Long range spatial correlation between two Brownian particles under external driving

TL;DR

This paper investigates the long-range spatial correlations between two driven Brownian particles, revealing a $1/r^2$ decay in their steady-state distribution through perturbative analysis of the Fokker-Planck equation.

Contribution

It introduces a perturbative system reduction method to analyze the steady distribution of two driven Brownian particles and uncovers a specific long-range correlation decay.

Findings

Existence of a $1/r^2$ long-range correlation between particles

Analytical expression for the steady distribution under external driving

Methodology applicable to similar stochastic systems

Abstract

We study the large distance behavior of a steady distribution of two Brownian particles under external driving in a two-dimensional space. Employing a method of perturbative system reduction, we analyze a Fokker-Planck equation that describes the time evolution of the probability density for the two particles. The expression we obtain shows that there exist a long range correlation between the two particles, of $1/r^2$ type.