Geometric phase in eigenspace evolution of invariant and adiabatic action operators

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...

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Published inPhysical review letters Vol. 95; no. 5; p. 050406
Main Authors Teo, Jeffrey C Y, Wang, Z D
Format Journal Article
LanguageEnglish
Published United States 29.07.2005
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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.
AbstractList 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.
Author Teo, Jeffrey C Y
Wang, Z D
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BackLink https://www.ncbi.nlm.nih.gov/pubmed/16090857$$D View this record in MEDLINE/PubMed
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Snippet The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with N-fold degeneracy. The corresponding...
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Title Geometric phase in eigenspace evolution of invariant and adiabatic action operators
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