Survival Probability of a local excitation in a Non-Markovian environment: Survival Collapse, Zeno and Anti-Zeno effects

E. RUFEIL FIORI; H. M. PASTAWSKI

PHYSICA B - CONDENSED MATTER

Año: 2009

0921-4526

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 theFermi Golden Rule and give the conditions for the observation of the Zeno and Anti-Zeno effect.