Department of Physics, Indiana University, Bloomington, Indiana 47405, USA.
Phys Rev Lett. 2010 Apr 30;104(17):170406. doi: 10.1103/PhysRevLett.104.170406.
We introduce an adiabatic perturbation theory for quantum systems with degenerate energy spectra. This perturbative series enables one to rigorously establish conditions for the validity of the adiabatic theorem of quantum mechanics for degenerate systems. The same formalism can be used to find nonadiabatic corrections to the non-Abelian Wilczek-Zee geometric phase. These corrections are relevant to assess the validity of the practical implementation of the concept of fractional exchange statistics. We illustrate the formalism with an exactly solvable time-dependent problem.
我们介绍了一种具有简并能谱的量子系统的绝热微扰理论。这个微扰级数使得人们能够严格地建立量子力学绝热定理在简并系统中成立的条件。同样的形式体系也可以用来寻找非绝热修正对非阿贝尔 Wilczek-Zee 几何相位的影响。这些修正对于评估分数交换统计概念的实际实现的有效性是相关的。我们用一个完全可解的时变问题来说明这个形式体系。
