Integrability of the Multi-Species TASEP with Species-Dependent Rates

Eunghyun Lee

doi:10.3390/sym13091578

Abstract

Assume that each species l has its own jump rate bl in the multi-species totally asymmetric simple exclusion process. We show that this model is integrable in the sense that the Bethe ansatz method is applicable to obtain the transition probabilities for all possible N-particle systems with up to N different species.

Highlights

The multi-species asymmetric simple exclusion process on Z is a generalization of the asymmetric simple exclusion process (ASEP) on Z in the sense that each particle may belong to a different species labelled by an integer l ∈ {1, 2, · · · }
The main result of this paper is that the multi-species totally asymmetric simple exclusion process (TASEP) with species-dependent rates is an integrable model, and we provide a formula analogous to (2.12) in [4] using the Bethe ansatz method
We have shown that the Bethe ansatz method is still applicable to the multi-species TASEP with species-dependent rates

Summary

Introduction

The multi-species asymmetric simple exclusion process on Z is a generalization of the asymmetric simple exclusion process (ASEP) on Z in the sense that each particle may belong to a different species labelled by an integer l ∈ {1, 2, · · · }. The multi-species asymmetric simple exclusion process can be considered in a more general context—that is, the coloured six vertex model [9]. Another direction of generalizing the ASEP and other models studied in the integrable probability is to make the jump rates inhomogeneous. The main result of this paper is that the multi-species TASEP with species-dependent rates is an integrable model, and we provide a formula analogous to (2.12) in [4] using the Bethe ansatz method. The matrix of the transition probabilities of the multi-species TASEP with species-dependent rates is. The proofs of Lemma 1 and Theorem 1 are given

Forward Equations

Solutions of the Forward Equations via Bethe Ansatz

Initial Condition

Findings

Conclusions