dorsal/arxiv
View SchemaNon-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants
| Authors | Ali Mostafazadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9810064 |
| URL | https://arxiv.org/abs/quant-ph/9810064 |
| DOI | 10.1088/0305-4470/31/49/015 |
| Journal | J.Phys.A31:9975-9982,1998 |
Abstract
For a periodic Hamiltonian, periodic dynamical invariants may be used to obtain non-degenerate cyclic states. This observation is generalized to the degenerate cyclic states, and the relation between the periodic dynamical invariants and the Floquet decompositions of the time-evolution operator is elucidated. In particular, a necessary condition for the occurrence of cyclic non-adiabatic non-Abelian geometrical phase is derived. Degenerate cyclic states are obtained for a magnetic dipole interacting with a precessing magnetic field.
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"abstract": "For a periodic Hamiltonian, periodic dynamical invariants may be used to\nobtain non-degenerate cyclic states. This observation is generalized to the\ndegenerate cyclic states, and the relation between the periodic dynamical\ninvariants and the Floquet decompositions of the time-evolution operator is\nelucidated. In particular, a necessary condition for the occurrence of cyclic\nnon-adiabatic non-Abelian geometrical phase is derived. Degenerate cyclic\nstates are obtained for a magnetic dipole interacting with a precessing\nmagnetic field.",
"arxiv_id": "quant-ph/9810064",
"authors": [
"Ali Mostafazadeh"
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"quant-ph",
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"doi": "10.1088/0305-4470/31/49/015",
"journal_ref": "J.Phys.A31:9975-9982,1998",
"title": "Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants",
"url": "https://arxiv.org/abs/quant-ph/9810064"
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