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Karthik 2025-05-09 00:33:03 +02:00
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commit 78f435df89
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Estimations/VisualizeCosineModulatedAnsatz.m
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@ -195,5 +195,100 @@ colorbar;
title('Gaussian + Honeycomb lattice'); title('Gaussian + Honeycomb lattice');
xlabel('x'); ylabel('y'); xlabel('x'); ylabel('y');
%%
% Parameters
A = 1; % Modulation amplitude
p = 2 * pi / 10; % Magnitude of p_j (adjust wavelength)
L = 50; % Spatial extent
N = 500; % Grid resolution
% Coordinate grid
x = linspace(-L, L, N);
y = linspace(-L, L, N);
[X, Y] = meshgrid(x, y);
% Define p_j vectors at 0°, 120°, and 240°
angles = [0, 2*pi/3, 4*pi/3];
P = zeros(size(X));
for j = 1:3
pj = p * [cos(angles(j)); sin(angles(j))]; % 2D vector
dotprod = pj(1) * X + pj(2) * Y;
P = P + cos(dotprod);
end
P = A * P; % Apply modulation amplitude
% Plot
figure(20);
imagesc(x, y, P);
axis equal tight;
colormap turbo; colorbar;
xlabel('$x$', 'Interpreter', 'latex', 'FontSize', 14);
ylabel('$y$', 'Interpreter', 'latex', 'FontSize', 14);
title('Triangle Phase: $P(\mathbf{r}_\perp) = A \sum_{j=1}^3 \cos(\mathbf{p}_j \cdot \mathbf{r}_\perp)$', ...
'Interpreter', 'latex', 'FontSize', 16);
% Parameters
A = -1; % Modulation amplitude
p = 2 * pi / 10; % Magnitude of p_j (adjust wavelength)
L = 50; % Spatial extent
N = 500; % Grid resolution
% Coordinate grid
x = linspace(-L, L, N);
y = linspace(-L, L, N);
[X, Y] = meshgrid(x, y);
r = cat(3, X, Y);
% Define p_j vectors at 0°, 120°, and 240°
angles = [0, 2*pi/3, 4*pi/3];
P = zeros(size(X));
for j = 1:3
pj = p * [cos(angles(j)); sin(angles(j))]; % 2D vector
dotprod = pj(1) * X + pj(2) * Y;
P = P + cos(dotprod);
end
P = A * P; % Apply modulation amplitude
% Plot
figure(21);
imagesc(x, y, P);
axis equal tight;
colormap turbo; colorbar;
xlabel('$x$', 'Interpreter', 'latex', 'FontSize', 14);
ylabel('$y$', 'Interpreter', 'latex', 'FontSize', 14);
title('Honeycomb Phase: $P(\mathbf{r}_\perp) = A \sum_{j=1}^3 \cos(\mathbf{p}_j \cdot \mathbf{r}_\perp)$', ...
'Interpreter', 'latex', 'FontSize', 16);
% Parameters
A = 1;
p = 2 * pi / 10; % Wavevector magnitude
theta = pi/2; % Angle of the wavevector (45° for diagonals)
L = 50;
N = 500;
% Grid
x = linspace(-L, L, N);
y = linspace(-L, L, N);
[X, Y] = meshgrid(x, y);
% Define wavevector p
p_vec = p * [cos(theta); sin(theta)];
% Compute density
P = A * cos(p_vec(1) * X + p_vec(2) * Y);
% Plot
figure(22);
imagesc(x, y, P);
axis equal tight;
colormap turbo; colorbar;
xlabel('$x$', 'Interpreter', 'latex', 'FontSize', 14);
ylabel('$y$', 'Interpreter', 'latex', 'FontSize', 14);
title('Stripe Phase: $P(\mathbf{r}_\perp) = A \cos(\mathbf{p} \cdot \mathbf{r}_\perp)$', ...
'Interpreter', 'latex', 'FontSize', 16);