Quantum Chaos — Level Statistics: Poisson vs Wigner-Dyson

Chaos param. h: 0.00
Matrix size N: 80
Histogram bins: 20
Regenerate Integrable (h=0) Chaotic (h=1) r̄ = — (Poisson: 0.386, GOE: 0.530) | Regime: —

Quantum chaos diagnosis via level spacing statistics. Integrable systems: Poisson P(s)=e⁻ˢ (levels cluster, degeneracies allowed). Chaotic systems: Wigner-Dyson (GOE) P(s)≈(π/2)s·e^(−πs²/4) (level repulsion). The ratio statistic r=min(sₙ,sₙ₊₁)/max(sₙ,sₙ₊₁) avoids unfolding. As chaos parameter h increases from 0 to 1, the distribution smoothly evolves from Poisson to GOE.