Escape Rates in Bistable Systems Induced by Quasi-Monochromatic Noise

TL;DR

This paper investigates how quasi-monochromatic noise influences escape rates in bistable systems, revealing a critical bandwidth that shifts the escape mechanism from oscillatory to white-noise-like behavior.

Contribution

It introduces a path integral approach to analyze escape dynamics under quasi-monochromatic noise, highlighting the critical bandwidth effect on escape mechanisms.

Findings

Critical bandwidth parameter determines escape behavior

Path integral method accurately predicts mean first passage times

Transition from oscillatory to white-noise-like escape at critical bandwidth

Abstract

Path integral techniques are used to understand the behaviour of a particle moving in a bistable potential well and acted upon by quasi-monochromatic external noise. In the limit of small diffusion coefficient, a steepest descent evaluation of the path integral enables mean first passage times and the transition times from one well to the other to be computed. The results and general approach are compared with computer simulations of the process. It is found that the bandwidth parameter, $\Gamma$, has a critical value above which particle escape is by white-noise-like outbursts, but below which escape is by oscillatory type behaviour.