What happens when you poke a quantum system's unstable ground state?

Poking a quantum lattice model near a false vacuum triggers a spreading instability that mathematically mirrors how operators grow in chaotic quantum systems. By borrowing tools from that operator-growth framework — particularly the Krylov recursion method — the work derives a chaos bound analogous to the Lyapunov exponent: λ_L ≤ √(4α²−ν²). Solvable SYK-inspired models saturate this bound, while non-random all-to-all models almost always freeze up instead, suggesting these 'growth quenches' are a controllable laboratory for non-equilibrium quantum coherence.