Ray space Riccati evolution and geometric phases for N-level quantum systems - Quantum PhysicsReport as inadecuate




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Abstract: We present a simple derivation of the matrix Riccati equations governing thereduced dynamics as one descends from the group UN describing theSchroedinger evolution of an N-level quantum system to the various cosetspaces, Grassmanian manifolds, associated with it. The special case pertainingto the geometric phase in N-level systems is described in detail. Further, weshow how the matrix Riccati equation thus obtained can be reformulated as anequation describing Hamiltonian evolution in a classical phase space andestablish correspondences between the two descriptions.



Author: S. Chaturvedi, E. Ercolessi, G. Marmo, G. Morandi, N. Mukunda, R. Simon

Source: https://arxiv.org/







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