Long time deviations from the exponential decay law: possible effects in particle physics and cosmology

TL;DR

This paper investigates how the long-time nonexponential decay behavior of unstable quantum states can lead to significant energy deviations, potentially impacting particle physics and cosmology.

Contribution

It introduces a model showing that the energy of unstable states tends to a minimal value over time and can exhibit large transient energies, suggesting new quantum effects with cosmological implications.

Findings

Instantaneous energy approaches minimal energy at long times.

Energy can be significantly larger during transition periods.

Potential relevance to broad resonances and cosmological phenomena.

Abstract

An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. We find that the instantaneous energy of the unstable state for a large class of models of unstable states tends to the minimal energy of the system ${\cal E}_{min}$ as $t\rightarrow\infty$ which is much smaller than the energy of this state for $t$ of the order of the lifetime of the considered state. Analyzing the transition time region between exponential and non-exponential form of the survival amplitude we find that the instantaneous energy of the considered unstable state can take large values, much larger than the energy of this state for $t$ from the exponential time region. Taking into account results obtained for a model considered, it is hypothesized that this purely quantum mechanical effect may be responsible for the properties of broad resonances such as $\sigma$ meson as well as having astrophysical and cosmological consequences.