Non-crystallographic reduction of generalized Calogero-Moser models

TL;DR

This paper introduces a reduction method for Calogero-Moser models using non-crystallographic Coxeter groups, leading to new integrable systems with potentials scaled by the golden ratio, expanding the class of solvable models.

Contribution

It presents a novel reduction technique embedding non-crystallographic Coxeter groups into crystallographic ones, resulting in new integrable Calogero-Moser systems with unique potential terms.

Findings

Recovered generalized Calogero Hamiltonian for rational potentials.

Derived new integrable models with potentials scaled by the golden ratio.

Demonstrated classical equations of motion from a Lie algebraic Lax pair.

Abstract

We apply a recently introduced reduction procedure based on the embedding of non-crystallographic Coxeter groups into crystallographic ones to Calogero-Moser systems. For rational potentials the familiar generalized Calogero Hamiltonian is recovered. For the Hamiltonians of trigonometric, hyperbolic and elliptic type, we obtain novel integrable dynamical systems with a second potential term which is rescaled by the golden ratio. We explicitly show for the simplest of these non-crystallographic models how the corresponding classical equations of motion can be derived from a Lie algebraic Lax pair based on the larger, crystallographic Coxeter group.