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Long Time Behaviour of Unstable Multilevel Systems in Presence of Zero Energy Resonance

Author： Miyamoto Manabu

Publisher： Springer Publishing Company

ISSN： 1230-1612

Source： Open Systems and Information Dynamics, Vol.13, Iss.3, 2006-09, pp. : 291-300

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

Long time behaviour of the survival probability for unstable multilevel systems is studied based on the N-level Friedrichs model in the presence of zero energy resonance, that means the divergence of the resolvent at zero energy. With resort 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 form factors, logarithmically slower decay of the survival probability can be realized.

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