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Added Gaussian+Modulation code snippets

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Karthik 2025-05-09 00:25:18 +02:00
parent b204f37068
commit 9c8f4c036c
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109
Estimations/VisualizeCosineModulatedAnsatz.m
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@ -88,3 +88,112 @@ title('Honeycomb Lattice ansatz for $|\Psi(x,y)|^2$', 'Interpreter', 'latex', 'F
xlabel('x'); xlabel('x');
ylabel('y'); ylabel('y');
colormap parula; colormap parula;
%% GAUSSIAN + STRIPES
c = 1; % Fourier coefficient
k = 5 * pi; % Use π to get just a couple of modulations across domain
n = 5;
sigma_y = 0.5; % Narrow along Y to limit rows
sigma_x = 0.3; % Wider along X
% Grid
x = linspace(-2, 2, 500);
y = linspace(-2, 2, 500);
[X, Y] = meshgrid(x, y);
% Gaussian envelope — anisotropic (narrow in y)
G = exp(-((X.^2)/(2*sigma_x^2) + (Y.^2)/(2*sigma_y^2)));
% Modulation function
modulation = (1 + (c * cos(n * k * Y))) / (1 + 0.5 * c^2);
% Combine
f_modulated = G .* modulation;
% Plot
figure(4);
imagesc(x, y, f_modulated);
axis xy; axis equal tight;
colormap('hot');
colorbar;
title('Gaussian + Stripe Modulation');
xlabel('x'); ylabel('y');
%% GAUSSIAN + TRIANGULAR LATTICE
% Parameters
c1 = 0.2;
c2 = 0.2;
k = 5 * pi; % Use π to get just a couple of modulations across domain
n = 5;
sigma_y = 0.5; % Narrow along Y to limit rows
sigma_x = 0.3; % Wider along X
% Grid
x = linspace(-2, 2, 500);
y = linspace(-2, 2, 500);
[X, Y] = meshgrid(x, y);
% Gaussian envelope — anisotropic (narrow in y)
G = exp(-((X.^2)/(2*sigma_x^2) + (Y.^2)/(2*sigma_y^2)));
% Triangular lattice modulation
modulation = 1 + ...
(c1 * cos(n * k * (2/sqrt(3)) * Y)) + ...
(2 * c2 * cos(n * k * (1/sqrt(3)) * Y) .* cos(n * k * X));
% Normalize
modulation = modulation / (1 + c1 + 2*c2);
% Combine with Gaussian
f_modulated = G .* modulation;
% Plot
figure(5);
imagesc(x, y, f_modulated);
axis xy; axis equal tight;
colormap('hot');
colorbar;
title('Gaussian + Triangular lattice');
xlabel('x'); ylabel('y');
%% GAUSSIAN + HONEYCOMB LATTICE
% Parameters
c1 = 0.2;
c2 = 0.2;
k = 5 * pi; % Use π to get just a couple of modulations across domain
n = 5;
sigma_y = 0.5; % Narrow along Y to limit rows
sigma_x = 0.3; % Wider along X
% Grid
x = linspace(-2, 2, 500);
y = linspace(-2, 2, 500);
[X, Y] = meshgrid(x, y);
% Anisotropic Gaussian envelope
G = exp(-((X.^2)/(2*sigma_x^2) + (Y.^2)/(2*sigma_y^2)));
% Honeycomb lattice modulation
modulation = 1 - ...
(c1 * cos(n * k * (2/sqrt(3)) * X)) - ...
(2 * c2 * cos(n * k * (1/sqrt(3)) * X) .* cos(n * k * Y));
% Normalize (optional)
modulation = modulation / (1 + c1 + 2*c2);
% Combine with Gaussian
f_modulated = G .* modulation;
% Plot
figure(6);
imagesc(x, y, f_modulated);
axis xy; axis equal tight;
colormap('hot');
colorbar;
title('Gaussian + Honeycomb lattice');
xlabel('x'); ylabel('y');