Circular Unitary Ensemble
CUE eigenvalue statistics, level repulsion & quantum chaos
Parameters
Matrix size N:
40
Ensemble:
CUE (β=2)
Generate New Matrix
Accumulate (×10)
Statistics
Samples:
1
Mean spacing:
—
Level var. Σ²:
—
Key Equations
CUE: Haar measure on U(N), eigenvalues on unit circle
Joint PDF: ∏ᵢ<ⱼ |e^{iθᵢ}-e^{iθⱼ}|^β
Wigner surmise: p(s) = (πs/2)e^{-πs²/4} (β=2)
Level repulsion: p(s)~s^β as s→0