Dynamics of a metastable state nonlinearly coupled to a heat bath driven by an external noise

TL;DR

This paper investigates how external noise modulating a heat bath affects the escape rate from a metastable state in a nonlinear coupled system, deriving a generalized Langevin equation and analyzing the dynamics numerically.

Contribution

It introduces a generalized Langevin equation with space-dependent friction and noise, accounting for external noise modulation, and studies its impact on escape rates in a nonlinear system.

Findings

External noise can enhance escape rates when properly tuned.

Derived a space-dependent Langevin equation and Fokker-Planck equation.

Numerical results agree with theoretical predictions.

Abstract

Based on a system-reservoir model, where the system is nonlinearly coupled to a heat bath and the heat bath is modulated by an external stationary Gaussian noise, we derive the generalized Langevin equation with space dependent friction and multiplicative noise and construct the corresponding Fokker-Planck equation, valid for short correlation time, with space dependent diffusion coefficient to study the escape rate from a metastable state in the moderate to large damping regime. By considering the dynamics in a model cubic potential we analyze the result numerically which are in good agreement with the theoretical prediction. It has been shown numerically that the enhancement of rate is possible by properly tuning the correlation time of the external noise.