Enhancement of stability in randomly switching potential with metastable state

TL;DR

This paper investigates how noise can unexpectedly stabilize a metastable state in a Brownian particle system with a randomly switching potential, deriving analytical expressions and identifying conditions for noise-enhanced stability and resonant activation.

Contribution

It provides an analytical derivation of the mean first passage time in a switching potential and identifies conditions for noise-enhanced stability and resonant activation phenomena.

Findings

Noise stabilizes the metastable state, increasing the mean first passage time.

Maximum MFPT occurs at a finite white noise intensity.

Resonant activation observed for initial metastable configurations.

Abstract

The overdamped motion of a Brownian particle in randomly switching piece-wise metastable linear potential shows noise enhanced stability (NES): the noise stabilizes the metastable system and the system remains in this state for a longer time than in the absence of white noise. The mean first passage time (MFPT) has a maximum at a finite value of white noise intensity. The analytical expression of MFPT in terms of the white noise intensity, the parameters of the potential barrier, and of the dichotomous noise is derived. The conditions for the NES phenomenon and the parameter region where the effect can be observed are obtained. The mean first passage time behaviours as a function of the mean flipping rate of the potential for unstable and metastable initial configurations are also analyzed. We observe the resonant activation phenomenon for initial metastable configuration of the potential profile.