Resonant spectra and the time evolution of the survival and nonescape probabilities.
The time evolution of quantum decay of an arbitrary state initially located within an interaction region of finite range is investigated. We compare the survival [ital S]([ital t]) and nonescape [ital P]([ital t]) probabilities. Our approach considers the full resonant spectra of the system using a novel representation of the time-dependent Green function. It is shown that, for an initial state near a resonance, [ital S]([ital t]) and [ital P]([ital t]) exhibit at long times a different behavior; not only the onset to a power law decay occurs at a different time, but also instead of the well known [ital S]([ital t])[similar to][ital t][sup [minus]3] we obtain [ital P]([ital t])[similar to][ital t][sup [minus]1].