**164**, 01032 (2017)

https://doi.org/10.1051/epjconf/201716401032

## The true quantum face of the “exponential” decay: Unstable systems in rest and in motion

University of Zielona Góra, Institute of Physics, ul. Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland

^{a} e-mail: K.Urbanowski@if.uz.zgora.pl;k.a.urbanowski@gmail.com

Published online: 5 December 2017

Results of theoretical studies and numerical calculations presented in the literature suggest that the survival probability *P*_{0}(*t*) has the exponential form starting from times much smaller than the lifetime *τ* up to times t ⪢*τ* and that *P*_{0}(*t*) exhibits inverse power–law behavior at the late time region for times longer than the so–called crossover time T ⪢ *τ* (The crossover time *T* is the time when the late time deviations of *P*_{0}(*t*) from the exponential form begin to dominate). More detailed analysis of the problem shows that in fact the survival probability *P*_{0}(*t*) can not take the pure exponential form at any time interval including times smaller than the lifetime *τ* or of the order of *τ* and it has has an oscillating form. We also study the survival probability of moving relativistic unstable particles with definite momentum . These studies show that late time deviations of the survival probability of these particles from the exponential–like form of the decay law, that is the transition times region between exponential–like and non-exponential form of the survival probability, should occur much earlier than it follows from the classical standard considerations.

*© The Authors, published by EDP Sciences, 2017*

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