Integrability of the multi-species ASEP with long-range jumps on $\mathbb{Z}$

TL;DR

This paper introduces an integrable multi-species ASEP model with long-range jumps on the integer lattice, providing exact transition probabilities via Bethe ansatz, extending understanding of multi-species exclusion processes.

Contribution

The paper proves the integrability of a novel multi-species ASEP with long-range jumps and derives explicit transition probabilities using Bethe ansatz techniques.

Findings

Model is proven to be integrable.

Exact transition probability formulas are obtained.

Extends the class of solvable multi-species exclusion processes.

Abstract

Let us consider a two-sided multi-species stochastic particle model with finitely many particles on $\mathbb{Z}$ defined as follows. Suppose that each particle is labelled by a positive integer $l$ and waits a random time exponentially distributed with rate $1$. It then chooses the right direction to jump with probability $p$ or the left direction with probability $q=1-p$. If the particle chooses the right direction, it jumps to the nearest site occupied by a particle $l'<l$ (with the convention that an empty site is considered as a particle with labelled $0$). If the particle chooses the left direction, it follows the rule of the multi-species totally asymmetric simple exclusion process (mTASEP). We show that this model is integrable and provide the exact formula of the transition probability using the Bethe ansatz.