Correlations of density and current fluctuations in single-file motion of hard spheres and in driven lattice gas with nearest-neighbor interaction

TL;DR

This study investigates the scaling behavior of density and current fluctuations in one-dimensional driven systems, revealing KPZ universality in lattice gases with interactions and superdiffusive behavior in single-file Brownian motion.

Contribution

It demonstrates that nonequilibrium steady states in these systems follow KPZ scaling, contrasting with equilibrium-like behavior in the absence of external potentials.

Findings

Current correlations decay as t^{-4/3} in KPZ regime.

Density fluctuations spread superdiffusively as t^{2/3}.

In absence of potential, system exhibits Edwards-Wilkinson scaling.

Abstract

We analyze correlations between density fluctuations and between current fluctuations in a one-dimensional driven lattice gas with repulsive nearest-neighbor interaction and in single-file Brownian motion of hard spheres dragged across a cosine potential with constant force. By extensive kinetic Monte Carlo and Brownian dynamics simulations we show that density and current correlation functions in nonequilibrium steady states follow the scaling behavior of the Kardar-Parisi-Zhang (KPZ) universality class. In a coordinate frame comoving with the collective particle velocity, the current correlation function decays as $\sim -t^{-4/3}$ with time $t$. Density fluctuations spread superdiffusively as $\sim t^{2/3}$ at long times and their spatio-temporal behavior is well described by the KPZ scaling function. In the absence of the cosine potential, the correlation functions in the system of dragged hard spheres show scaling behavior according to the Edwards-Wilkinson universality class. In the coordinate frame comoving with the mean particle velocity, they behave as in equilibrium, with current correlations decaying as $\sim -t^{-3/2}$ and density fluctuations spreading diffusively as $\sim t^{1/2}$.