The semi-infinite q-boson system with boundary interaction

Abstract

Upon introducing a one-parameter quadratic deformation of the q-boson algebra and a diagonal perturbation at the end point, we arrive at a semi-infinite q-boson system with a two-parameter boundary interaction. The eigenfunctions are shown to be given by Macdonald's hyperoctahedral Hall-Littlewood functions of type BC. It follows that the n-particle spectrum is bounded and absolutely continuous and that the corresponding scattering matrix factorizes as a product of two-particle bulk and one-particle boundary scattering matrices.

9 pages

References in corpus (1)

• The Bose Gas and Asymmetric Simple Exclusion Process on the Half-Line

Cited by in corpus (6)

• Spectral theory for the q-Boson particle system
• Refined Cauchy and Littlewood identities, plane partitions and symmetry classes of alternating sign matrices
• Orthogonality of Bethe Ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove
• From Quantum Bäcklund Transforms to Topological Quantum Field Theory
• Quantum Integrals for a Semi-Infinite $q$-Boson System with Boundary Interactions
• Boundary Interactions for the Semi-Infinite q-Boson System and Hyperoctahedral Hall-Littlewood Polynomials