The recurrence time in quantum mechanics

TL;DR

This paper provides an exact computation of recurrence times in generic non-integrable quantum systems, revealing universal behavior and dependencies on system parameters, with implications for experimental observation of quantum recurrences.

Contribution

It introduces a universal function for recurrence times in quantum systems, extending results to integrable models, and explores how near-critical quenches can significantly reduce recurrence times.

Findings

Recurrence times are generally doubly exponential in system volume for non-integrable systems.

For integrable systems, recurrence times grow exponentially with system size.

Small quenches near quantum critical points can drastically decrease recurrence times.

Abstract

Generic quantum systems --as much as their classical counterparts-- pass arbitrarily close to their initial state after sufficiently long time. Here we provide an essentially exact computation of such recurrence times for generic non-integrable quantum models. The result is a universal function which depends on just two parameters, an energy scale and the effective dimension of the system. As a by-product we prove that the density of orthogonalization times is zero if at least nine levels are populated and connections with the quantum speed limit are discussed. We also extend our results to integrable, quasi-free fermions. For generic systems the recurrence time is generally doubly exponential in the system volume whereas for the integrable case the dependence is only exponential. The recurrence time can be decreased by several orders of magnitude by performing a small quench close to a quantum critical point. This setup may lead to the experimental observation of such \emph{fast} recurrences.