Enhancement of the escape time in metastable states with colored noise

TL;DR

This paper investigates how colored noise influences the escape time from metastable states, revealing noise-enhanced stability effects and identifying different dynamical regimes based on noise correlation strength.

Contribution

It provides a detailed analysis of escape times under colored noise, highlighting the impact of noise correlation time on stability and escape dynamics, which was less understood before.

Findings

Noise enhanced stability (NES) occurs for all initial unstable states.

Increasing correlation time shifts and amplifies the NES maximum.

Strong colored noise broadens the NES region and alters initial condition effects.

Abstract

We present a study of the escape time from a metastable state in the presence of colored noise, generated by Ornstein-Uhlenbeck process. We analyze the role of the correlated noise and of unstable initial conditions of an overdamped Brownian particle on the enhancement of the average escape time as a function of the noise intensity. We observe the noise enhanced stability (NES) effect for all the initial unstable states and for all values of the correlation time $\tau_c$ investigated. We can distinguish two dynamical regimes characterized by: (a) a weak correlated noise and (b) a strong correlated noise, depending on the value of $\tau_c$ with respect to the relaxation time. With increasing $\tau_c$ we find : (i) a shift of the maximum of the average escape time towards higher values of noise intensity and an enhancement of the value of this maximum; (ii) a broadening of the NES region, which becomes very large in the strong colored noise regime; (iii) in this regime (b), the absence of the peculiar initial condition $x_c$ which separates the set of the initial unstable states lying into the divergency region from those which give only a nonmonotonic behavior of the average escape time.