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 $S\left(t\right)\mathrm{}$ and nonescape $P\left(t\right)\mathrm{}$ 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, $S\left(t\right)\mathrm{}$ and $P\left(t\right)\mathrm{}$ 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 $S\left(t\right)\mathrm{}\sim t^{-3\mathrm{}}$ we obtain $P\left(t\right)\mathrm{}\sim t^{-1\mathrm{}}$.

• Received 12 May 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.337