A bound on chaos

TL;DR

This paper proposes a universal upper bound on the rate of chaos growth in thermal quantum systems, linking it to temperature and fundamental constants, and provides a mathematical proof under plausible assumptions.

Contribution

It introduces a conjecture and a rigorous argument establishing a maximum Lyapunov exponent for chaos in large quantum systems.

Findings

Lyapunov exponent bound: λ_L ≤ 2πk_B T/ħ

Chaos growth cannot exceed exponential rate set by temperature

Provides a mathematical proof under physical assumptions

Abstract

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent $\lambda_L \le 2 \pi k_B T/\hbar$. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.