Metastable transitions in inertial Langevin systems: what can be different from the overdamped case?

TL;DR

This paper explores how metastable transitions in inertial Langevin systems differ fundamentally from overdamped systems, revealing new behaviors and transition mechanisms through a novel analytical and computational approach.

Contribution

It introduces a new framework combining time-reversed dynamics and an adapted string method to analyze metastable transitions in non-gradient Langevin systems.

Findings

Heteroclinic connections may not exist in Langevin systems with weak dissipation.

Transition paths can differ significantly from the overdamped limit.

Efficient methods to find instantons in velocity-dependent friction systems.

Abstract

Metastable transitions in Langevin dynamics can exhibit rich behaviors that are markedly different from its overdamped limit. In addition to local alterations of the transition path geometry, more fundamental global changes may exist. For instance, when the dissipation is weak, heteroclinic connections that exist in the overdamped limit do not necessarily have a counterpart in the Langevin system, potentially leading to different transition rates. Furthermore, when the friction coefficient depends on the velocity, the overdamped limit no longer exists, but it is still possible to efficiently find instantons. The approach we employed for these discoveries was based on (i) a simple rewriting of the Freidlin-Wentzell action in terms of time-reversed dynamics, and (ii) an adaptation of the string method, which was originally designed for gradient systems, to this specific non-gradient system.