Berry Phase and Hannay's Angle in a Quantum-Classical Hybrid System

TL;DR

This paper investigates how subsystem couplings influence Berry phase and Hannay's angle in a quantum-classical hybrid system, revealing significant effects on Berry phase but minimal impact on Hannay's angle.

Contribution

It provides a detailed analysis of the effects of subsystem couplings on geometric phases in quantum-classical hybrid systems under the Born-Oppenheimer approximation.

Findings

Berry phase is sharply affected by subsystem couplings.

Hannay's angle is only slightly affected by couplings.

Couplings significantly alter quantum geometric phases.

Abstract

Berry phase, which had been discovered for more than two decades, provides us a very deep insight on the geometric structure of quantum mechanics. Its classical counterpart--Hannay's angle is defined if closed curves of action variables return to the same curves in phase space after a time evolution. In this paper, we study the Berry phase and Hannay's angle in a quantum-classical hybrid system under the Born-Oppenheimer approximation. By quantum-classical hybrid system, we denote a composite system consists of a quantum subsystem and a classical subsystem. The effects of subsystem-subsystem couplings on the Berry phase and Hannay's angle are explored. The results show that the Berry phase has been changed sharply by the couplings, whereas the couplings have small effect on the Hannay's angle.