A Remark on Integrability of Stochastic Systems Solvable by Matrix Product Ansatz

TL;DR

This paper demonstrates that a multi-species exclusion process with variable hopping rates can be exactly solved using the coordinate Bethe ansatz, revealing a new solution to the quantum Yang-Baxter equation.

Contribution

It introduces a novel integrable multi-species exclusion process solvable via Bethe ansatz, with a new solution to the quantum Yang-Baxter equation.

Findings

Exact solution of the process via coordinate Bethe ansatz

Factorization of the N-body S-matrix into two-body S-matrices

Identification of a new solution to the quantum Yang-Baxter equation

Abstract

Within the Matrix Product Formalism we have already introduced a multi- species exclusion process in which different particles hop with different rates and fast particles stochastically overtake slow ones. In this letter we show that on an open chain, the master equation of this process can be exactly solved via the coordinate Bethe ansatz. It is shown that the N-body S-matrix of this process is factorized into a product of two-body S-matrices, which in turn satisfy the quantum Yang-Baxter equation (QYBE). This solution is to our knowledge, a new solution of QYBE.