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

Yuki Ishiguro; Jun Sato

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arXiv · 2405.09261

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

Yuki Ishiguro·Jun Sato

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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.

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Yuki Ishiguro, Jun Sato. 2024-05-15. Exact analysis of the two-dimensional asymmetric simple exclusion process with attachment and detachment of particles. https://arxiv.org/abs/2405.09261

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