Scattering theory of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars--Schneider--van Diejen models

TL;DR

This paper analyzes the scattering behavior of two integrable many-particle systems, revealing that their scattering maps are factorized, and leverages duality to construct wave and scattering maps.

Contribution

It introduces a novel analysis of scattering maps for hyperbolic BC(n) Sutherland and rational BC(n) Ruijsenaars-Schneider-van Diejen models using action-angle duality.

Findings

Scattering maps are factorized for both models

Constructed wave and scattering maps using duality

Provided new insights into integrable system scattering properties

Abstract

In this paper, we investigate the scattering properties of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars-Schneider-van Diejen many-particle systems with three independent coupling constants. Utilizing the recently established action-angle duality between these classical integrable models, we construct their wave and scattering maps. In particular, we prove that for both particle systems the scattering map has a factorized form.