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arXiv · 0812.1009

Survival Probability of a Local Excitation in a Non-Markovian Environment: Survival Collapse, Zeno and Anti-Zeno effects

E. Rufeil Fiori·H. M. Pastawski
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Abstract

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.

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E. Rufeil Fiori, H. M. Pastawski. 2009-03-20. Survival Probability of a Local Excitation in a Non-Markovian Environment: Survival Collapse, Zeno and Anti-Zeno effects. https://doi.org/10.1016/j.physb.2009.06.109

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