Dynamics of Repulsion Processes

TL;DR

This paper analyzes the dynamics of one-dimensional stochastic lattice gases with long-range repulsive interactions under zero-temperature conditions, deriving analytical expressions for diffusion coefficients and particle displacement variance.

Contribution

It introduces a novel analytical approach to study long-range repulsive interactions in lattice gases with zero-temperature dynamics.

Findings

Derived density-dependent diffusion coefficient analytically.

Computed variance of tagged particle displacement.

Established behavior of the system under specified interaction decay.

Abstract

We study dynamical behaviors of one-dimensional stochastic lattice gases with repulsive interactions whose span can be arbitrary large. We endow the system with a zero-temperature dynamics, so that the hops to empty sites which would have led to the increase of energy are forbidden. We assume that the strength of interactions sufficiently quickly decreases with the separation between the particles, so that interactions can be treated in a lexicographic order. For such repulsion processes with symmetric nearest-neighbor hopping we analytically determine the density-dependent diffusion coefficient. We also compute the variance of the displacement of a tagged particle.