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arXiv · 1512.01612

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

Dong Wang·David Waugh
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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.

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BibTeXRIS

Dong Wang, David Waugh. 2016-04-14. The Transition Probability of the $q$-TAZRP ($q$-Bosons) with Inhomogeneous Jump Rates. https://doi.org/10.3842/sigma.2016.037

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