The Extention of Berry's Theory on Geometric Phase

Zhang Zhongcan; Fang Zhenyun; Hu Chenguo; Sun Shijun

Chinese Physics C> 1999, Vol. 23> Issue(10) : 980-991

The Extention of Berry's Theory on Geometric Phase

Phvsics Department of College of Science of Chongqing University, Chongqung 400044

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To the cyclic Hamiltonian system, where we have done the parameter transition t→R(t), we study the problem of the acquirement of Berry geometric phase γ_n (C) by the "strict" evolution from the non-adiabatic to the adiabatic-limit. Our results show that there exist four types of evolution states, all of which can satisfy the above "strict" evolution along the same closed curve C in the space formed by the parameter R and can obtain the same Berry geometric phase γn(C). When Berry first found the geometric phase γ_n(C), he only considered one evolution state, which is just the adiabatic approximation case of one of the four "strict" evolution states mentioned above. So Berry's theory on geometric phase can be extended into the four types of strict evolution shown in this paper.

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Zhang Zhongcan, Fang Zhenyun, Hu Chenguo and Sun Shijun. The Extention of Berry's Theory on Geometric Phase[J]. Chinese Physics C, 1999, 23(10): 980-991.

Zhang Zhongcan, Fang Zhenyun, Hu Chenguo and Sun Shijun. The Extention of Berry's Theory on Geometric Phase[J]. Chinese Physics C, 1999, 23(10): 980-991. shu

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Received: 1998-04-28
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

The Extention of Berry's Theory on Geometric Phase

Corresponding author: Zhang Zhongcan,

Phvsics Department of College of Science of Chongqing University, Chongqung 400044

Received Date: 1998-04-28

Accepted Date: 1900-01-01

Available Online: 1999-10-05

Abstract: To the cyclic Hamiltonian system, where we have done the parameter transition t→R(t), we study the problem of the acquirement of Berry geometric phase γ_n (C) by the "strict" evolution from the non-adiabatic to the adiabatic-limit. Our results show that there exist four types of evolution states, all of which can satisfy the above "strict" evolution along the same closed curve C in the space formed by the parameter R and can obtain the same Berry geometric phase γn(C). When Berry first found the geometric phase γ_n(C), he only considered one evolution state, which is just the adiabatic approximation case of one of the four "strict" evolution states mentioned above. So Berry's theory on geometric phase can be extended into the four types of strict evolution shown in this paper.

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The Extention of Berry's Theory on Geometric Phase

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