Matrix product formula for $U_q(A_2^{(1)})$-zero range process

Abstract

The $U_q(A_n^{(1)})$-zero range processes introduced recently by Mangazeev, Maruyama and the authors are integrable discrete and continuous time Markov processes associated with the stochastic $R$ matrix derived from the well-known $U_q(A_n^{(1)})$ quantum $R$ matrix. By constructing a representation of the relevant Zamolodchikov-Faddeev algebra, we present, for $n=2$, a matrix product formula for the steady state probabilities in terms of $q$-boson operators.

15 pages. Section 1 revised

References in corpus (11)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Condensation in the zero range process: stationary and dynamical properties
• Factorised Steady States in Mass Transport Models
• On integrability of zero-range chipping models with factorized steady state
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• On the Yang-Baxter equation for the six-vertex model
• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• Exact solutions of exactly integrable quantum chains by a matrix product ansatz
• Multispecies TASEP and the tetrahedron equation
• A deformation of affine Hecke algebra and integrable stochastic particle system

Cited by in corpus (6)

• Matrix Product representation of the stationary state of the open Zero Range Process
• Integrable Structure of Multispecies Zero Range Process
• Density and current profiles in $U_q(A_2^{(1)})$ zero range process
• Steady state representations for the harmonic process
• Matrix product solution of the stationary states of two-species open zero range processes
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish