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

Chaturvedi, S and Ercolessi, E and Marmo, G and Morandi, G and Mukunda, N and Simon, R (2007) Ray space 'Riccati' evolution and geometric phases for N-level quantum systems. In: Pramana- Journal of Physics, 69 (3). pp. 317-327.


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We present a simple derivation of the matrix Riccati equations governing the reduced dynamics as one descends from the group U(N) describing the Schr¨odinger evolution of an N-level quantum system to the various coset spaces and Grassmanian manifolds associated with it. The special case pertaining to the geometric phase in Nlevel 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.

Item Type: Journal Article
Publication: Pramana- Journal of Physics
Publisher: Indian Academy of Sciences
Additional Information: Copyright of this article belongs to Indian Academy of Sciences.
Keywords: Quantum dynamics;Riccati equations;geometric phase.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 18 Aug 2008
Last Modified: 19 Sep 2010 04:49
URI: http://eprints.iisc.ac.in/id/eprint/15626

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