绝热定理表述的改进以及Berry相位和Wilczek-Zee算符导出的简化

IMPROVEMENT OF THE STATEMENT OF ADIABATICTHEOREM AND SIMPLIFICATION OF THEDERIVATION OF BERRY PHASES ANDWILCZEK-ZEE OPERATORS

用Hamiltouian随时间的变化率来定量地界定量子系统的“缓慢变化”,从而对绝热定理的表述做了改进,使它更精确;其证明过程变得更简单,绝热近似的误差估计也被做得更直捷,并得到了(?)/(?)(?)相对于能量本征函数的非对角元的估计式.据此,对Berry相位和Wilczek-Zee算符的导出做了简化.而Berry相因于作为wilczek-Zee算符的特例这一点,也被表述得更加严格和清楚.

By defining the 'slow change' of a quantum system in terms of the speed of time-dependent Hamihonian, a more rigorous statement of adiabatic theorem (AT) is given. The demonstration of AT is thus simplified significantly and the error estimation of adiabatic approximation is expressed more explicitly. By this way a. series of inequalities about the non-diagonal elements of δ/δt with respect to the energy eigen-functions are obtained. Accordingly, the Berry phases and the Wilczek-Zee (W-Z) operators are rederived in a quite brief manner. From this rederivation the fact that the Berry phase factors are the particular cases of W-Z operators can be seen more clearly.