关于Berry几何位相理论的推广

The Extention of Berry's Theory on Geometric Phase

对于可参数化时间t的周期Hamiltonian系统，由non－adiabatic到adiabatic－limit的“严格”演变以获得Berry几何相γn（C）的问题．结果表明，存在“四种类型”的演变态，它们都可以满足在参数R空间中的同一条闭合曲线C上作这样的“严格演变”，并且还都可以获得同一个Berry几何相γn（C）；而Berry发现这一几何相γn（C）时所考虑和采用的“演变态”，恰好属于本文“四种类型”的“严格”演变态之一的adiabaticapproximation情形．据此，可以把Berry几何位相理论推广到本文所研究的“四种类型”的“严格”演变中．

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 γn (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 γn (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.