From 9c8f4c036cde6e2b32e780be03da6713980a7a43 Mon Sep 17 00:00:00 2001
From: Karthik <arecibokck@gmail.com>
Date: Fri, 9 May 2025 00:25:18 +0200
Subject: [PATCH] Added Gaussian+Modulation code snippets

---
 Estimations/VisualizeCosineModulatedAnsatz.m | 109 +++++++++++++++++++
 1 file changed, 109 insertions(+)

diff --git a/Estimations/VisualizeCosineModulatedAnsatz.m b/Estimations/VisualizeCosineModulatedAnsatz.m
index 1787409..f58badb 100644
--- a/Estimations/VisualizeCosineModulatedAnsatz.m
+++ b/Estimations/VisualizeCosineModulatedAnsatz.m
@@ -88,3 +88,112 @@ title('Honeycomb Lattice ansatz for $|\Psi(x,y)|^2$', 'Interpreter', 'latex', 'F
 xlabel('x');
 ylabel('y');
 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');
+
+
+