Classical picture of post-exponential decay

TL;DR

This paper demonstrates that the post-exponential decay behavior of a quantum particle can be effectively modeled by a classical ensemble with matching energy distribution and decay parameters, capturing the main decay features.

Contribution

It shows that classical particles with the same half-life and energy distribution can replicate quantum post-exponential decay, clarifying the classical-quantum correspondence in decay processes.

Findings

Classical ensemble reproduces quantum decay behavior accurately.

Interference oscillations are the main quantum feature not captured.

Classical model matches quantum decay at the ensemble level.

Abstract

Post-exponential 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 post-exponential 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 1D example is provided to illustrate the general argument.