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1 Computational Methods in Science and Technology

1 2010

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Long Time Deviations from the Exponential Decay Law: Possible Observational Effects

Urbanowski K., Piskorski J.

Computational Methods in Science and Technology

2010

Vol. 16, No. 2

201-205

An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. We find that the instantaneous energy of the unstable state for a large class of models of unstable states tends to the minimal energy of the system epsilon min as t rightwards arrow infinity which is much smaller than the energy of this state for t of the order of the lifetime of the considered state. Analyzing the transition time region between the exponential and non-exponential form of the survival amplitude, we find that the instantaneous energy of the considered unstable state can take large values, much larger than the energy of this state for t from the exponential time region. Taking into account results obtained for a considered model, it is hypothesized that this purely quantum mechanical effect may be responsible for the properties of broad resonances such as sigma meson as well as having astrophysical and cosmological consequences.