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 setup.
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Communicated by Jean-Michel Maillet.
This work was supported in part by the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) Grants # 1130226 and # 1141114.
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van Diejen, J.F., Emsiz, E. Spectrum and Eigenfunctions of the Lattice Hyperbolic Ruijsenaars–Schneider System with Exponential Morse Term. Ann. Henri Poincaré 17, 1615–1629 (2016). https://doi.org/10.1007/s00023-015-0434-9
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DOI: https://doi.org/10.1007/s00023-015-0434-9