Integrable boundaries for the q-Hahn process

Abstract

Taking inspiration from the harmonic process with reservoirs introduced by Giardinà, 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.

v1: One figure and 16 pages v2: added symmetric limit and improved conclusion

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Cited by in corpus (4)

• Integrable heat conduction model
• The steady state of the boundary-driven multiparticle asymmetric diffusion model
• Steady state representations for the harmonic process
• Triangular solutions to the reflection equation for $U_q(\widehat{s{l}_n})$