循环量子系统中状态演化的Bloch定理和同步几何相位的统一  

BLOCH THEOREM FOR THE EVOLUTION OF STATES IN THE CYCLIC QUANTUM SYSTEMS AND THE UNIFICATION OF RESONANT GEOMETRIC PHASES

作　　者：李伯臧[1] 张德刚[2] 吴建华[3] 阎凤利[4] 

机构地区：[1]中国科学院物理研究所 [2]四川师范大学固体物理研究所 [3]北京大学物理系 [4]河北师范大学物理系

出　　处：《物理学报》1997年第2期227-237,共11页Acta Physica Sinica

基　　金：国家自然科学基金

摘　　要：对于Ｈａｍｉｌｔｏｎｉａｎ随时间作周期变化的量子系统中状态的演化，Ｂｌｏｃｈ定理亦成立，并可据此定义一种新的几何相位———Ｂｌｏｃｈ相位．证明用这种新的几何相位可以把迄今发现的所有同步（即量子态演化一周后获得的）几何相位统一起来，即Ｂｌｏｃｈ相位等于Ｐａｎｃｈａｒａｔｎａｍ相位、ＡｈａｒｏｎｏｖＡｎａｎｄａｎ相位和ＬｅｗｉｓＲｉｅｓｅｎｆｅｌｄ相位，并且在绝热条件下化为Ｂｅｒｙ相位．为此，先对Ｐａｎｃｈａｒａｔｎａｍ相位、ＡｈａｒｏｎｏｖＡｎａｎｄａｎ相位和ＬｅｗｉｓＲｉｅｓｅｎｆｅｌｄ相位的定义作等价的改变，使它们变得有物理意义，并把ＬｅｗｉｓＲｉｅｓｅｎｆｅｌｄ相位和Ｂｅｒｒｙ相位推广到简并情形．Abstract The Bloch theorem holds also for the evolution of states in the cyclic quantum systems in which the Hamiltonian varies cyclically with time.In light of the theorem a new type of geometric phases——Bloch phases——is defined.In this paper it is shown that the resonant (i.e.,acquired by certain states after evolving a cycle)geometric phases so far discovered can all be unified into the Bloch phases.That is,the Bloch phases are identical with the Pancharatnam phases,Aharonov Anandan phases and Lewis Riesenfeld phases,and reduce to the Berry phases in adiabatic approximation.To this end,the equivalent alternation of defining the former three types of quantum phases and the generalization of Lewis Riesenfeld phases and Berry phases to the degenerate case are made.In addition,two methods are given for efficiently searching for the Bloch phases.

关 键 词：循环 量子系统 几何相位 状态演化 量子力学 

分 类 号：O413.1[理学—理论物理]