Langevin dynamics with dichotomous noise; direct simulation and applications

TL;DR

This paper introduces a direct simulation method for Langevin equations driven by dichotomous noise, enabling analysis of nonequilibrium currents and barrier fluctuations without relying solely on Fokker-Planck equations.

Contribution

A novel numerical simulation approach for Langevin dynamics with dichotomous noise, applied to nonequilibrium current and resonant activation studies.

Findings

Validated the simulation method against Fokker-Planck algorithms.

Analyzed current behavior under asymmetric dichotomous noise.

Explored resonant activation phenomena in fluctuating barriers.

Abstract

We consider the motion of a Brownian particle moving in a potential field and driven by dichotomous noise with exponential correlation. Traditionally, the analytic as well as the numerical treatments of the problem, in general, rely on Fokker-Planck description. We present a method for direct numerical simulation of dichotomous noise to solve the Langevin equation. The method is applied to calculate nonequilibrium fluctuation induced current in a symmetric periodic potential using asymmetric dichotomous noise and compared to Fokker-Planck-Master equation based algorithm for a range of parameter values. Our second application concerns the study of resonant activation over a fluctuating barrier.