Generalized Exclusion Processes: Transport Coefficients

TL;DR

This paper investigates a class of generalized exclusion processes with varying maximal occupancy, computing their diffusion coefficients and analyzing tagged particle behavior, revealing how these properties depend on occupancy and density.

Contribution

It introduces a unified analysis of generalized exclusion processes, deriving diffusion coefficients for different maximal occupancies and exploring tagged particle dynamics.

Findings

Diffusion coefficient is independent of spatial dimension.

For $k=1$ and $k=\infty$, the diffusion coefficient is constant.

For $2 \\leq k<\infty$, the diffusion coefficient depends on density and $k$.

Abstract

A class of generalized exclusion processes parametrized by the maximal occupancy, $k\geq 1$, is investigated. For these processes with symmetric nearest-neighbor hopping, we compute the diffusion coefficient and show that it is independent on the spatial dimension. In the extreme cases of $k=1$ (simple symmetric exclusion process) and $k=\infty$ (non-interacting symmetric random walks) the diffusion coefficient is constant; for $2\leq k<\infty$, the diffusion coefficient depends on the density and the maximal occupancy $k$. We also study the evolution of a tagged particle. It exhibits a diffusive behavior which is characterized by the coefficient of self-diffusion which we probe numerically.