Zero energy resonance and the logarithmically slow decay of unstable multilevel systems
Journal Article
·
· Journal of Mathematical Physics
- Department of Physics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan)
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 proportional to (log t){sup -1} of the reduced time evolution operator can be realized.
- OSTI ID:
- 20860754
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 47; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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