Quantum Chaos — Level Statistics: Poisson vs Wigner-Dyson

Quantum Level Statistics

Integrable systems: Poisson (uncorrelated levels). Chaotic systems: Wigner-Dyson (level repulsion). BGS conjecture connects classical chaos to RMT.

Chaos parameter λ: 0.5 Matrix size N: 200 Ensemble type:

■ Wigner-Dyson (GOE)
■ Poisson: p(s)=e⁻ˢ
■ Empirical histogram

Brody param β: —