Integrable multispecies totally asymmetric stochastic interacting particle systems with homogeneous rates

TL;DR

This paper extends the classification of integrable multispecies asymmetric particle systems with homogeneous rates, identifying new models and extension schemes that generalize previous two-species results to arbitrary species numbers.

Contribution

It demonstrates that 7 of 28 two-species integrable rules can be extended to multispecies models and introduces new parameterized integrable models and alternative extension schemes.

Findings

7 cases extended to arbitrary species number

New integrable models with one or two parameters

Alternative extension scheme for 8 cases

Abstract

We study one dimensional stochastic particle systems with exclusion interaction that each site can be occupied by at most one particle, and homogeneous jumping rates. Alimohammadi and Ahmadi previously classified 28 Yang-Baxter integrable two-particle interaction rules for the two species models with homogeneous rates. In this work, we show that 7 of these 28 cases can be naturally extended to integrable models with an arbitrary number of species $N \geq 2$. Moreover, we discover new integrable models with one or two parameters that generalize these 7 cases. For 8 of the remaining 21 cases, we propose an alternative extension scheme that yields integrable $N$ species models.