Transition Probabilities of the Bethe Ansatz Solvable Interacting Particle Systems

TL;DR

This paper derives exact transition probabilities for several Bethe ansatz solvable interacting particle systems, enabling precise analysis of their dynamics and current distributions.

Contribution

It provides the first explicit formulas for transition probabilities of non-determinantal Bethe ansatz solvable systems like PushASEP, avalanche process, and zero range process.

Findings

Exact transition probabilities derived for PushASEP, avalanche process, and zero range process.

Current distributions for avalanche and zero range processes obtained from ASEP results.

Enhanced understanding of dynamics in non-determinantal integrable particle systems.

Abstract

This paper presents the exact expressions of the transition probabilities of some non-determinantal Bethe ansatz solvable interacting particle systems: the two-sided PushASEP, the asymmetric avalanche process and the asymmetric zero range process. The time integrated currents of the asymmetric avalanche process and the asymmetric zero range process are immediate from the results of the asymmtric simple exclusion process.