Role of the initial conditions on the enhancement of the escape time in static and fluctuating potentials

TL;DR

This paper investigates how initial conditions influence noise-driven escape times of an overdamped Brownian particle in static and fluctuating cubic potentials, revealing noise-enhanced stability and critical initial states affecting escape behavior.

Contribution

It identifies a specific initial condition that separates divergent and nonmonotonic escape time behaviors in static potentials and explores fluctuations in escape times under fluctuating potentials.

Findings

Noise enhanced stability observed for all initial states studied.

Existence of a critical initial condition $x_c$ affecting escape time divergence.

Large fluctuations in escape times at $x_c$ under fluctuating potentials.

Abstract

We present a study of the noise driven escape of an overdamped Brownian particle moving in a cubic potential profile with a metastable state. We analyze the role of the initial conditions of the particle on the enhancement of the average escape time as a function of the noise intensity for fixed and fluctuating potentials. We observe the noise enhanced stability effect for all the initial unstable states investigated. For a fixed potential we find a peculiar initial condition $x_c$ which separates the set of the initial unstable states in two regions: those which give rise to divergences from those which show nonmonotonic behavior of the average escape time. For fluctuating potential at this particular initial condition and for low noise intensity we find large fluctuations of the average escape time.