Quantum Poincar\'e Recurrences

TL;DR

This paper demonstrates that quantum effects alter the decay rate of Poincaré recurrences in chaotic systems, leading to a universal algebraic decay exponent of 1, with potential experimental observation in mesoscopic systems and cold atoms.

Contribution

It reveals that quantum tunneling and localization effects produce a universal decay exponent of 1 in Poincaré recurrences for chaotic systems.

Findings

Quantum effects modify decay rates of Poincaré recurrences.

Universal decay exponent p=1 due to tunneling and localization.

Experimental evidence expected in mesoscopic systems and cold atoms.

Abstract

We show that quantum effects modify the decay rate of Poincar\'e recurrences P(t) in classical chaotic systems with hierarchical structure of phase space. The exponent p of the algebraic decay P(t) ~ 1/t^p is shown to have the universal value p=1 due to tunneling and localization effects. Experimental evidence of such decay should be observable in mesoscopic systems and cold atoms.