Self-duality and shock dynamics in the $n$-component priority ASEP

TL;DR

This paper investigates the $n$-component priority ASEP with reflecting boundaries, establishing explicit invariant measures, proving reversibility, and utilizing quantum algebra symmetries to derive self-duality and shock dynamics.

Contribution

It provides explicit invariant measures, constructs duality functions via quantum algebra symmetry, and characterizes shock coalescence in the $n$-ASEP.

Findings

Explicit invariant measures obtained

Self-duality established using quantum algebra symmetry

Explicit time evolution of shock measures derived

Abstract

We study the $n$-component priority asymmetric simple exclusion process ($n$-ASEP) with reflecting boundaries. We obtain all invariant measures in explicit form and prove reversibility. Using the symmetry of the generator of the process under the quantum algebra $U_q[\mathfrak{gl}(n+1)]$ we construct duality functions with respect to which the $n$-ASEP is self-dual, both for the finite and the infinite integer lattice. For the $n$-ASEP on the infinite lattice we use self-duality to derive in explicit form the time evolution of a family of measures with $K$ shocks in terms of the transition probability of $K$ coloured particles in a shock exclusion process with particle-dependent hopping rates and nearest-neighbour colour exchange. This process is a gas of particles that forms a bound state, corresponding to shock coalescence on macroscopic scale.