dorsal/arxiv
View SchemaBerry's phases and topological properties in the Born-Oppenheimer approximation
| Authors | Kazuo Fujikawa |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510049 |
| URL | https://arxiv.org/abs/quant-ph/0510049 |
| DOI | 10.1142/9789812773210_0062 |
Abstract
The level crossing problem is neatly formulated by the second quantized formulation, which exhibits a hidden local gauge symmetry. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial (and thus no monopole singularity) for arbitrarily large but finite time interval $T$. The topological proof of the Longuet-Higgins' phase-change rule, for example, thus fails in the practical Born-Oppenheimer approximation where $T$ is identified with the period of the slower system. The crucial difference between the Aharonov-Bohm phase and the geometric phase is explained. It is also noted that the gauge symmetries involved in the adiabatic and non-adiabatic geometric phases are quite different.
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"abstract": "The level crossing problem is neatly formulated by the second quantized\nformulation, which exhibits a hidden local gauge symmetry. The analysis of\ngeometric phases is reduced to a simple diagonalization of the Hamiltonian. If\none diagonalizes the geometric terms in the infinitesimal neighborhood of level\ncrossing, the geometric phases become trivial (and thus no monopole\nsingularity) for arbitrarily large but finite time interval $T$. The\ntopological proof of the Longuet-Higgins\u0027 phase-change rule, for example, thus\nfails in the practical Born-Oppenheimer approximation where $T$ is identified\nwith the period of the slower system. The crucial difference between the\nAharonov-Bohm phase and the geometric phase is explained. It is also noted that\nthe gauge symmetries involved in the adiabatic and non-adiabatic geometric\nphases are quite different.",
"arxiv_id": "quant-ph/0510049",
"authors": [
"Kazuo Fujikawa"
],
"categories": [
"quant-ph"
],
"doi": "10.1142/9789812773210_0062",
"title": "Berry\u0027s phases and topological properties in the Born-Oppenheimer approximation",
"url": "https://arxiv.org/abs/quant-ph/0510049"
},
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