  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.
