Cooling nonlinear lattices toward localisation

TL;DR

This paper investigates how surface damping in nonlinear lattices leads to energy localization in the form of discrete breathers, affecting relaxation dynamics and resulting in quasi-stationary states with trapped energy.

Contribution

It introduces a detailed analysis of energy relaxation and localization mechanisms in nonlinear lattices, highlighting the role of boundary conditions and spectral gaps in 1D and 2D systems.

Findings

Localized vibrations slow down dissipation significantly.

In 1D, strong on-site coupling causes stretched-exponential relaxation.

In 2D, spectral gaps activate localization, with breather interactions characterized statistically.

Abstract

We describe the energy relaxation process produced by surface damping on lattices of classical anharmonic oscillators. Spontaneous emergence of localised vibrations dramatically slows down dissipation and gives rise to quasi-stationary states where energy is trapped in the form of a gas of weakly interacting discrete breathers. In one dimension (1D), strong enough on--site coupling may yield stretched--exponential relaxation which is reminiscent of glassy dynamics. We illustrate the mechanism generating localised structures and discuss the crucial role of the boundary conditions. For two--dimensional (2D) lattices, the existence of a gap in the breather spectrum causes the localisation process to become activated. A statistical analysis of the resulting quasi-stationary state through the distribution of breathers' energies yield information on their effective interactions.