Transition times in the low-noise limit of stochastic dynamics

TL;DR

This paper analyzes the distribution of transition times for particles moving between potential wells in low-noise overdamped Langevin dynamics, revealing a universal form and practical estimation methods from experiments.

Contribution

It reduces the multidimensional transition time problem to a one-dimensional analysis and proposes a universal distribution applicable in low-noise limits.

Findings

Transition time distribution is universal and compact.

Transition barriers can be estimated from single-temperature experiments.

Transition paths are confined to a thin tube around the most probable trajectory.

Abstract

We study the transition time distribution for a particle moving between two wells of a multidimensional potential in the low-noise limit of overdamped Langevin dynamics. Possible transition paths are restricted to a thin tube surrounding the most probable trajectory. We demonstrate that finding the transition time distribution reduces to a one-dimensional problem. The resulting transition time distribution has a universal and compact form. We suggest that transition barriers can be estimated from a single-temperature experiment if both the life times and the transition times are measured.