# Non-exponential and oscillatory decays in quantum mechanics

## TL;DR

This paper revisits quantum decay processes, demonstrating non-exponential decay at all times, and explores oscillatory decay behaviors through numerical models, with implications for understanding experimental oscillations.

## Contribution

It introduces a more physical definition of decay rate, showing non-exponential decay in quantum systems and revealing conditions for oscillatory decay patterns.

## Key findings

- Decay is non-exponential at short and long times.
- Oscillations can occur in decay curves under certain conditions.
- The results have implications for interpreting GSI oscillation experiments.

## Abstract

The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.