The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates

Abstract

In this paper we consider the q-deformed totally asymmetric zero range process (q-TAZRP), also known as the q-boson (stochastic) particle system, on the Z lattice, such that the jump rate of a particle depends on the site where it is on the lattice. We derive the transition probability for an n particle process in Bethe ansatz form as a sum of n! n-fold contour integrals. Our result generalizes the transition probability formula by Korhonen and Lee for q-TAZRP with a homogeneous lattice, and our method follows the same approach as theirs.