# Density and current profiles in $U_q(A^{(1)}_2)$ zero range process

## TL;DR

This paper analyzes how fixed first-class particles affect the distribution and flow of second-class particles in an integrable zero range process derived from the stochastic $R$ matrix of $U_q(A^{(1)}_2)$, providing exact formulas for density and current.

## Contribution

It introduces exact formulas for density and current profiles of second-class particles influenced by fixed first-class particles in an integrable zero range process.

## Key findings

- Exact formulas for local density of second-class particles
- Exact formulas for current of second-class particles
- Influence of fixed first-class particles on second-class particle distribution

## Abstract

The stochastic $R$ matrix for $U_q(A^{(1)}_n)$ introduced recently gives rise to an integrable zero range process of $n$ classes of particles in one dimension. For $n=2$ we investigate how finitely many first class particles fixed as defects influence the grand canonical ensemble of the second class particles. By using the matrix product stationary probabilities involving infinite products of $q$-bosons, exact formulas are derived for the local density and current of the second class particles in the large volume limit.