Scattering theory of discrete (pseudo) Laplacians on a Weyl chamber
Mathematical Physics
2010-09-27 v1 math.MP
Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math-ph/0412097,
title = {Scattering theory of discrete (pseudo) Laplacians on a Weyl chamber},
author = {J. F. van Diejen},
journal= {arXiv preprint arXiv:math-ph/0412097},
year = {2010}
}
Comments
31 pages, LaTeX