize space +t.TileSpacing = 'compact'; % Minimize space between tiles +t.Padding = 'compact'; % Minimize padding around the layout + +%% %{ figure(13) clf @@ -71,65 +362,3 @@ ylabel('$k_{roton} (\mu m^{-1})$','fontsize',16,'interpreter','latex'); grid on legend('location', 'northeast','fontsize', 16, 'Interpreter','latex') %} - -% Create a tiled layout with tighter spacing -figure(17) -clf -set(gcf,'Position',[50 50 1200 900]) -t = tiledlayout(2, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid - -% First subplot -nexttile; % Equivalent to subplot(2, 2, 1) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - eps_dd_values = data_struct(idx).eps_dd_values; - plot(theta_values, eps_dd_values, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); -ylabel('$\epsilon_{dd}$', 'fontsize', 16, 'interpreter', 'latex'); -grid on -legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size - -% Second subplot -nexttile; % Equivalent to subplot(2, 2, 2) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - eps_dd_values = data_struct(idx).eps_dd_values; - plot(theta_values, (1 ./ eps_dd_values) * (add / BohrRadius), '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); -ylabel('$a_s (\times a_o)$', 'fontsize', 16, 'interpreter', 'latex'); -grid on -legend('location', 'southeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size - -% Third subplot -nexttile; % Equivalent to subplot(2, 2, 3) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - n_values = data_struct(idx).n_values; - plot(theta_values, n_values * 1E-15, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); -ylabel('$n (\times 10^{3} \mu m^{-2})$', 'fontsize', 16, 'interpreter', 'latex'); -grid on -legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size - -% Fourth subplot -nexttile; % Equivalent to subplot(2, 2, 4) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - k_roton_values = data_struct(idx).k_roton_values; - plot(theta_values, k_roton_values * 1E-6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$','fontsize',16,'interpreter','latex'); -ylabel('$k_{roton} (\mu m^{-1})$','fontsize',16,'interpreter','latex'); -grid on -legend('location', 'northeast','fontsize', 10, 'Interpreter','latex') - -% Adjust layout to minimize space -t.TileSpacing = 'compact'; % Minimize space between tiles -t.Padding = 'compact'; % Minimize padding around the layout diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ExtractingKRoton.m b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ExtractingKRoton.m index 8b56ae8..bb7ce0f 100644 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ExtractingKRoton.m +++ b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ExtractingKRoton.m @@ -36,13 +36,21 @@ DyMagneticMoment = 9.93*BohrMagneton; %-------DEPLOY-------% nadd2s = 0.005:0.005:0.5; -as_to_add = 0.35:0.001:1.15; +as_to_add = 0.250:0.001:1.15; data_struct = struct; -wz_values = [150, 300, 500, 750]; + +% wz_values = [150, 300, 500, 750]; +% kvec = linspace(0, 5e6, 1000); % Vector of magnitudes of k vector + +wz_values = [1000, 3000, 5000, 7000]; +kvec = linspace(0, 15e6, 1000); % Vector of magnitudes of k vector + +% wz_values = [10000, 13000, 15000]; +% kvec = linspace(0, 25e6, 1000); % Vector of magnitudes of k vector + theta_values = 0:5:45; % Range of theta values phi = 0; % Azimuthal angle of momentum vector -kvec = linspace(0, 5e6, 1000); % Vector of magnitudes of k vector for mainloop_idx = 1:length(wz_values) format long @@ -135,8 +143,80 @@ for mainloop_idx = 1:length(wz_values) %} end -save('ExtractingKRoton_Result.mat', 'data_struct'); +save('.