Dynamical Thermalization of Disordered Nonlinear Lattices

TL;DR

This paper investigates how energy disperses in a disordered nonlinear lattice, demonstrating the emergence of thermalization characterized by ergodic chaos and a Gibbs distribution, with thermalizing modes increasing with nonlinearity.

Contribution

It numerically demonstrates dynamical thermalization in disordered nonlinear lattices and links thermalization extent to nonlinearity strength.

Findings

Finite fraction of modes thermalize

Thermalization fraction increases with nonlinearity

Modes follow Gibbs distribution during thermalization

Abstract

We study numerically how the energy spreads over a finite disordered nonlinear one-dimensional lattice, where all linear modes are exponentially localized by disorder. We establish emergence of dynamical thermalization, characterized as an ergodic chaotic dynamical state with a Gibbs distribution over the modes. Our results show that the fraction of thermalizing modes is finite and grows with the nonlinearity strength.