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

TL;DR

This paper provides an exact analysis of the decay dynamics of a local excitation in a non-Markovian environment, revealing regimes like quadratic, exponential, and power-law decay, and discusses conditions for Zeno and Anti-Zeno effects.

Contribution

It offers a detailed, exact evaluation of decay regimes and identifies conditions for survival collapse, Zeno, and Anti-Zeno effects in a non-Markovian environment.

Findings

Identification of quadratic, exponential, and power-law decay regimes.

Conditions for survival collapse reducing survival probability significantly.

Assessment of the applicability of the Fermi Golden Rule and Zeno effects.

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.