  We analyze, both analytically and numerically, the time-dependence of the
return probability in closed systems of interacting particles. Main attention
is paid to the interplay between two regimes, one of which is characterized by
the Gaussian decay of the return probability, and another one is the well known
regime of the exponential decay. Our analytical estimates are confirmed by the
numerical data obtained for two models with random interaction. In view of
these results, we also briefly discuss the dynamical model which was recently
proposed for the implementation of a quantum computation.
