On integrability of zero-range chipping models with factorized steady state

TL;DR

This paper investigates the conditions under which zero-range chipping models with factorized steady states are integrable, identifying a family of solvable models via Bethe ansatz and providing new mathematical tools and conjectures for their analysis.

Contribution

It introduces a three-parameter family of integrable zero-range models solvable by Bethe ansatz, expanding the class of known stochastic particle systems with factorized steady states.

Findings

Identified a three-parametric family of solvable models

Derived Bethe equations for the spectrum on a ring

Proposed an integral formula for the Green function

Abstract

Conditions of integrability of general zero range chipping models with factorized steady state, which were proposed in [Evans, Majumdar, Zia 2004 J. Phys. A 37 L275], are examined. We find a three-parametric family of hopping probabilities for the models solvable by the Bethe ansatz, which includes most of known integrable stochastic particle models as limiting cases. The solution is based on the quantum binomial formula for two elements of an associative algebra obeying generic homogeneous quadratic relations, which is proved as a byproduct. We use the Bethe ansatz to solve an eigenproblem for the transition matrix of the Markov process. On its basis we conjecture an integral formula for the Green function of evolution operator for the model on an infinite lattice and derive the Bethe equations for the spectrum of the model on a ring.