Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators

Details Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators

2005-02-25

arxiv.org/abs/quant-ph/0502168v2

Phys. Rev. Lett. 95, 050406 (2005)

Physics

Quantum Physics

Added Refs. and corrected typos; 4 pages

Scientific paper

10.1103/PhysRevLett.95.050406

The 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.

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