Mean escape time over a fluctuating barrier

TL;DR

This paper introduces an approximate method to analyze activation over fluctuating potential barriers, accurately capturing behavior across different fluctuation correlation times and validated against numerical simulations.

Contribution

It proposes a novel approach that separately considers slow and fast barrier fluctuations, providing exact results in limiting cases and excellent agreement elsewhere.

Findings

Accurately models activation over fluctuating barriers for any correlation time.

Provides exact solutions for extreme fluctuation correlation limits.

Shows excellent agreement with numerical simulations for both dichotomic and Gaussian perturbations.

Abstract

An approximate method for studying activation over a fluctuating barrier of potential is proposed. It involves considering separately the slow and fast components of barrier fluctuations, and it applies for any value of their correlation time $\tau$. It gives exact results for the limiting values $\tau \to 0$ and $\tau \to \infty$, and the agreement with numerics in between is also excellent, both for dichotomic and Gaussian barrier perturbations.