The true quantum face of the "exponential" decay law

TL;DR

This paper challenges the common belief about quantum decay laws by proving that the survival probability cannot be purely exponential and is inherently oscillatory, even during the supposed exponential decay regime.

Contribution

The paper provides a fundamental proof that quantum decay processes are always oscillatory and do not exhibit a purely exponential decay interval, revising the traditional three-regime decay model.

Findings

Decay law is inherently oscillatory during the exponential regime.

Purely exponential decay does not occur in quantum unstable systems.

Survival probability exhibits oscillations modulated by system parameters.

Abstract

Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature od the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, "exponential" (or "canonical") described by the decay law of the exponential form, and late time characterized by the decay law having inverse--power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the "exponential" regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.