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Karthik 2025-01-14 19:04:37 +01:00
parent 0833bddee8
commit f3ac9e3b12
2 changed files with 52 additions and 117 deletions
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2
Estimations/DipolarDispersionAndRotonInstabilityBoundary/DipolarDispersion2D.m
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@ -168,7 +168,7 @@ for theta = theta_values
cbar1.Label.Interpreter = 'latex'; cbar1.Label.Interpreter = 'latex';
xlabel('$k_x l_o$','fontsize',16,'interpreter','latex'); xlabel('$k_x l_o$','fontsize',16,'interpreter','latex');
ylabel('$k_y l_o$','fontsize',16,'interpreter','latex'); ylabel('$k_y l_o$','fontsize',16,'interpreter','latex');
title(['$\theta = ',num2str(Params.theta), '; \eta = ', num2str(Params.eta),'$'],'fontsize',16,'interpreter','latex') title(['2-D Dispersion: $\theta = ',num2str(Params.theta), '; \eta = ', num2str(Params.eta),'$'],'fontsize',16,'interpreter','latex')
% Capture the frame and write to video % Capture the frame and write to video
% frame = getframe(gcf); % Capture the current figure % frame = getframe(gcf); % Capture the current figure

167
Estimations/DipolarDispersionAndRotonInstabilityBoundary/ExtractingKRoton.m
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@ -28,19 +28,17 @@ Dy164Mass = 163.929174751*AtomicMassUnit;
Dy164IsotopicAbundance = 0.2826; Dy164IsotopicAbundance = 0.2826;
DyMagneticMoment = 9.93*BohrMagneton; DyMagneticMoment = 9.93*BohrMagneton;
%% k_roton at the instability boundary for tilted dipoles %% Roton instability boundary for tilted dipoles
wz = 2 * pi * 72.4; % Trap frequency in the tight confinement direction
theta = 0; % Polar angle of dipole moment
wz = 2 * pi * 500; % Trap frequency in the tight confinement direction
lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length
add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length
gdd = VacuumPermeability*DyMagneticMoment^2/3; gdd = VacuumPermeability*DyMagneticMoment^2/3;
% nadd2s = 0.2:0.005:0.75; nadd2s = 0.05:0.001:0.25;
% as_to_add = 0.4:0.002:0.5; as_to_add = 0.76:0.001:0.81;
nadd2s = 0.05:0.005:0.25;
as_to_add = 0.50:0.001:0.80;
var_widths = zeros(length(as_to_add), length(nadd2s)); var_widths = zeros(length(as_to_add), length(nadd2s));
x0 = 5; x0 = 5;
@ -64,13 +62,11 @@ for idx = 1:length(nadd2s)
end end
end end
% ====================================================================================================================================================== % %% ====================================================================================================================================================== %
theta = 0; % Polar angle of dipole moment
phi = 0; % Azimuthal angle of momentum vector phi = 0; % Azimuthal angle of momentum vector
k = linspace(0, 2.25e6, 1000); % Vector of magnitudes of k vector k = linspace(0, 2.25e6, 1000); % Vector of magnitudes of k vector
instability_boundary = zeros(length(as_to_add), length(nadd2s)); instability_boundary = zeros(length(as_to_add), length(nadd2s));
k_roton = zeros(length(as_to_add), length(nadd2s));
ScatteringLengths = zeros(length(as_to_add), 1); ScatteringLengths = zeros(length(as_to_add), 1);
AtomNumber = zeros(length(nadd2s), 1); AtomNumber = zeros(length(nadd2s), 1);
w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction
@ -99,119 +95,58 @@ for idx = 1:length(nadd2s)
DeltaK = ((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) + ((2 * AtomNumberDensity) .* Ukk) + (3 * gQF * AtomNumberDensity^(3/2)); DeltaK = ((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) + ((2 * AtomNumberDensity) .* Ukk) + (3 * gQF * AtomNumberDensity^(3/2));
EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK); EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK);
instability_boundary(jdx, idx) = ~isreal(EpsilonK); instability_boundary(jdx, idx) = ~isreal(EpsilonK);
k_roton_indices = find(imag(EpsilonK) ~= 0); end
if ~isempty(k_roton_indices) end
k_roton(jdx, idx) = k(k_roton_indices(1));
else figure(6)
k_roton(jdx, idx) = NaN; clf
set(gcf,'Position',[50 50 950 750])
imagesc(nadd2s, as_to_add, instability_boundary); % Specify x and y data for axes
set(gca, 'YDir', 'normal'); % Correct the y-axis direction
colorbar; % Add a colorbar
