Quantum Chaos & OTOC

Out-of-time-order correlator C(t) = −⟨[W(t),V]²⟩ as a probe of quantum scrambling and chaos

1.20
3.0
1.00
Chaotic (GUE)
Integrable (Poisson)
Scrambling time:
t* ≈ (1/λ_L) log N

Bound (Maldacena):
λ_L ≤ 2πk_BT/ℏ

C(t) ~ e2λ_L t for t < t*, then saturates at ∼2⟨V²⟩⟨W²⟩
t = 0.00
C(t) chaotic = 0.00
Phase: early