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arXiv:quant-ph/0402210

Zeno era and non-decaying subspaces for multilevel Friedrichs model

Ioannis E. Antoniou, Evgueni Karpov, G. P. Pronko, E. A. Yarevsky

Published Feb 27, 2004• 0 citations
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Abstract

We study the short-time and medium-time behavior of the survival probability of decaying states in the framework of the $N$-level Friedrichs model. The degenerated and nearly degenerated systems are discussed in detail. We show that in these systems decay can be considerably slowed down or even stopped by appropriate choice of initial conditions. We analyze the behaviour of the multilevel system within the so-called Zeno era. We examine and compare two different definitions of the Zeno time. We demonstrate that the Zeno era can be considerably enlarged by proper choice of the system parameters.

DOI
10.48550/arxiv.quant-ph/0402210

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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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