Intermittent many-body dynamics at equilibrium

TL;DR

This paper investigates the equilibrium dynamics of many-body systems, revealing power-law distributions of excursions and sticky behaviors near localized modes, which help predict transitions to nonergodic states.

Contribution

It introduces a novel method to analyze equilibrium fluctuations in many-body systems and links sticky dynamics to nonergodic transitions, extending to different lattice models.

Findings

Power-law distribution of excursion times with diverging variance.

Sticky dynamics near q-breathers and discrete breathers.

Predictive exponent for transition to nonergodic behavior.

Abstract

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain (FPU), as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q-breathers localized in normal mode space. Measuring the exponent allows to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices (KG) where the sticky dynamics is due to discrete breathers localized in real space.