Interacting Brownian Motion with Resetting

TL;DR

This paper investigates the dynamics of two interacting Brownian particles in one dimension with resetting to a fixed point, analyzing their steady-state distributions and relaxation behavior under a bias towards each other.

Contribution

It introduces a model of interacting Brownian particles with resetting and derives their steady-state distributions and relaxation dynamics.

Findings

Derived explicit steady-state distributions.

Analyzed relaxation behavior towards equilibrium.

Identified effects of bias and resetting on particle interactions.

Abstract

We study two Brownian particles in dimension $d=1$, diffusing under an interacting resetting mechanism to a fixed position. The particles are subject to a constant drift, which biases the Brownian particles toward each other. We derive the steady-state distributions and study the late time relaxation behavior to the stationary state.