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

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.

8 pages, 2 figures

References in corpus (3)

• Adiabatic Geometric Phase for a General Quantum States
• Equivalence of Two Approaches for Quantum-Classical Hybrid Systems
• Dynamics of quantum-classical hybrid system: effect of matter-wave pressure

Cited by in corpus (4)

• Generalized gauge transformation with $PT$-symmetric non-unitary operator and classical correspondence of non-Hermitian Hamiltonian for a periodically driven system
• Quantum Shape Effects
• The effects of light-wave nonstaticity on accompanying geometric-phase evolutions
• Anti-adiabatic evolution in quantum-classical hybrid system