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

TL;DR

This paper analyzes the scattering behavior of the hyperbolic C(n) Sutherland model, demonstrating a factorized scattering map and proposing a Lax matrix for a related rational model, advancing understanding of their duality.

Contribution

It proves the factorized form of the scattering map for the hyperbolic C(n) Sutherland model and introduces a Lax matrix for the rational C(n) Ruijsenaars-Schneider-van Diejen model.

Findings

Scattering map has a factorized form for all coupling constants.

Proposed a Lax matrix for the rational C(n) Ruijsenaars-Schneider-van Diejen model.

Sets the stage for establishing duality between the models.

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.