Diffusion on the interval acted upon by a oscillating space-homogeneous force

TL;DR

This paper analyzes a one-dimensional diffusion process with reflecting boundaries under a combined oscillating and constant force, deriving integral equations for the Green function and exploring its long-term behavior and probability distributions.

Contribution

It introduces a method to derive the Green function for diffusion under oscillating forces and examines the non-equilibrium stationary regime's properties.

Findings

Derived integral equations for the Green function.

Identified nontrivial features in the asymptotic probability density.

Analyzed the time-averaged behavior of the diffusion process.

Abstract

We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and the constant component. Using techniques presented in the paper [1] we derive the set of integral equations whose comprise the Green function for our diffusion process. In the later part we focus on the time-asymptotic stationary regime of considered non-equilibrium process. Some of its time-asymptotic characteristics, e.g. time-averaged and time-asymptotic probability density of the particle coordinate, exhibit nontrivial features.