Calogero-Moser models with internal degrees of freedom revisited

TL;DR

This paper revisits classical Calogero-Moser models with internal degrees of freedom, highlighting their integrability and relevance in quantum chaos, and introduces a unified matrix dynamics framework for analyzing and relating these models.

Contribution

It provides a unified matrix dynamics approach to analyze Calogero-Moser models with internal degrees of freedom, revealing equivalences and enabling new model constructions.

Findings

Models exhibit complete integrability.

Internal degrees influence eigenvalue dynamics.

Unified framework relates different models.

Abstract

We discuss various examples of classical Calogero-Moser models with internal degrees of freedom. These models besides of having some attractive properties, like the complete integrability, are of interest eg., in studying spectral properties of quantum chaotic systems. The role of internal degrees of freedom is important in at least two aspects. Firstly, they come in play as dynamically evolving couplings between repelling pairs of eigenvalues, hence they influence the speed of eigenvalue dynamics. Secondly their initial values determine the "reachable sets" of couplings between particular pairs accessible during the evolution. The considered models are studied in a framework of matrix dynamics in a unifed way based on a reduction of a linear model in an extended phase-space. Such an approach enables showing an equivalencies among various types of similar models employing "vectorial degrees of freedom" and constructing new systems of similar type.