  The decay dynamics of a local excitation interacting with a non-Markovian
environment, modeled by a semi-infinite tight-binding chain, is exactly
evaluated. We identify distinctive regimes for the dynamics. Sequentially: (i)
early quadratic decay of the initial-state survival probability, up to a
spreading time $t_{S}$, (ii) exponential decay described by a self-consistent
Fermi Golden Rule, and (iii) asymptotic behavior governed by quantum diffusion
through the return processes and leading to an inverse power law decay. At this
last cross-over time $t_{R}$ a survival collapse becomes possible. This could
reduce the survival probability by several orders of magnitude. The cross-overs
times $t_{S}$ and $t_{R}$ allow to assess the range of applicability of the
Fermi Golden Rule and give the conditions for the observation of the Zeno and
Anti-Zeno effect.
