Can low-frequency breathers exist in a quasi-1D crystal?

TL;DR

This study explores the existence of low-frequency breathers in a quasi-1D crystal modeled as coupled chains, finding that such breathers do not persist due to phonon emission, contrasting with predictions from the FK model.

Contribution

It demonstrates through numerical simulation that low-frequency breathers predicted by the FK model cannot exist in a realistic quasi-1D crystal due to phonon radiation effects.

Findings

Low-frequency breathers do not exist in the coupled chain system.

Kink-antikink collisions result in phonon radiation instead of breather formation.

Acoustic phonons cause the decay of potential breathers.

Abstract

We investigate a quasi-1D crystal: 2D system of coupled linear chains of particles with strong intra-chain and weak inter-chain interactions. Nonlinear dynamics of one of these chains when the rest of them are fixed is reduced to the well known Frenkel-Kontorova (FK) model. Its continuum limit, sine-Gordon (sG) equation, predicts two types of soliton solutions: topological solitons and breathers. It is known that the quasi-1D topological solitons exist also in a 2D system of coupled chains and even in a 3D model of a polymer crystal. Numerical simulation shows that the breathers inherent to the FK model do not exist in the system of chains. The effect changes scenario of kink-antikink collision at small velocities: it always results only in intensive phonon radiation while kink-antikink recombination in the FK model results in long-living low-frequency sG breather creation. The reason of the difference is that the model of coupled chains catches 'acoustic' part of phonon spectrum of a crystal while the FK model does not. Low-frequency SG breathers in a crystal intensively emit resonant 'acoustic' phonons and come to ruin.