Role of initial state reconstruction in short- and long-time deviations from exponential decay

We consider the role of the reconstruction of the initial state in the deviation from exponential decay at short and long times. The long-time decay can be attributed to a wave that was, in a classical-like, probabilistic sense, fully outside the initial state or the inner region at intermediate times, i.e., to a completely reconstructed state, whereas the decay during the exponential regime is due instead to a nonreconstructed wave. At short times, quantum interference between reconstructed and nonreconstructed paths is responsible for the deviation from the exponential decay. We may thus conclude that state reconstruction is a "consistent history" for long-time deviations but not for short ones.