title: Geometric phase in eigenspace evolution of invariant and adiabatic action operators.
abstract: 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 Stiefel U(N) bundle over a Grassmann manifold. Most significantly, for an arbitrary initial state, this holonomy captures the inherent geometric feature of the state evolution that may not be cyclic. Moreover, a rigorous theory of geometric phase in the evolution of the eigenspace of an adiabatic action operator is also formulated, with the corresponding holonomy being elaborated by a pullback U(N) bundle.
authors.affiliation: Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China.
authors.forename: Jeffrey C Y
authors.initials: JC
authors.lastname: Teo
authors.forename: Z D
authors.initials: ZD
authors.lastname: Wang