All-to-all random interactions — maximal quantum chaos
The SYK model — N Majorana fermions with all-to-all random 4-body interactions J_{ijkl} — saturates the Maldacena-Shenker-Standford bound on quantum chaos: Lyapunov exponent λ_L = 2πk_BT/ℏ. Its spectral form factor (shown) exhibits the universal dip-ramp-plateau structure of random matrix theory (GUE), signaling quantum ergodicity and a holographic dual to near-extremal black holes.