Velocity correlations and mobility in single-file diffusion

Abstract

We study the velocity correlations of a tagged particle in an infinite assembly of interacting particles with a given density in one dimension. The assembly is in contact with a heat bath, and the particles interact via a hard-core repulsion with each other. We evaluate the two-time velocity correlation function exactly as function of time when an ensemble average is taken over initial conditions. This correlation function decays rapidly with time and becomes negative, with the rate of decay increasing with the density. This is followed by a slow decay toward zero through a power-law behavior of the form -t^-3/2 at large times for all densities. We also consider mobility of the assembly in the presence of a constant force acting on the particles, as well as the mobility of a tagged particle when only the tagged particle is driven by the force. The power spectrum of velocity fluctuations is also presented.