dorsal/arxiv
View SchemaGeometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators
| Authors | Jeffrey C. Y. Teo, Z. D. Wang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502168 |
| URL | https://arxiv.org/abs/quant-ph/0502168 |
| DOI | 10.1103/PhysRevLett.95.050406 |
| Journal | Phys. Rev. Lett. 95, 050406 (2005) |
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 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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"abstract": "The theory of geometric phase is generalized to a cyclic evolution of the\neigenspace of an invariant operator with $N$-fold degeneracy.\n The corresponding geometric phase is interpreted as a holonomy inherited from\nthe universal connection of a Stiefel U(N)-bundle over a Grassmann manifold.\nMost significantly, for an arbitrary initial state, this geometric phase\ncaptures the inherent geometric feature of the state evolution. Moreover, the\ngeometric phase in the evolution of the eigenspace of an adiabatic action\noperator is also addressed, which is elaborated by a pullback U(N)-bundle.\nSeveral intriguing physical examples are illustrated.",
"arxiv_id": "quant-ph/0502168",
"authors": [
"Jeffrey C. Y. Teo",
"Z. D. Wang"
],
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"quant-ph"
],
"doi": "10.1103/PhysRevLett.95.050406",
"journal_ref": "Phys. Rev. Lett. 95, 050406 (2005)",
"title": "Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators",
"url": "https://arxiv.org/abs/quant-ph/0502168"
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