\Results\ExtractingKRoton_Result.mat', 'data_struct'); +%% Extracting values from the roton instability boundary for tilted dipoles - fixed atom number, trap frequency + +%-------DEPLOY-------% + +N = 1E5; +add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length +area = 100; % in square micrometers +ppmum = N / area; +nadd2s = ppmum*1E12*add^2; +as_to_add = 0.150:0.001:1.15; + +data_struct = struct; + +wz_values = [500, 750, 1000, 2000]; +kvec = linspace(0, 15e6, 1000); % Vector of magnitudes of k vector + +theta_values = 0:5:90; % Range of theta values +phi = 90; % Azimuthal angle of momentum vector + +for mainloop_idx = 1:length(wz_values) + format long + + PlanckConstantReduced = 6.62607015E-34/(2*pi); + AtomicMassUnit = 1.660539066E-27; + Dy164Mass = 163.929174751*AtomicMassUnit; + VacuumPermeability = 1.25663706212E-6; + BohrMagneton = 9.274009994E-24; + DyMagneticMoment = 9.93*BohrMagneton; + + wz = 2 * pi * wz_values(mainloop_idx); % Trap frequency in the tight confinement direction + lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length + add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length + gdd = VacuumPermeability*DyMagneticMoment^2/3; + var_widths = zeros(length(as_to_add), length(nadd2s)); + + x0 = 5; + Aineq = []; + Bineq = []; + Aeq = []; + Beq = []; + lb = [1]; + ub = [10]; + nonlcon = []; + fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); + + for idx = 1:length(nadd2s) + for jdx = 1:length(as_to_add) + AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms + as = (as_to_add(jdx) * add); % Scattering length + gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength + TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); + sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); + var_widths(jdx, idx) = sigma; + end + end + + eps_dd_values = zeros(length(theta_values), 1); + k_roton_values = zeros(length(theta_values), 1); + + for idx = 1:length(theta_values) + theta = theta_values(idx); + [eps_dd_values(idx), k_roton_values(idx)] = extractFromBoundaryPoint(theta, phi, nadd2s, as_to_add, var_widths, wz, lz, kvec); + end + + data_struct(mainloop_idx).wz_value = wz / (2 * pi); + data_struct(mainloop_idx).theta_values = theta_values; + data_struct(mainloop_idx).eps_dd_values = eps_dd_values; + data_struct(mainloop_idx).k_roton_values = k_roton_values; + +end + +save('.\Results\ExtractingKRoton_Result_FixedDensity_phi90.mat', 'data_struct'); %% function [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi) Go = sqrt(pi) * (k * MeanWidth/sqrt(2)) .* exp((k * MeanWidth/sqrt(2)).^2) .* erfc((k * MeanWidth/sqrt(2))); @@ -314,3 +394,110 @@ function [eps_dd, AtomNumberDensity, k_roton] = extractFromBoundaryCurve(theta, k_roton = NaN; end end + +function [eps_dd, k_roton] = extractFromBoundaryPoint(theta, phi, nadd2s, as_to_add, var_widths, wz, lz, kvec) + + format long + + PlanckConstantReduced = 6.62607015E-34/(2*pi); + AtomicMassUnit = 1.660539066E-27; + Dy164Mass = 163.929174751*AtomicMassUnit; + VacuumPermeability = 1.25663706212E-6; + BohrMagneton = 9.274009994E-24; + DyMagneticMoment = 9.93*BohrMagneton; + add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length + gdd = VacuumPermeability*DyMagneticMoment^2/3; + phase_diagram = zeros(length(as_to_add), length(nadd2s)); + w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction + l0 = sqrt(PlanckConstantReduced/(Dy164Mass * w0)); % Defining a harmonic oscillator length + + for idx = 1:length(nadd2s) + for jdx = 1:length(as_to_add) + AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms + as = (as_to_add(jdx) * add); % Scattering length + eps_dd = add/as; % Relative interaction strength + gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength + gdd = VacuumPermeability*DyMagneticMoment^2/3; + MeanWidth = var_widths(jdx, idx) * lz; % Mean width of Gaussian ansatz + + [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(kvec, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space + + % == Quantum Fluctuations term == % + gammaQF = (32/3) * gs * (as^3/pi)^(1/2) * (1 + ((3/2) * eps_dd^2)); + gamma5 = sqrt(2/5) / (sqrt(pi) * MeanWidth)^(3/2); + gQF = gamma5 * gammaQF; + + % == Dispersion relation == % + DeltaK = ((PlanckConstantReduced^2 .