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.

5 pages, 3 figures

References in corpus (4)

• Quantum Zeno dynamics: mathematical and physical aspects
• Hermitian and non-Hermitian formulations of the time evolution of quantum decay
• A quantum decay model with exact explicit analytical solution
• Bound Eigenstate dynamics under a sudden shift of the well's wall

Cited by in corpus (4)

• Nonexponential tunneling decay of a single ultracold atom
• Formal Aspects of Quantum Decay
• Influence of initial states on memory effects: A study of early-time superradiance
• Exact analytical non-Hermitian formulation of the time evolution of decay of one and two identical quantum particles