Time as a dynamical variable in quantum decay

TL;DR

This paper introduces a theoretical framework that treats time as a dynamical variable in quantum decay, linking decay rates to the wave function in the time domain and explaining observed oscillations as resonance interference.

Contribution

It presents a novel approach to quantum decay by using the time representation, providing new insights into decay oscillations and the relation between resonance lifetime and time of flight.

Findings

Recovery of exponential decay law for Gamow states

Interpretation of decay oscillations as resonance interference

Equivalence of resonance lifetime and time of flight

Abstract

We present a theoretical analysis of quantum decay in which the survival probability is replaced by a decay rate that is equal to the absolute value squared of the wave function in the time representation. The wave function in the time representation is simply the Fourier transform of the wave function in the energy representation, and it is also the probability amplitude generated by the Positive Operator Valued Measure of a time operator. The present analysis endows time with a dynamical character in quantum decay, and it is applicable only when the unstable system is monitored continuously while it decays. When the analysis is applied to the Gamow state, one recovers the exponential decay law. The analysis allows us to interpret the oscillations in the decay rate of the GSI anomaly, of neutral mesons, and of fluorescence quantum beats as the result of the interference of two resonances in the time representation. In addition, the analysis allows us to show that the time of flight of a resonance coincides with its lifetime.