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

Abstract

Consider 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 ${\mathit{X}}_{\mathit{T}}$(E,t) grows in time t as ${\mathit{X}}_{\mathit{T}}$(E,t)=√αt, rather than the linear time dependence found for noninteracting (ghost) bath particles. The prefactor α 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 good agreement with the results of numerical simulations. © 1996 The American Physical Society.