An introduction to classical monodromy: applications to molecules in external fields

TL;DR

This paper introduces classical monodromy in integrable Hamiltonian systems, focusing on molecules in external fields, and presents a semi-theoretical method to detect monodromy through phase space topology analysis.

Contribution

It develops a semi-theoretical approach to identify classical monodromy in systems with azimuthal symmetry, validated through numerical examples.

Findings

Monodromy occurs in molecules with external fields and azimuthal symmetry.

The proposed method effectively detects monodromy in various systems.

Numerical tests confirm the method's validity for different configurations.

Abstract

An integrable Hamiltonian system presents monodromy if the action-angle variables cannot be defined globally. As a prototype of classical monodromy with azimuthal symmetry, we consider a linear molecule interacting with external fields and explore the topology structure of its phase space. Based on the behavior of closed orbits around singular points or regions of the energy-momentum plane, a semi-theoretical method is derived to detect classical monodromy. The validity of the monodromy test is numerically illustrated for several systems with azimuthal symmetry.