Quantum Chaos — Wigner-Dyson Level Statistics

In quantum chaotic systems, energy level spacings follow the Wigner-Dyson distribution (GOE/GUE ensembles), showing level repulsion. Integrable systems instead display Poisson statistics with level clustering. This simulation generates random matrix spectra and computes the nearest-neighbor spacing distribution.

Energy Spectrum (unfolded levels)
Nearest-Neighbor Spacing P(s)