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

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