The notion of persistence applied to breathers in thermal equilibrium

TL;DR

This paper investigates the statistical properties of thermal breathers in nonlinear Klein-Gordon chains at thermal equilibrium, revealing power-law persistence distributions and insights into energy diffusion behavior.

Contribution

It introduces the use of persistence distribution analysis for thermal breathers and compares behaviors in chains with different nonlinearities, providing new understanding of their dynamics.

Findings

Persistence distributions follow a power-law in static excitations.

High-frequency spectra collapse when properly rescaled.

Energy diffusion remains normal but with very small coefficients.

Abstract

We study the thermal equilibrium of nonlinear Klein-Gordon chains at the limit of small coupling (anticontinuum limit). We show that the persistence distribution associated to the local energy density is a useful tool to study the statistical distribution of so-called thermal breathers, mainly when the equilibrium is characterized by long-lived static excitations; in that case, the distribution of persistence intervals turns out to be a powerlaw. We demonstrate also that this generic behaviour has a counterpart in the power spectra, where the high frequencies domains nicely collapse if properly rescaled. These results are also compared to non linear Klein-Gordon chains with a soft nonlinearity, for which the thermal breathers are rather mobile entities. Finally, we discuss the possibility of a breather-induced anomalous diffusion law, and show that despite a strong slowing-down of the energy diffusion, there are numerical evidences for a normal asymptotic diffusion mechanism, but with exceptionnally small diffusion coefficients.