Explicit solutions of the classical Calogero & Sutherland systems for any root system

TL;DR

This paper presents a method to explicitly solve classical Calogero and Sutherland systems for any root system by diagonalizing certain matrices, extending known results beyond type A root systems.

Contribution

It generalizes explicit solution techniques to all root systems, not just type A, for classical Calogero and Sutherland models.

Findings

Explicit solutions obtained via matrix diagonalization.

Method applicable to any root system.

Extension to higher Hamiltonian flows.

Abstract

Explicit solutions of the classical Calogero (rational with/without harmonic confining potential) and Sutherland (trigonometric potential) systems is obtained by diagonalisation of certain matrices of simple time evolution. The method works for Calogero & Sutherland systems based on any root system. It generalises the well-known results by Olshanetsky and Perelomov for the A type root systems. Explicit solutions of the (rational and trigonometric) higher Hamiltonian flows of the integrable hierarchy can be readily obtained in a similar way for those based on the classical root systems.