Survival probability of a local excitation in a non-Markovian environment: Survival collapse, Zeno and anti-Zeno effects

ELENA RUFEIL FIORI; H. M. PASTAWSKI

PHYSICA B - CONDENSED MATTER

ELSEVIER SCIENCE BV

Lugar: Amsterdan; Año: 2009 vol. 404 p. 2812 - 2815

0921-4526

<!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US;} @page Section1 {size:612.0pt 792.0pt; margin:70.85pt 3.0cm 70.85pt 3.0cm; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> 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 distinct ive regimes for the dynamics. Sequentially: (i) early quadratic decay of the initial state survival probability, up to a spreading time tS, (ii) exponential decay described by a self consistent Fermi Golden Rule, and (iii) asymptotic behavior governed by quantum diffusion through the return processes, leading to aninverse power law decay. At this last cross-overtime tR a survival collapse becomes possible.This could reduce the survival probability by several orders of magnitude. The cross-overtimes tS and tR 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.