Spectral Form Factor

K(t) = |Σ e^iE_nt|² / Z² — quantum chaos fingerprint

Ensemble

Matrix size N: 200

Samples: 30

K(t) averaged

Theoretical (GOE/GUE)

Diagonal (dip)

K(t) = (1/Z²)|Tr e^iHt|² averaged over the ensemble.
GOE/GUE show the dip → ramp → plateau structure: a signature of level repulsion and quantum chaos.
Poisson (integrable systems) shows only a flat plateau — no ramp.