Target Searches of Interacting Brownian Particles

TL;DR

This paper investigates how interactions among Brownian particles influence their target search times within a finite domain, deriving analytical corrections and validating them through simulations.

Contribution

It introduces an analytical approach to quantify the effect of inter-particle interactions on search times, including a universal relation for dilute systems.

Findings

Derived integral equation for mean first-passage time

Obtained leading order correction for dilute systems

Validated predictions with Langevin dynamics simulations

Abstract

We study the target search of interacting Brownian particles in a finite domain, focusing on the effect of inter-particle interactions on the search time. We derive the integral equation for the mean first-passage time and acquire its solution as a series expansion in the orders of the Mayer function. For dilute systems relevant to most target search problems, we analytically obtain the leading order correction to the search time and prove a universal relation given by the particle density and the second virial coefficient. Finally, we validate our theoretical prediction by Langevin dynamics simulations for the various types of the interaction potential.