具有线性Hamilton算子的齐次Kähler流形中的Berry相
Berry phase in homogeneous Kähler manifolds with linear Hamiltonians
摘要：
本文研究了齐次Kähler流形X=G/H上相干态循环量子运动的全（动力学加几何（Berry））相位，X =G/H可以看作经典系统的相空间，在特殊情况下，X = G/H是某些李群G的余伴随轨道.当哈密顿量在李群的生成元中是线性的时，两个相位都可以用{ \em classical}对象精确计算。特别地，几何相位由相干态空间中的（纯经典）运动所包围的辛区域给出。
英文摘要：
We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous Kähler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of {\em classical} objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states.
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