On the scattering theory of the classical hyperbolic C(n) Sutherland model

Abstract

In this paper we study the scattering theory of the classical hyperbolic Sutherland model associated with the C(n) root system. We prove that for any values of the coupling constants the scattering map has a factorized form. As a byproduct of our analysis, we propose a Lax matrix for the rational C(n) Ruijsenaars-Schneider-van Diejen model with two independent coupling constants, thereby setting the stage to establish the duality between the hyperbolic C(n) Sutherland and the rational C(n) Ruijsenaars-Schneider-van Diejen models.

15 pages

References in corpus (2)

• On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
• Spin Calogero models associated with Riemannian symmetric spaces of negative curvature

Cited by in corpus (7)

• The hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars-Schneider-van Diejen models: Lax matrices and duality
• Action-angle duality between the C(n)-type hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen models
• Duality between the trigonometric BC(n) Sutherland system and a completed rational Ruijsenaars-Schneider-van Diejen system
• Scattering theory of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars--Schneider--van Diejen models
• Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
• An integrable BC(n) Sutherland model with two types of particles
• Integrable many-body systems of Calogero-Ruijsenaars type