OTOC: Quantum Scrambling

System:

Scrambling rate λ_L 1.00

Temperature β⁻¹ 1.00

N (system size) 8

Scrambling time t*—

Dissipation time t_d—

Lyapunov bound 2π/β—

λ_L / bound—

OTOC: F(t) = ⟨W(t)†V†W(t)V⟩_β measures how much operator W(t)=e^iHtWe^-iHt fails to commute with V.

Chaos signature: F(t) ≈ 1 − ε·e^{λ_L t} (early time). Scrambling at t* ~ log(N)/λ_L.

MSS bound (Maldacena-Shenker-Stanform 2016): λ_L ≤ 2π/β. Black holes saturate this bound.