Multichannel decay law

TL;DR

This paper derives the general non-exponential decay probabilities for unstable quantum states across multiple channels, highlighting deviations from exponential decay that could be significant in quantum tunneling and particle physics.

Contribution

It provides the first comprehensive expression for multichannel decay probabilities applicable to both nonrelativistic and relativistic quantum states, revealing long-lasting deviations from exponential decay.

Findings

Partial decay probabilities are non-exponential.

Decay channel ratios are not constant over time.

Deviations from exponential decay can persist long enough to be experimentally relevant.

Abstract

It is well known, both theoretically and experimentally, that the survival probability for an unstable quantum state, formed at $t=0,$ is not a simple exponential function, even if the latter is a good approximation for intermediate times. Typically, unstable quantum states/particles can decay in more than a single decay channel. In this work, the general expression for the probability that an unstable state decays into a certain $i$-th channel between the initial time $t=0$ and an arbitrary $t>0$ is provided, both for nonrelativistic quantum states and for relativistic particles. These partial decay probabilities are also not exponential and their ratio turns out to be not a simple constant, as it would be in the exponential limit. Quite remarkably, these deviations may last relatively long, thus making them potentially interesting in applications. Thus, multichannel decays represent a promising and yet unexplored framework to search for deviations from the exponential decay law in quantum mechanical systems, such as quantum tunnelling, and in the context of particle decays.