Geometry of mixed states and degeneracy structure of geometric phases for multi-level quantum systems: a unitary group approach

Ercolessi, E and Marmo, G and Morandi, G and Mukunda, N (2001) Geometry of mixed states and degeneracy structure of geometric phases for multi-level quantum systems: a unitary group approach. In: International Journal of Modern Physics A, 16 (31). 5007 -5032.

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Abstract

We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same methods in the case of SU(3) we study the effect of degeneracies on geometric phases for three-level systems. This is shown to lead to a highly nontrivial generalization of the result for two-level systems in which degeneracy results in a "monopole" structure in parameter space. The rich structures that arise are related to the geometry of adjoint orbits in SU(3). The limiting case of a two-level degeneracy in a three-level system is shown to lead to the known monopole structure.

Item Type:	Journal Article
Publication:	International Journal of Modern Physics A
Publisher:	World Scientific Publishing Company
Additional Information:	Copyright of this article belongs to World Scientific Publishing Company
Keywords:	02.20; 03.65
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003) Division of Physical & Mathematical Sciences > Physics
Date Deposited:	12 Nov 2007
Last Modified:	19 Sep 2010 04:41
URI:	http://eprints.iisc.ac.in/id/eprint/12417

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