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

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.