G（4，2）格拉斯曼流形的几何相位
Geometrical phases for the G(4,2) Grassmannian manifold
摘要：
我们推广通常的阿贝尔Berry相位，例如在一个系统中产生的两个非退化状态的情况下，系统具有两个双退化能量本征空间。描述第一种情况的状态空间的参数流形形式上由G（2，1）格拉斯曼流形给出，而对于广义系统则由G（4，2）格拉斯曼流形给出.对于后者的流形表现出更丰富的结构比它的阿贝尔对应，我们计算的连接组件，场强和相关的几何相位，发展非平凡的退化特征空间。一个简单的原子模型，提出了他们的物理实现。
英文摘要：
We generalize the usual abelian Berry phase generated for example in a system with two non-degenerate states to the case of a system with two doubly degenerate energy eigenspaces. The parametric manifold describing the space of states of the first case is formally given by the G(2,1) Grassmannian manifold, while for the generalized system it is given by the G(4,2) one. For the latter manifold which exhibits a much richer structure than its abelian counterpart we calculate the connection components, the field strength and the associated geometrical phases that evolve non-trivially both of the degenerate eigenspaces. A simple atomic model is proposed for their physical implementation.
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