Fluctuations in the relaxation dynamics of mixed chaotic systems

TL;DR

This paper investigates the relaxation dynamics in mixed chaotic systems, revealing that fluctuations in recurrence times cause very slow convergence of the decay exponent, challenging the notion of a universal decay rate.

Contribution

It introduces an ensemble approach using rate equations to analyze fluctuations in Poincare recurrence times in mixed chaotic systems.

Findings

Fluctuations lead to slow convergence of the decay exponent.

The decay exponent varies significantly across different systems.

Hierarchical phase space structure influences relaxation dynamics.

Abstract

The relaxation dynamics in mixed chaotic systems are believed to decay algebraically with a universal decay exponent that emerges from the hierarchical structure of the phase space. Numerical studies, however, yield a variety of values for this exponent. In order to reconcile these result we consider an ensemble of mixed chaotic systems approximated by rate equations, and analyze the fluctuations in the distribution of Poincare recurrence times. Our analysis shows that the behavior of these fluctuations, as function of time, implies a very slow convergence of the decay exponent of the relaxation.