* kvec.^2) ./ (2 * Dy164Mass)) + ((2 * AtomNumberDensity) .* Ukk) + (3 * gQF * AtomNumberDensity^(3/2)); + EpsilonK = sqrt(((PlanckConstantReduced^2 .* kvec.^2) ./ (2 * Dy164Mass)) .* DeltaK); + phase_diagram(jdx, idx) = ~isreal(EpsilonK); + end + end + + matrix = phase_diagram; + + % Initialize arrays to store row and column indices of transitions + row_indices = []; + col_indices = []; + + % Loop through the matrix to find transitions from 0 to 1 + [rows, cols] = size(matrix); + for j = 1:cols + for i = 2:rows + if matrix(i-1, j) == 1 && matrix(i, j) == 0 + row_indices = [row_indices; i-1]; + col_indices = [col_indices; j]; + break; % Stop after the first transition in the column + end + end + end + + % Now extract the values from the corresponding vectors + xvals = zeros(length(col_indices), 1); + yvals = zeros(length(row_indices), 1); + for k = 1:length(row_indices) + row = row_indices(k); + col = col_indices(k); + xvals(k) = nadd2s(col); + yvals(k) = as_to_add(row); + end + + instability_boundary = [xvals, yvals]; + + if ~isempty(instability_boundary) + val = instability_boundary(2); + AtomNumberDensity = instability_boundary(1) / add^2; % Areal density of atoms + as = val * add; % Scattering length + eps_dd = 1/val; % Relative interaction strength + gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength + x0 = 5; + Aineq = []; + Bineq = []; + Aeq = []; + Beq = []; + lb = [1]; + ub = [10]; + nonlcon = []; + fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); + TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); + sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); + MeanWidth = sigma * lz; % Mean width of Gaussian ansatz + [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(kvec, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space + + % == Quantum Fluctuations term == % + gammaQF = (32/3) * gs * (as^3/pi)^(1/2) * (1 + ((3/2) * eps_dd^2)); + gamma5 = sqrt(2/5) / (sqrt(pi) * MeanWidth)^(3/2); + gQF = gamma5 * gammaQF; + DeltaK = ((PlanckConstantReduced^2 .* kvec.^2) ./ (2 * Dy164Mass)) + ((2 * AtomNumberDensity) .* Ukk) + (3 * gQF * AtomNumberDensity^(3/2)); + EpsilonK = sqrt(((PlanckConstantReduced^2 .* kvec.^2) ./ (2 * Dy164Mass)) .* DeltaK); + 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a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/bwhpc_matlab_gpe_sim_cpu.slurm b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/bwhpc_matlab_gpe_sim_cpu.slurm new file mode 100644 index 0000000..ad3e154 --- /dev/null +++ b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/bwhpc_matlab_gpe_sim_cpu.slurm @@ -0,0 +1,38 @@ +#!/bin/bash +########### Begin SLURM header ########### +#Partition +#SBATCH --partition=cpu-single +# Request number of nodes and CPU cores per node for job +#SBATCH --nodes=1 +#SBATCH --ntasks-per-node=1 +#SBATCH --cpus-per-task=10 +#SBATCH --mem=2G +# Estimated wallclock time for job +#SBATCH --time=00:30:00 +#SBATCH --job-name=simulation +#SBATCH --error=simulation.err +#SBATCH --output=simulation.out + +########### End SLURM header ########## + +echo "Working Directory: $PWD" +echo "Running on host $HOSTNAME" +echo "Job id: $SLURM_JOB_ID" +echo "Job name: $SLURM_JOB_NAME" +echo "Number of nodes allocated to job: $SLURM_JOB_NUM_NODES" +echo "Number of cores allocated to job: $SLURM_JOB_CPUS_PER_NODE" + + +# Load module +module load math/matlab/R2023a + +echo Directory is `pwd` +echo "Initiating Job..." + +# Start a Matlab program +matlab -nodisplay -nosplash -r "ExtractingKRoton" + +# notice for tests +echo "Job terminated successfully" + +exit