dorsal/arxiv
View SchemaBerry's phase for compact Lie groups
| Authors | E. Strahov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0011120 |
| URL | https://arxiv.org/abs/quant-ph/0011120 |
| DOI | 10.1063/1.1358879 |
Abstract
The Lie group adiabatic evolution determined by a Lie algebra parameter dependent Hamiltonian is considered. It is demonstrated that in the case when the parameter space of the Hamiltonian is a homogeneous K\"ahler manifold its fundamental K\"ahler potentials completely determine Berry geometrical phase factor. Explicit expressions for Berry vector potentials (Berry connections) and Berry curvatures are obtained using the complex parametrization of the Hamiltonian parameter space. A general approach is exemplified by the Lie algebra Hamiltonians corresponding to SU(2) and SU(3) evolution groups.
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"abstract": "The Lie group adiabatic evolution determined by a Lie algebra parameter\ndependent Hamiltonian is considered. It is demonstrated that in the case when\nthe parameter space of the Hamiltonian is a homogeneous K\\\"ahler manifold its\nfundamental K\\\"ahler potentials completely determine Berry geometrical phase\nfactor. Explicit expressions for Berry vector potentials (Berry connections)\nand Berry curvatures are obtained using the complex parametrization of the\nHamiltonian parameter space. A general approach is exemplified by the Lie\nalgebra Hamiltonians corresponding to SU(2) and SU(3) evolution groups.",
"arxiv_id": "quant-ph/0011120",
"authors": [
"E. Strahov"
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"quant-ph"
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"doi": "10.1063/1.1358879",
"title": "Berry\u0027s phase for compact Lie groups",
"url": "https://arxiv.org/abs/quant-ph/0011120"
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