Berry phase and Hannay’s angle in the Born–Oppenheimer hybrid systems

Journal Article · Sun Dec 15 04:00:00 EST 2013 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2013.08.006· OSTI ID:22224244

Liu, H. D. ^[1]; Yi, X. X. ^[2]

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1. National Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088 (China)
2. School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China)

In this paper, we investigate the Berry phase and Hannay’s angle in the Born–Oppenheimer (BO) hybrid systems and obtain their algebraic expressions in terms of one form connection. The semiclassical relation of Berry phase and Hannay’s angle is discussed. We find that, besides the usual connection term, the Berry phase of quantum BO composite system also contains a novel term brought forth by the coupling induced effective gauge potential. This quantum modification can be viewed as an effective Aharonov–Bohm effect. Moreover, the similar phenomenon is founded in Hannay’s angle of classical BO composite system, which indicates that the Berry phase and Hannay’s angle possess the same relation as the usual one. An example is used to illustrate our theory. This scheme can be used to generate artificial gauge potentials for neutral atoms. Besides, the quantum–classical hybrid BO system is also studied to compare with the results in full quantum and full classical composite systems. -- Highlights: •We have derived the Berry phase and Hannay’s angle in BO hybrid systems. •The Berry phase contains a novel term brought by the effective gauge potential. •This mechanism can be used to generate artificial gauge potentials for neutral atoms. •The relation between Hannay’s angles and Berry phases is established.

• OSTI ID: 22224244
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Vol. 339; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ATOMS
COMPARATIVE EVALUATIONS
COUPLING
HYBRIDIZATION
MODIFICATIONS
POTENTIALS
PROGRAMMING LANGUAGES
SEMICLASSICAL APPROXIMATION