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Geometric phase for mixed states: a differential geometric approach

Chaturvedi, S and Ercolessi, E and Marmo, G and Morandi, G and Mukunda, N and Simon, R (2004) Geometric phase for mixed states: a differential geometric approach. In: Europian Physical Journal C, 35 (3). pp. 413-423.

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A new definition and interpretation of the geometric phase for mixed state cyclic unitary evolution in quantum mechanics are presented. The pure state case is formulated in a framework involving three selected principal fiber bundles, and the well-known Kostant-Kirillov-Souriau symplectic structure on (co-) adjoint orbits associated with Lie groups. It is shown that this framework generalizes in a natural and simple manner to the mixed state case. For simplicity, only the case of rank two mixed state density matrices is considered in detail. The extensions of the ideas of null phase curves and Pancharatnam lifts from pure to mixed states are also presented.

Item Type: Journal Article
Publication: Europian Physical Journal C
Publisher: Springer-Verlag / Societ`a Italiana di Fisica
Additional Information: Copyright of this article belongs to Springer.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003)
Date Deposited: 19 Dec 2008 04:32
Last Modified: 19 Sep 2010 04:54
URI: http://eprints.iisc.ac.in/id/eprint/16997

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