Spectrum and eigenfunctions of the lattice hyperbolic Ruijsenaars-Schneider system with exponential Morse term

Abstract

We place the hyperbolic quantum Ruijsenaars-Schneider system with an exponential Morse term on a lattice and diagonalize the resulting $n$-particle model by means of multivariate continuous dual $q$-Hahn polynomials that arise as a parameter reduction of the Macdonald-Koornwinder polynomials. This allows to compute the $n$-particle scattering operator, to identify the bispectral dual system, and to confirm the quantum integrability in a Hilbert space set-up.

13 pages, LaTeX

References in corpus (2)

• Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications
• Branching Formula for Macdonald-Koornwinder Polynomials

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