Integrable boundary interactions for Ruijsenaars' difference Toda chain

TL;DR

This paper introduces a boundary interaction for Ruijsenaars' difference Toda chain, demonstrating its quantum integrability and related spectral properties using specialized hypergeometric functions.

Contribution

It provides a novel boundary interaction model for the Ruijsenaars' chain and diagonalizes its Hamiltonian using deformed hyperoctahedral $q$-Whittaker functions, linking to Macdonald-Koornwinder polynomials.

Findings

Establishment of quantum integrability for the boundary-extended chain

Derivation of the bispectral dual system

Construction of the $n$-particle scattering operator

Abstract

We endow Ruijsenaars' open difference Toda chain with a one-sided boundary interaction of Askey-Wilson type and diagonalize the quantum Hamiltonian by means of deformed hyperoctahedral $q$-Whittaker functions that arise as a $t=0$ degeneration of the Macdonald-Koornwinder multivariate Askey-Wilson polynomials. This immediately entails the quantum integrability, the bispectral dual system, and the $n$-particle scattering operator for the chain in question.