Algebraic Symmetry and Self-Duality of an Open ASEP

TL;DR

This paper investigates the algebraic symmetry and self-duality of an open ASEP model with specific boundary conditions, using a mapping to an XXZ quantum spin chain and leveraging known results.

Contribution

It establishes algebraic symmetry and self-duality for an open ASEP with particular boundary conditions through a Hamiltonian mapping.

Findings

Proves algebraic symmetry in the open ASEP model.

Demonstrates self-duality property of the model.

Connects ASEP with XXZ quantum spin chain via Hamiltonian mapping.

Abstract

We consider the asymmetric simple exclusion process (ASEP) with open boundary condition at the left boundary, where particles exit at rate {\gamma} and enter at rate {\alpha} = {\gamma}{\tau}^2, and where {\tau} is the asymmetry parameter in the bulk. At the right boundary, particles neither enter nor exit. By mapping the generator to the Hamiltonian of an XXZ quantum spin chain with reflection matrices, and using previously known results, we show algebraic symmetry and self-duality for the model.