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28 March 2024
 
  » arxiv » quant-ph/0502168

 Article overview


Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators
Jeffrey C. Y. Teo ; Z. D. Wang ;
Date 25 Feb 2005
Subject quant-ph
AbstractThe theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection of a Stiefel U(N)-bundle over a Grassmann manifold. Most significantly, for an arbitrary initial state, this geometric phase captures the inherent geometric feature of the state evolution. Moreover, the geometric phase in the evolution of the eigenspace of an adiabatic action operator is also addressed, which is elaborated by a pullback U(N)-bundle. Several intriguing physical examples are illustrated.
Source arXiv, quant-ph/0502168
Other source [GID 644628] pmid16090857
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