  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.
