Integrable Stochastic Processes Associated with the $D_2$ Algebra

TL;DR

This paper introduces an integrable stochastic process linked to the $D_2$ algebra, decomposing into two simple exclusion processes, with exact solutions and potential generalizations to asymmetric cases.

Contribution

It presents the first integrable stochastic model associated with the $D_2$ algebra, including its exact solutions and boundary condition analysis.

Findings

Model decomposes into two symmetric simple exclusion processes.

Exact solutions for spectrum, eigenstates, and observables are provided.

Generalization to asymmetric processes is discussed.

Abstract

We introduce an integrable stochastic process associated with the $D_2$ quantum group, which can be decomposed into two symmetric simple exclusion processes. We establish the integrability of the model under three types of boundary conditions (periodic, twisted, and open boundaries), and present its exact solution, including the spectrum, eigenstates, and some observables. This integrable model can be generalized to the asymmetric case, decomposing into two asymmetric simple exclusion processes, and its exact solutions are also studied.