Capturing non-exponential dynamics in the presence of two decay channels

TL;DR

This paper investigates non-exponential decay behaviors in quantum systems with two decay channels, demonstrating that while survival probabilities often follow exponential decay, certain ratios exhibit persistent oscillations indicating deviations.

Contribution

It introduces a quantum mechanical model of two-channel decay via tunneling, revealing observable oscillations that serve as signatures of non-exponential decay.

Findings

Survival probability closely follows exponential decay with small early deviations.

Ratios of decay probabilities and currents show persistent oscillations.

Oscillations serve as clear indicators of non-exponential decay behavior.

Abstract

The most unstable quantum states and elementary particles possess more than a single decay channel. At the same time, it is well known that typically the decay law is not simply exponential. Therefore, it is natural to ask how to spot the non-exponential decay when (at least) two decay channels are opened. In this work, we study the tunneling phenomenon of an initially localized particle in two spatially opposite directions through two different barriers, mimicking two decay channels. In this framework, through a specific quantum mechanical examples which can be accurately solved, we study general properties of a two-channel decay that apply for various unstable quantum states (among which also for unstable particles). Apart from small deviations at early times, the survival probability and the partial tunneling probability along the chosen direction are very well described by the exponential-decay model. In contrast, the ratios of the decay probabilities and probability currents are evidently not a simple constant (as they would be in the exponential limit) but display time-persisting oscillations. Hence, these ratios are optimal witnesses of deviations from the exponential decay law.