On the maximal superintegrability of strongly isochronous Hamiltonians

TL;DR

This paper demonstrates that strongly isochronous Hamiltonians are maximally superintegrable and shows how Hamiltonian reduction preserves this property, with applications to rational spin Calogero–Moser models.

Contribution

It establishes the superintegrability of strongly isochronous Hamiltonians and connects Hamiltonian reduction to preserving isochronicity and superintegrability.

Findings

All strongly isochronous Hamiltonians are maximally superintegrable.

Hamiltonian reduction under certain conditions preserves isochronicity.

Rational spin Calogero–Moser models in harmonic potential are maximally superintegrable.

Abstract

We study strongly isochronous Hamiltonians that generate periodic time evolution with the same basic period for a dense set of initial values. We explain that all such Hamiltonians are maximally superintegrable, and show that if the system is subjected to Hamiltonian reduction based on a compact symmetry group and certain conditions are met, then the reduced Hamiltonian is strongly isochronous with the original basic period. We utilize these simple observations for demonstrating the maximal superintegrability of rational spin Calogero--Moser type models in confining harmonic potential.