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

Abstract

Abstract.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 ⃗ p 0. 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.