The Aharonov-Anandan phase of a classical dynamical system seen mathematically as a quantum dynamical system

TL;DR

This paper explores the connection between classical Hannay's angle and the quantum Aharonov-Anandan phase by viewing classical integrable systems through a quantum lens, revealing a mathematical relationship.

Contribution

It demonstrates that the non-adiabatic Hannay's angle in classical systems can be related to the Aharonov-Anandan phase when classical systems are interpreted as quantum systems.

Findings

Hannay's angle linked to Aharonov-Anandan phase

Mathematical framework connecting classical and quantum phases

Insight into geometric phases in classical and quantum systems

Abstract

It is shown that the non-adiabatic Hannay's angle of an integrable non-degenerate classical hamiltonian dynamical system may be related to the Aharonov-Anandan phase it develops when it is looked mathematically as a quantum dynamical system.