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近简并二能级系统的几何位相
引用本文:董坤坤, 李铭. 近简并二能级系统的几何位相[J]. 华南师范大学学报(自然科学版), 2018, 50(6): 1-5. DOI: 10.6054/j.jscnun.2018109
作者姓名:董坤坤  李铭
作者单位:1.华南师范大学物理与电信工程学院//广东省量子调控与材料重点实验室,广州510006
摘    要:在有能量简并或接近简并的情况下,一个绝热演化系统的现有的量子绝热条件并不适用。本文重新推导了二能级系统的绝热演化,得到了包含近简并情况的几何相位的普遍结果。然后以一个实际的二能级系统石墨烯为例,本文通过数值计算得到了石墨烯在不同波矢位置的几何相位。数值结果表明,在能级近简并(包括简并)处,系统经过周期性绝热演化后,波函数只存在一个常规的动力学相位,不存在几何相位。离开简并位置,系统逐渐积累几何位相,最后才收敛到传统的Berry位相。

关 键 词:Berry相位,几何相位,近简并,绝热定理
收稿时间:2018-01-21
修稿时间:2018-05-12

The geometric phase of a near-degenerate two-level system
DONG K K, LI M. The geometric phase of a near-degenerate two-level system[J]. Journal of South China Normal University (Natural Science Edition), 2018, 50(6): 1-5. DOI: 10.6054/j.jscnun.2018109
Authors:DONG K K  LI M
Affiliation:1.Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials//School of Physics and Telecommunication Engineering,South China Normal University,Guangzhou 510006,China
Abstract:For a degenerate or near degenerate system its adiabatic evolution does not satisfy the conventional adiabatic condition. In the present work the adiabatic evolution of a near degenerate two-level system has been studied and a common result for the geometric phase has been obtained. The geometric phase of the two level graphene is taken as an example to be numerically computed. The numerical results show that a periodic adiabatic evolution around the degenerate point (the Dirac points of wave vectors of graphene) does not give any geometric phase but only a conventional dynamic phase. Away from the Dirac point, however, a geometric phase accumulates in the system after a full cycle of adiabatic evolution around a Dirac point of graphene, and finally converges to the conventional Berry phase.
Keywords:Berry phase   Geometric phase   near-degenerate   adiabatic theorem
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