dorsal/arxiv
View SchemaZero energy resonance and the logarithmically slow decay of unstable multilevel systems
| Authors | Manabu Miyamoto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609177 |
| URL | https://arxiv.org/abs/quant-ph/0609177 |
| DOI | 10.1063/1.2227260 |
| Journal | J. Math. Phys. 47, 082103 (2006) |
Abstract
The long time behavior of the reduced time evolution operator for unstable multilevel systems is studied based on the N-level Friedrichs model in the presence of a zero energy resonance.The latter means the divergence of the resolvent at zero energy. Resorting to the technique developed by Jensen and Kato [Duke Math. J. 46, 583 (1979)], the zero energy resonance of this model is characterized by the zero energy eigenstate that does not belong to the Hilbert space. It is then shown that for some kinds of the rational form factors the logarithmically slow decay of the reduced time evolution operator can be realized.
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"abstract": "The long time behavior of the reduced time evolution operator for unstable\nmultilevel systems is studied based on the N-level Friedrichs model in the\npresence of a zero energy resonance.The latter means the divergence of the\nresolvent at zero energy. Resorting to the technique developed by Jensen and\nKato [Duke Math. J. 46, 583 (1979)], the zero energy resonance of this model is\ncharacterized by the zero energy eigenstate that does not belong to the Hilbert\nspace. It is then shown that for some kinds of the rational form factors the\nlogarithmically slow decay of the reduced time evolution operator can be\nrealized.",
"arxiv_id": "quant-ph/0609177",
"authors": [
"Manabu Miyamoto"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2227260",
"journal_ref": "J. Math. Phys. 47, 082103 (2006)",
"title": "Zero energy resonance and the logarithmically slow decay of unstable multilevel systems",
"url": "https://arxiv.org/abs/quant-ph/0609177"
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