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 $\mathbb{Z}$ 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.

References in corpus (5)

• Asymptotics in ASEP with Step Initial Condition
• Exact Solution of the Master Equation for the Asymmetric Exclusion Process
• Spectral theory for the q-Boson particle system
• Order of current variance and diffusivity in the rate one totally asymmetric zero range process
• Transition Probabilities of the Bethe Ansatz Solvable Interacting Particle Systems

Cited by in corpus (8)

• Integral formulas of ASEP and $q$-TAZRP on a ring
• Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process
• On the TASEP with Second Class Particles
• Probability distributions of multi-species q-TAZRP and ASEP as double cosets of parabolic subgroups
• Distributions of a particle's position and their asymptotics in the $q$-deformed totally asymmetric zero range process with site dependent jumping rates
• Some conditional probabilities in the TASEP with second class particles
• Asymptotics of free fermions in a quadratic well at finite temperature and the Moshe-Neuberger-Shapiro random matrix model
• Integrability of the multi-species TASEP with species-dependent rates