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Integrability of the multi-species ASEP with long-range jumps on $\mathbb{Z}$ by Lee, Eunghyun is a scholarly article available to read on EtoBox.

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

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.

Author

Lee, Eunghyun

Published

2024

Language

EN