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arXiv · 0706.0964

Ray space Riccati evolution and geometric phases for N-level quantum systems

S. Chaturvedi·E. Ercolessi·G. Marmo·G. Morandi·N. Mukunda·R. Simon
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Abstract

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.

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S. Chaturvedi, E. Ercolessi, G. Marmo, G. Morandi, N. Mukunda, R. Simon. 2007-06-07. Ray space Riccati evolution and geometric phases for N-level quantum systems. https://doi.org/10.1007/s12043-007-0135-0

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