Analytical study of quadratic and non-quadratic short-time behavior of quantum decay

Abstract

The short-time behavior of quantum decay of an unstable state initially located within an interaction region of finite range is investigated using a resonant expansion of the survival amplitude. It is shown that in general the short-time behavior of the survival probability $S(t)$ has a dependence on the initial state and may behave either as $S(t)=1-\mathcal{O}(t^{3/2})$ or as $S(t)=1-\mathcal{O}(t^2)$. The above cases are illustrated by solvable models. The experiment reported in Ref. [1] does not distinguish between the above short-time behaviors.

arXiv comment5 pages, 3 figures

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Cited by in corpus (8)

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• Nonexponential tunneling decay of a single ultracold atom
• Formal Aspects of Quantum Decay
• The exponential-nonexponential transition in quantum decay as a phenomenon of interference in time domain of the decaying particle with itself
• Influence of initial states on memory effects: A study of early-time superradiance
• Decay properties of unstable Tonks-Girardeau gases from a split trap
• Exact analytical non-Hermitian formulation of the time evolution of decay of one and two identical quantum particles
• Inferring the smoothness of the autocorrelation function from that of the initial state