近简并二能级系统的几何位相

The Geometric Phase of a Near-Degenerate Two-Level System

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量子绝热条件并不适用.文中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位相的普遍结果.然后以一个实际的二能级系统石墨烯为例,通过数值计算得到了石墨烯在不同波矢位置的几何位相.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位相,不存在几何位相.离开简并位置,系统逐渐积累几何位相,最后才收敛得到传统的Berry位相.

The adiabatic evolution of a degenerate or near degenerate system does not satisfy the conventional adiabatic condition.The adiabatic evolution of a near degenerate two-level system was restudied and a common result for the geometric phase was obtained.The geometric phase of the two-level graphene was taken as an example for numerical computation.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 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.