Noise induced stability in fluctuating, bistable potentials

TL;DR

This paper investigates how noise can stabilize a Brownian particle in a bistable potential with fluctuating barriers, revealing a resonance-like effect where intermediate fluctuation rates maximize stability, analyzed through exact and approximate methods.

Contribution

It provides a detailed analysis of noise-induced stability in fluctuating bistable potentials using exact solutions and effective rate equations, highlighting the role of fluctuation rates.

Findings

Intermediate fluctuation rates enhance occupancy of higher energy minima.

Effective rate equations accurately describe the system for not too fast fluctuations.

Exact solutions of the Fokker-Planck equation confirm the stability enhancement.

Abstract

The over-damped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is enhanced. The model works as a detector for potential fluctuations being not too fast and not too slow. This effect occurs due to the different time scales in the problem. We present a detailed analysis of this effect using the exact solution of the Fokker-Planck equation for a simple model. Further we show that for not too fast fluctuations the system can be well described by effective rate equations. The results of the rate equations agree quantitatively with the exact results.