Metastable transitions in inertial Langevin systems: what can be different from the overdamped case?
For researchers studying rare events in stochastic dynamics, this work highlights important qualitative differences from the commonly used overdamped approximation.
The paper investigates metastable transitions in inertial Langevin systems, revealing that weak dissipation can lead to fundamentally different transition rates compared to the overdamped limit, and that velocity-dependent friction eliminates the overdamped limit but still allows efficient instanton computation.
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.