Instantons and the quantum bound to chaos

TL;DR

This paper explores why quantum systems' out-of-time-ordered correlators (OTOCs) have a universal Lyapunov exponent bound, using instanton analysis and ring-polymer molecular dynamics to connect quantum fluctuations with classical barrier-crossing models.

Contribution

It demonstrates that RPMD can reproduce the quantum bound on chaos by linking instanton stability to OTOC behavior in barrier-crossing systems.

Findings

RPMD OTOC obeys the quantum chaos bound.

Quantum thermal fluctuations around instantons stabilize OTOCs.

Instantons are likely key structures in systems with exponential OTOC growth.

Abstract

We investigate why the Lyapunov exponents $\lambda$ of out-of-time-ordered correlators (OTOCs) satisfy a universal bound $\lambda < 2 \pi k_B T/{\hbar}$ by probing imaginary-time path-integral space using ring-polymer molecular dynamics (RPMD) for a barrier-crossing model. We find that the RPMD OTOC satisfies the same bound as the quantum OTOC, which is caused by the stability of quantum thermal fluctuations around the instanton on the barrier. We expect that similar instantons (or other delocalised structures) will be found in many other systems with exponentially growing OTOCs.