Seeking non-exponential decay

Vladimir Zelevinsky, Alexander Volya

F. Miglietta, A. Rimini

Mark R. A. Shegelski, Rebecca A. Booth

We study the time dependence of a quantum particle initially localized'behind two delta-function barriers of strengths v 1 and v 2 . We determine the conditions under which the decay is exponential by varying the ratio v 1 /v 2 and the separation between the delta-barriers. We find that exponential decay occurs even when v 1 /v 2 is of order one. We also find cases of non-exponential decay. An interesting example of non-exponential decay is when the two barriers are very close. We show that the exponential decay is due to poles in the complex k-plane, where k denotes the wave numbers of the energy eigenstates, and we find that the decay rates are fully understood in many cases as being due to a single pole.

A. Steyerl, S. S. Malik

Murray Peshkin, Alexander Volya, Vladimir Zelevinsky

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.