Algebraic Bethe Ansatz for the two species ASEP with different hopping rates

TL;DR

This paper proves the integrability of a two-species ASEP with different hopping rates on a ring and derives Bethe equations using the Nested Algebraic Bethe Ansatz, providing formulas for particle velocities and their large-system limits.

Contribution

It generalizes previous results by deriving Bethe equations for arbitrary particle numbers and provides explicit formulas for particle velocities in a two-species ASEP.

Findings

Proves integrability of the two-species ASEP with different hopping rates.

Derives Bethe equations for arbitrary particle configurations.

Provides formulas for particle velocities and their large-system limits.

Abstract

An ASEP with two species of particles and different hopping rates is considered on a ring. Its integrability is proved and the Nested Algebraic Bethe Ansatz is used to derive the Bethe Equations for states with arbitrary numbers of particles of each type, generalizing the results of Derrida and Evans. We present also formulas for the total velocity of particles of a given type and their limit for large size of the system and finite densities of the particles.