Mechanisms for transient localization in a diatomic nonlinear chain

TL;DR

This paper explores the mechanisms behind transient nonlinear localization in a diatomic Lennard-Jones chain, revealing how discrete breathers and nonlinear coupling contribute to energy bursts at finite temperature.

Contribution

It identifies two distinct mechanisms for transient localization: discrete breathers in the phonon gap and nonlinear coupling effects, supported by numerical simulations and multiple-scale analysis.

Findings

Discrete breathers can be thermally excited in the phonon gap.

Nonlinear coupling causes energy localization related to mass ratios.

A simplified model provides insight into localization dynamics.

Abstract

We investigate transient nonlinear localization, namely the self-excitation of energy bursts in an atomic lattice at finite temperature. As a basic model we consider the diatomic Lennard-Jones chain. Numerical simulations suggest that the effect originates from two different mechanisms. One is the thermal excitation of genuine discrete breathers with frequency in the phonon gap. The second is an effect of nonlinear coupling of fast, lighter particles with slow vibrations of the heavier ones. The quadratic term of the force generate an effective potential that can lead to transient grow of local energy on time scales the can be relatively long for small mass ratios. This heuristics is supported by a multiple-scale approximation based on the natural time-scale separation. For illustration, we consider a simplified single-particle model that allows for some insight of the localization dynamics.