Self-Duality for the Two-Component Asymmetric Simple Exclusion Process

TL;DR

This paper establishes self-duality for a two-component ASEP using quantum algebra symmetries, constructs invariant measures explicitly, and discusses their properties, advancing understanding of multi-species exclusion processes.

Contribution

It introduces a novel self-duality framework for the two-component ASEP based on quantum algebra symmetries and explicitly constructs all invariant measures.

Findings

Self-duality proven for the two-component ASEP.

Explicit construction of all invariant measures.

Sum rule for the duality functions established.

Abstract

We study a two-component asymmetric simple exclusion process (ASEP) that is equivalent to the ASEP with second-class particles. We prove self-duality with respect to a family of duality functions which are shown to arise from the reversible measures of the process and the symmetry of the generator under the quantum algebra $U_q[\mathfrak{gl}_3]$. We construct all invariant measures in explicit form and discuss some of their properties. We also prove a sum rule for the duality functions.