Motion of a driven tracer particle in a one-dimensional symmetric lattice gas

TL;DR

This paper investigates the sublinear, square-root time growth of a driven tracer particle's displacement in a one-dimensional symmetric lattice gas, revealing how interactions influence its dynamics.

Contribution

It introduces a theoretical framework to describe the tracer's motion under driving force in an interacting lattice gas, deriving an implicit expression for the growth rate.

Findings

Displacement grows as √(α t), not linearly.

Prefactor α depends on force and particle concentration.

Analytical results match numerical simulations.

Abstract

We study the dynamics of a tracer particle subject to a constant driving force $E$ in a one-dimensional lattice gas of hard-core particles whose transition rates are symmetric. We show that the mean displacement of the driven tracer grows in time, $t$, as $ \sqrt{\alpha t}$, rather than the linear time dependence found for driven diffusion in the bath of non-interacting (ghost) particles. The prefactor $\alpha$ is determined implicitly, as the solution of a transcendental equation, for an arbitrary magnitude of the driving force and an arbitrary concentration of the lattice gas particles. In limiting cases the prefactor is obtained explicitly. Analytical predictions are seen to be in a good agreement with the results of numerical simulations.