Survival probability of surface excitations in a 2d lattice: Non-Markovian effects and survival collapse

Abstract

The evolution of a surface excitation in a two dimentional model is analyzed. 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 survival probability down by several orders of magnitude. We identify this strongly destructive interference as an antiresonance in the time domain.