A sharp bound on the rate of growth of chaos in thermal quantum systems

A bound on chaos

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 correlation function can develop no faster than exponentially, with a lyapunov exponent.We give a precise mathematical argument,based on plausible physical assumptions, establishing this conjecture.