The decay of a local spin excitation in ail inhomogeneous spin chain is evaluated exactly: (i) It starts quadratically up to a spreading time t(S). (ii) It follows an exponential behavior governed by a self-consistent Fermi Golden Ride. (iii) At longer times, the exponential is overrun by an inverse power law describing return processes governed by quantum diffusion. At this last transition time t(R) a survival collapse becomes possible, bringing the polarization down by several orders of magnitude. We identify this strongly destructive interference as an antiresonance in the time domain. These general phenomena are suitable for observation through ail NMR experiment. (c) 2005 Elsevier B.V. All rights reserved.