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

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.