Attraction and condensation of driven tracers in a narrow channel

TL;DR

This paper investigates how driven particles in a confined environment induce bath-mediated attractions, combining analytical and numerical methods to understand the underlying mechanisms and effective interactions.

Contribution

It introduces a quantitative analytical framework for emergent tracer interactions and demonstrates its applicability to realistic Brownian particle systems.

Findings

Analytical derivation of effective attractive potential between tracers.

Numerical validation in a model of driven Brownian discs.

Identification of the mechanism behind bath-mediated attraction.

Abstract

Emergent bath-mediated attraction and condensation arise when multiple particles are simultaneously driven through an equilibrated bath under geometric constraints. While such scenarios are observed in a variety of non-equilibrium phenomena, with an abundance of experimental and numerical evidence, little quantitative understanding of how these interactions arise is currently available. Here we approach the problem by studying the behavior of two driven "tracer" particles, propagating through a bath in a 1D lattice with excluded-volume interactions. We analytically explore the mechanism responsible for the tracers' emergent interactions and compute the resulting effective attractive potential. This mechanism is then numerically shown to extend to a realistic model of hard driven Brownian discs confined to a narrow 2D channel.