Density and current profiles in $U_q(A_2^{(1)})$ zero range process

Abstract

The stochastic $R$ matrix for $U_q(A_n^{(1)})$ 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.

31 pages, 12 figures. Minor revision from version 1

References in corpus (11)

• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Condensation in the zero range process: stationary and dynamical properties
• Stochastic six-vertex model
• On integrability of zero-range chipping models with factorized steady state
• Spatial Particle Condensation for an Exclusion Process on a Ring
• Matrix product solution of the multispecies partially asymmetric exclusion process
• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• A deformation of affine Hecke algebra and integrable stochastic particle system
• Algebraic construction of multi-species q-Boson system
• Matrix product formula for $U_q(A_2^{(1)})$-zero range process
• A $q$-boson representation of Zamolodchikov-Faddeev algebra for stochastic $R$ matrix of $U_q(A_n^{(1)})$

Cited by in corpus (3)

• Current statistics in the q-boson zero range process
• Matrix Product representation of the stationary state of the open Zero Range Process
• Matrix product solution of the stationary states of two-species open zero range processes