Exact analysis of the two-dimensional asymmetric simple exclusion process with attachment and detachment of particles

TL;DR

This paper derives the exact steady state of a two-dimensional asymmetric simple exclusion process with particle attachment and detachment, expanding understanding beyond one-dimensional models and revealing detailed physical properties.

Contribution

It constructs the exact steady state for the 2D ASEP with non-conserved particle number, a significant extension of prior one-dimensional solutions.

Findings

Exact steady state constructed for 2D ASEP with attachment/detachment

Physical quantities computed exactly, revealing system properties

Extends solvability to multi-dimensional driven-diffusive systems

Abstract

The asymmetric simple exclusion process (ASEP) is a paradigmatic driven-diffusive system that describes the asymmetric diffusion of particles with hardcore interactions in a lattice. Although the ASEP is known as an exactly solvable model, most exact results are limited to one-dimensional systems. Recently, the exact steady state in the multi-dimensional ASEP has been proposed [1]. The research focused on the situation where the number of particles is conserved. In this paper, we consider the two-dimensional ASEP with the attachment and detachment of particles (ASEP-LK), where particle number conservation is violated. By employing the result in Ref. [1], we construct the exact steady state of the ASEP-LK and reveal its properties through the exact computation of physical quantities.