Stochastic metastability by spontaneous localization

TL;DR

This paper investigates the formation and longevity of breathers in a stochastic lattice system, revealing long-lived localized excitations and non-Gaussian velocity distributions through extensive numerical simulations.

Contribution

It introduces a detailed numerical study of metastable breathers in a stochastic lattice, highlighting their long lifetimes and the impact of coupling strength on stability.

Findings

Breathers can persist for long times, delaying thermal equilibrium.

Velocity distributions of breathers are non-Gaussian and analytically describable.

Breather lifetime follows a power-law as coupling approaches the anticontinuous limit.

Abstract

Nonequilibrium, quasi-stationary states of a one-dimensional "hard" $\phi^4$ deterministic lattice, initially thermalized to a particular temperature, are investigated when brought into contact with a stochastic thermal bath at lower temperature. For lattice initial temperatures sufficiently higher than those of the bath, energy localization through the formation of nonlinear excitations of the breather type during the cooling process occurs. These breathers keep the nonlinear lattice away from thermal equilibrium for relatively long times. In the course of time some breathers are destroyed by fluctuations, allowing thus the lattice to reach another nonequilibrium state of lower energy. The number of breathers thus reduces in time; the last remaining breather, however, exhibits amazingly long life-time demonstrated by extensive numerical simulations using a quasi-symplectic integration algorithm. For the single-breather states we have calculated the lattice velocity distribution unveiling non-gaussian features describable in a closed functional form. Moreover, the influence of the coupling constant on the life-time of a single breather has been explored. The latter exhibits power-law behaviour as the coupling constant approaches the anticontinuous limit.