Volume 107, Number 4, August 2014
|Number of page(s)||7|
|Published online||12 August 2014|
Non-exponential and oscillatory decays in quantum mechanics
1 Argonne National Laboratory, Physics Division - Argonne, IL 60439, USA
2 Florida State University, Physics Department - Tallahassee, FL 32306, USA
3 National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University - East Lansing, MI 48824, USA
Received: 19 June 2014
Accepted: 21 July 2014
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.
PACS: 03.65.Xp – Tunneling, traversal time, quantum Zeno dynamics
© EPLA, 2014
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