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

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

2007-06-07

arxiv.org/abs/0706.0964v1

Pramana69:317-328,2007

Physics

Quantum Physics

14 pages

Scientific paper

10.1007/s12043-007-0135-0

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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