N能级量子系统的光线空间Riccati演化和几何相位
Ray space Riccati evolution and geometric phases for N-level quantum systems
摘要：
我们给出了从描述N能级量子系统Schroedinger演化的群U（N）下降到各种陪集空间Grassmanian流形时控制约化动力学的矩阵Riccati方程的一个简单推导，并详细描述了N能级系统中几何相位的特殊情况.此外，我们展示了如何矩阵Riccati方程，从而获得可以重新表述为一个方程描述哈密顿演化在经典的相空间，并建立两个描述之间的对应关系。
英文摘要：
We present a simple derivation of the matrix Riccati equations governing the reduced dynamics as one descends from the group U(N) describing the Schroedinger evolution of an N-level quantum system to the various coset spaces, Grassmanian manifolds, associated with it. The special case pertaining to the geometric phase in N-level systems is described in detail. Further, we show how the matrix Riccati equation thus obtained can be reformulated as an equation describing Hamiltonian evolution in a classical phase space and establish correspondences between the two descriptions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
