Driven k-mers: Correlations in space and time

TL;DR

This paper studies the static and dynamic properties of a generalized exclusion process with extended particles, revealing oscillatory correlations and a connection to the Tonks gas, with implications for nonequilibrium statistical mechanics.

Contribution

It introduces the k-ASEP model, analyzing correlations and decay behaviors, and links large-k limits to a nonequilibrium Tonks gas, providing new insights into extended particle systems.

Findings

Density correlations show oscillations in space and time.

Autocorrelation decays exponentially, with power-law decay at special densities.

Large k limit relates to a nonequilibrium Tonks gas, with corrections derived.

Abstract

Steady state properties of hard objects with exclusion interaction and a driven motion along a one-dimensional periodic lattice are investigated. The process is a generalization of the asymmetric simple exclusion process (ASEP) to particles of length k, and is called the k-ASEP. Here, we analyze both static and dynamic properties of the k-ASEP. Density correlations are found to display interesting features, such as pronounced oscillations in both space and time, as a consequence of the extended length of the particles. At long times, the density autocorrelation decays exponentially in time, except at a special k-dependent density when it decays as a power law. In the limit of large k at a finite density of occupied sites, the appropriately scaled system reduces to a nonequilibrium generalization of the Tonks gas describing the motion of hard rods along a continuous line. This allows us to obtain in a simple way the known two-particle distribution for the Tonks gas. For large but finite k, we also obtain the leading-order correction to the Tonks result.