Scattering theory of discrete (pseudo) Laplacians on a Weyl chamber

Details Scattering theory of discrete (pseudo) Laplacians on a Weyl chamber Scattering theory of discrete (pseudo) Laplacians on a Weyl chamber

2004-12-31

arxiv.org/abs/math-ph/0412097v1

American Journal of Mathematics 127, no. 2 (2005), 421--458

Physics

Mathematical Physics

31 pages, LaTeX

Scientific paper

10.1353/ajm.2005.0012

To a crystallographic root system we associate a system of multivariate orthogonal polynomials diagonalizing an integrable system of discrete pseudo Laplacians on the Weyl chamber. We develop the time-dependent scattering theory for these discrete pseudo Laplacians and determine the corresponding wave operators and scattering operators in closed form. As an application, we describe the scattering behavior of certain hyperbolic Ruijsenaars-Schneider type lattice Calogero-Moser models associated with the Macdonald polynomials.

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