Self-organized escape processes of linear chains in nonlinear potentials

TL;DR

This paper investigates how localized nonlinear modes called breathers in a coupled oscillator chain can facilitate escape from a metastable potential, highlighting their role in energy concentration and escape dynamics.

Contribution

It introduces the concept of self-organized escape via breathers in a nonlinear chain, showing their impact on overcoming barriers faster with low damping.

Findings

Breathers localize energy and trigger escape by overcoming the transition state.

Coalescence of breathers can enhance energy concentration for escape.

Lower damping increases breather lifetime, promoting escape.

Abstract

An enhancement of localized nonlinear modes in coupled systems gives rise to a novel type of escape process. We study a spatially one dimensional set-up consisting of a linearly coupled oscillator chain of $N$ mass-points situated in a metastable nonlinear potential. The Hamilton-dynamics exhibits breather solutions as a result of modulational instability of the phonon states. These breathers localize energy by freezing other parts of the chain. Eventually this localised part of the chain grows in amplitude until it overcomes the critical elongation characterized by the transition state. Doing so, the breathers ignite an escape by pulling the remaining chain over the barrier. Even if the formation of singular breathers is insufficient for an escape, coalescence of moving breathers can result in the required concentration of energy. Compared to a chain system with linear damping and thermal fluctuations the breathers help the chain to overcome the barriers faster in the case of low damping. With larger damping, the decreasing life time of the breathers effectively inhibits the escape process.