The semi-infinite q-boson system with boundary interaction

TL;DR

This paper introduces a semi-infinite q-boson system with boundary interaction, characterized by a two-parameter deformation, and demonstrates its eigenfunctions, spectrum properties, and scattering matrix factorization.

Contribution

It develops a new boundary q-boson model with explicit eigenfunctions and analyzes its spectral and scattering properties, extending previous integrable systems.

Findings

Eigenfunctions are given by Macdonald's hyperoctahedral Hall-Littlewood functions of type BC.

The n-particle spectrum is bounded and absolutely continuous.

The scattering matrix factorizes into bulk and boundary components.

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.