Zero energy resonance and the logarithmically slow decay of unstable multilevel systems

Details Zero energy resonance and the logarithmically slow decay of unstable multilevel systems Zero energy resonance and the logarithmically slow decay of unstable multilevel systems

2006-09-22

arxiv.org/abs/quant-ph/0609177v2

J. Math. Phys. 47, 082103 (2006)

Physics

Quantum Physics

31 pages, no figures

Scientific paper

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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