Classical picture of postexponential decay

Abstract

Postexponential decay of the probability density of a quantum particle leaving a trap can be reproduced accurately, except for interference oscillations at the transition to the postexponential regime, by means of an ensemble of classical particles emitted with constant probability per unit time and the same half-life as the quantum system. The energy distribution of the ensemble is chosen to be identical to the quantum distribution, and the classical point source is located at the scattering length of the corresponding quantum system. A one-dimensional example is provided to illustrate the general argument.