# Energy thresholds of discrete breathers in thermal equilibrium and relaxation processes

## TL;DR

This paper analytically estimates the size-dependent energy thresholds of discrete breathers in thermal equilibrium and relaxation processes in nonlinear chains, providing insights relevant for experimental detection.

## Contribution

It extends analytical estimates of energy thresholds to include thermal equilibrium and relaxation states, differing from previous single breather analyses.

## Key findings

- Energy thresholds in thermal equilibrium match previous single breather results.
- Long-lived breather thresholds differ from single breather results but align with numerical data.
- Results are relevant for experimental detection of discrete breathers.

## Abstract

So far, only the energy thresholds of single discrete breathers in nonlinear Hamiltonian systems have been analytically obtained. In this work, the energy thresholds of discrete breathers in thermal equilibrium and the energy thresholds of long-lived discrete breathers which can remain after a long time relaxation are analytically estimated for nonlinear chains. These energy thresholds are size dependent. The energy thresholds of discrete breathers in thermal equilibrium are same as the previous analytical results for single discrete breathers. The energy thresholds of long-lived discrete breathers in relaxation processes are different from the previous results for single discrete breathers but agree well with the published numerical results known to us. Because real systems are either in thermal equilibrium or in relaxation processes, the obtained results could be important for experimental detection of discrete breathers.