Integrable boundaries for the q-Hahn process

TL;DR

This paper introduces integrable boundary conditions for the q-Hahn process, a trigonometric deformation of the harmonic process, using the quantum inverse scattering method to preserve the model's integrability.

Contribution

It proposes a novel method to derive integrable boundaries for the q-Hahn process via transfer matrices, avoiding explicit K-matrix construction.

Findings

Boundary conditions preserve integrability of the q-Hahn process.

Method extends the Sklyanin's quantum inverse scattering framework.

Provides a new approach to boundary conditions in integrable stochastic models.

Abstract

Taking inspiration from the harmonic process with reservoirs introduced by Giardin\`a, Kurchan and the author in arXiv:1904.01048, we propose integrable boundary conditions for its trigonometric deformation which is known as the q-Hahn process. Following the formalism established by Mangazeev and Lu in arXiv:1903.00274 using the stochastic R-matrix, we argue that the proposed boundary conditions can be derived from a transfer matrix constructed in the framework of Sklyanin's extension of the quantum inverse scattering method and consequently preserve the integrable structure of the model. The approach avoids the explicit construction of the K-matrix.