Arvind, * and Mallesh, KS and Mukunda, N (1997) A generalized Pancharatnam geometric phase formula for threelevel quantum systems. In: Journal of Physics A: Mathematical and General, 30 (7). 24172431.

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Abstract
We describe a recently developed generalization of the PoincarĂ© sphere method, to represent pure states of a threelevel quantum system in a convenient geometrical manner. The construction depends on the properties of the group SU(3) and its generators in the defining representation, and uses geometrical objects and operations in an eightdimensional real Euclidean space. This construction is then used to develop a generalization of the well known Pancharatnam geometric phase formula, for evolution of a threelevel system along a geodesic triangle in state space.
Item Type:  Journal Article 

Publication:  Journal of Physics A: Mathematical and General 
Publisher:  Institute of Physics 
Additional Information:  The copyright of this article belongs to Institute of Physics 
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:  16 Aug 2004 
Last Modified:  19 Sep 2010 04:13 
URI:  http://eprints.iisc.ac.in/id/eprint/937 
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