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

Symmetry Integrability and Geometry-Methods and Applications

article

Dong Wang¹  David Waugh² 

[1] Department of Mathematics, National University of Singapore;BNP Paribas

关键词: zero range process;    transition probability;    interacting particle systems;    Bethe ansatz;   

DOI  :  10.3842/SIGMA.2016.037

来源: National Academy of Science of Ukraine

【 摘 要 】

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 ${\mathbb Z}$ 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.

【 授权许可】

Unknown