Multi-Species Asymmetric Exclusion Process in Ordered Sequential Update

TL;DR

This paper extends the asymmetric simple exclusion process to multiple species with ordered sequential and sub-lattice updates, analyzing stationary states and overtaking dynamics using Matrix Product Ansatz.

Contribution

It introduces a multi-species ASEP with specific update schemes and derives the algebraic structure of its stationary states using MPA, comparing different update methods.

Findings

Stationary states characterized for open and ring systems

Overtaking probabilities depend on particle speeds and update schemes

Comparison shows differences between ordered sequential and random sequential updates

Abstract

A multi-species generalization of the asymmetric simple exclusion process (ASEP) is studied in ordered sequential and sub-lattice parallel updating schemes. In this model particles hop with their own specific probabilities to their rightmost empty site and fast particles overtake slow ones with a definite probability. Using Matrix Product Ansatz (MPA), we obtain the relevant algebra, and study the uncorrelated stationary state of the model both for an open system and on a ring. A complete comparison between the physical results in these updates and those of random sequential introduced in [20,21] is made.