dorsal/arxiv
View SchemaGeometrical phases for the G(4,2) Grassmannian manifold
| Authors | Regina Karle, Jiannis Pachos |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0301140 |
| URL | https://arxiv.org/abs/quant-ph/0301140 |
| DOI | 10.1063/1.1572551 |
| Journal | J. Math. Phys. 44(6) 2463 (2003) |
Abstract
We generalize the usual abelian Berry phase generated for example in a system with two non-degenerate states to the case of a system with two doubly degenerate energy eigenspaces. The parametric manifold describing the space of states of the first case is formally given by the G(2,1) Grassmannian manifold, while for the generalized system it is given by the G(4,2) one. For the latter manifold which exhibits a much richer structure than its abelian counterpart we calculate the connection components, the field strength and the associated geometrical phases that evolve non-trivially both of the degenerate eigenspaces. A simple atomic model is proposed for their physical implementation.
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"abstract": "We generalize the usual abelian Berry phase generated for example in a system\nwith two non-degenerate states to the case of a system with two doubly\ndegenerate energy eigenspaces. The parametric manifold describing the space of\nstates of the first case is formally given by the G(2,1) Grassmannian manifold,\nwhile for the generalized system it is given by the G(4,2) one. For the latter\nmanifold which exhibits a much richer structure than its abelian counterpart we\ncalculate the connection components, the field strength and the associated\ngeometrical phases that evolve non-trivially both of the degenerate\neigenspaces. A simple atomic model is proposed for their physical\nimplementation.",
"arxiv_id": "quant-ph/0301140",
"authors": [
"Regina Karle",
"Jiannis Pachos"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1572551",
"journal_ref": "J. Math. Phys. 44(6) 2463 (2003)",
"title": "Geometrical phases for the G(4,2) Grassmannian manifold",
"url": "https://arxiv.org/abs/quant-ph/0301140"
},
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