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• W2498863984 abstract "To a crystallographic root system we associate a system of multivariate orthogonal poly- nomials 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. 1. Introduction. A fundamental property of the solitonic solutions of in- tegrable nonlinear wave equations is that their multi-particle scattering process decomposes into pairwise two-particle interactions (SCM, AS, N-Z, N, FT). This phenomenon is preserved at the quantum level: the corresponding solitonic quan- tum field theories are characterized by an Af-particle scattering matrix that fac- torizes in terms of two-particle scattering matrices (M, KBI). As it turns out, this type of factorization can be understood heuristically as being a consequence of the integrability of the models in question (Ku, RSc). An archetype example of an integrable system with factorized scattering is the celebrated nonlinear Schrodinger equation (NLS). The quantum version of this model boils down to a bosonic Af-particle system with a pairwise interaction via delta-functional potentials. The factorization of the scattering manifests itself through the asymptotics of the wave function, which is characterized by (products of) two-particle scattering matrices (or c-functions) (M, Ga, Ox, KBI). In recent work, Ruijsenaars constructed a remarkably large class of quan- tum integrable lattice models of Af-particles exhibiting factorized scattering (R4). The discrete systems in question arise by interpreting recurrence relations (or Pieri formulas) for symmetric multivariate orthogonal polynomials as quantum eigenvalue equations. Here the polynomial variable plays the role of the spectral parameter and the index (i.e., partition) labelling the polynomials is thought of as the discrete spatial variable. By analyzing the asymptotics of the polynomi- als as the degree tends to infinity, Ruijsenaars demonstrated that - for factorized orthogonality measures subject to certain technical conditions ensuring that the" @default.
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• W2498863984 date "2016-01-01" @default.
• W2498863984 modified "2023-09-23" @default.
• W2498863984 title "SCATTERING THEORY OF DISCRETE (PSEUDO) LAPLACIANS" @default.
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