xlabel('$na_{dd}^2$','fontsize',16,'interpreter','latex');
ylabel('$a_s/a_{dd}$','fontsize',16,'interpreter','latex');
title('Roton instability boundary','fontsize',16,'interpreter','latex')
%%
matrix = instability_boundary;
% 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];
col_indices = [col_indices; j];
break; % Stop after the first transition in the column
end end
end end
end end
%
k_roton_vals = (k_roton .* add);
%
figure(8)
clf
set(gcf,'Position',[50 50 950 750])
imagesc(AtomNumber*1E-5, ScatteringLengths, k_roton_vals); % Specify x and y data for axes
set(gca, 'YDir', 'normal'); % Correct the y-axis direction
cbar1 = colorbar;
cbar1.Label.Interpreter = 'latex';
% ylabel(cbar1,'$$','FontSize',16,'Rotation',270)
xlabel(' Atom number for a trap area of 100$\mu m^2 ~ (\times 10^5)$','fontsize',16,'interpreter','latex');
ylabel('Scattering length ($\times a_0$)','fontsize',16,'interpreter','latex');
title('Roton instability boundary','fontsize',16,'interpreter','latex')
%
% Get the size of the matrix
k_roton_vals = flipud(k_roton_vals);
[rows, cols] = size(k_roton_vals);
first_nonnan_row = zeros(1, cols); % Now extract the values from the corresponding vectors
xvals = zeros(length(col_indices), 1);
% Loop through each column yvals = zeros(length(row_indices), 1);
for col = 1:cols for k = 1:length(row_indices)
nonnan_rows = find(~isnan(k_roton_vals(:, col))); row = row_indices(k);
col = col_indices(k);
if ~isempty(nonnan_rows) xvals(k) = nadd2s(col);
first_nonnan_row(col) = nonnan_rows(1); yvals(k) = as_to_add(row);
else
first_nonnan_row(col) = NaN; % Use NaN to represent no non-zero elements in this column
end
end end
% Create column indices (1 to number of columns) % Plot the extracted values
column_indices = 1:cols; figure(7);
% plot(xvals, yvals, '-o');
% Use row and column indices to extract the first non-zero elements title('Instability Boundary');
k_roton_instability_boundary = arrayfun(@(r, c) k_roton_vals(r, c), first_nonnan_row(~isnan(first_nonnan_row)), column_indices(~isnan(first_nonnan_row))); xlabel('$na_{dd}^2$','fontsize',16,'interpreter','latex');
ylabel('$a_s/a_{dd}$','fontsize',16,'interpreter','latex')
figure(9)
clf
set(gcf,'Position',[50 50 950 750])
xvals = AtomNumber*1E-5;
yvals = k_roton_instability_boundary;
plot(xvals', yvals,LineWidth=2.0)
xlabel(' Atom number for a trap area of 100$\mu m^2 ~ (\times 10^5)$','fontsize',16,'interpreter','latex');
ylabel('$k_{\rho}a_{dd}$','fontsize',16,'interpreter','latex')
title('$k_{roton}$ at the instability boundary','fontsize',16,'interpreter','latex')
grid on
%% %%
function [Transf] = setupSpace(Params)
Transf.Xmax = 0.5*Params.Lx;
Transf.Ymax = 0.5*Params.Ly;
Nx = Params.Nx;
Ny = Params.Ny;
% Fourier grids
x = linspace(-0.5*Params.Lx,0.5*Params.Lx-Params.Lx/Params.Nx,Params.Nx);
Kmax = pi*Params.Nx/Params.Lx;
kx = linspace(-Kmax,Kmax,Nx+1);
kx = kx(1:end-1);
dkx = kx(2)-kx(1);
kx = fftshift(kx);
y = linspace(-0.5*Params.Ly,0.5*Params.Ly-Params.Ly/Params.Ny,Params.Ny);
Kmax = pi*Params.Ny/Params.Ly;
ky = linspace(-Kmax,Kmax,Ny+1);
ky = ky(1:end-1);
dky = ky(2)-ky(1);
ky = fftshift(ky);
[Transf.X,Transf.Y] = ndgrid(x,y);
[Transf.KX,Transf.KY] = ndgrid(kx,ky);
Transf.x = x;
Transf.y = y;
Transf.kx = kx;
Transf.ky = ky;
Transf.dx = x(2)-x(1);
Transf.dy = y(2)-y(1);
Transf.dkx = dkx;
Transf.dky = dky;
end
function VDk = compute2DPotentialInMomentumSpace(Transf, Params, MeanWidth)
% == Calculating the DDI potential in Fourier space with appropriate cutoff == %
% Interaction in K space
QX = Transf.KX*MeanWidth/sqrt(2);
QY = Transf.KY*MeanWidth/sqrt(2);
Qsq = QX.^2 + QY.^2;
absQ = sqrt(Qsq);
QDsq = QX.^2*cos(Params.phi)^2 + QY.^2*sin(Params.phi)^2;
% Bare interaction
Fpar = -1 + 3*sqrt(pi)*QDsq.*erfcx(absQ)./absQ; % Scaled complementary error function erfcx(x) = e^(x^2) * erfc(x)
Fperp = 2 - 3*sqrt(pi).*absQ.*erfcx(absQ);
Fpar(absQ == 0) = -1;
% Full DDI
VDk = (Fpar*sin(Params.alpha)^2 + Fperp*cos(Params.alpha)^2);
end
function [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi) 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))); Go = sqrt(pi) * (k * MeanWidth/sqrt(2)) .* exp((k * MeanWidth/sqrt(2)).^2) .* erfc((k * MeanWidth/sqrt(2)));
gamma4 = 1/(sqrt(2*pi) * MeanWidth); gamma4 = 1/(sqrt(2*pi) * MeanWidth);