Driven tracers in narrow channels

TL;DR

This paper investigates the steady-state behavior of a driven tracer in narrow channels using models like SSEP and hard disks, revealing how the tracer influences density, pressure, and flow in confined geometries.

Contribution

It introduces a detailed analysis of driven tracers in narrow channels using SSEP and hard disk models, providing new analytical and numerical insights into their steady-state properties.

Findings

Tracer acts as a dipolar source in velocity field

Analytical predictions match numerical simulations

Results extend from SSEP to hard disk systems

Abstract

Steady state properties of a driven tracer moving in a narrow two dimensional (2D) channel of quiescent medium are studied. The tracer drives the system out of equilibrium, perturbs the density and pressure fields, and gives the bath particles a nonzero average velocity, creating a current in the channel. Three models in which the confining effect of the channel is probed are analyzed and compared in this study: the first is the simple symmetric exclusion process (SSEP), for which the stationary density profile and the pressure on the walls in the frame of the tracer are computed. We show that the tracer acts like a dipolar source in an average velocity field. The spatial structure of this 2D strip is then simplified to a one dimensional SSEP, in which exchanges of position between the tracer and the bath particles are allowed. Using a combination of mean field theory and exact solution in the limit where no exchange is allowed, gives good predictions of the velocity of the tracer and the density field. Finally, we show that results obtained for the 1D SSEP with exchanges also apply to a gas of overdamped hard disks in a narrow channel. The correspondence between the parameters of the SSEP and of the gas of hard disks is systematic and follows from simple intuitive arguments. Our analytical results are checked numerically.