Non-Markovian decay beyond the Fermi Golden Rule: Survival collapse of the polarization in spin chains

The decay of a local spin excitation in an inhomogeneous spin chain is evaluated exactly: (i) It starts quadratically up to a spreading time tS. (ii) It follows an exponential behavior governed by a self-consistent Fermi Golden Rule. (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 tR 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 an NMR experiment.