Category: Physics

Summary: Mapping how mixed random matrices cross from Poisson-like to GOE-like spacing statistics as the chaotic component is increased.

Level-spacing ratios provide a compact way to distinguish spectra associated with integrable behavior from those associated with quantum chaos. This experiment asks how that crossover unfolds when a matrix is built as a controlled mixture of a diagonal random part and a GOE random part.

The script sweeps a mixing parameter, computes eigenvalue spacing ratios for multiple matrix sizes, and extracts the crossover point where the mean ratio sits halfway between the Poisson and GOE reference values. It then studies how that crossover scale changes with size in order to test the predicted square-root scaling.

The interest is not only in locating a threshold, but in resolving the full crossover shape. That makes the project useful for finite-size questions where universal asymptotic endpoints are known but the intermediate interpolation is not well tabulated.

Method: Dense random-matrix simulations measuring mean spacing ratios across a mixing-parameter sweep for multiple system sizes.

What is measured: Mean spacing ratio, crossover scale, size dependence of the crossover, and the inferred universal scaling curve.