Nonclassical face of quantum decay processes

Abstract

A detailed analysis of the quantum decay processes shows the survival probability \U0001d4ab(t) can not take that exponential form at any time interval including times smaller than the lifetime τ. We show that for times t ∼ τ and for the times later than τ the form of \U0001d4ab(t) looks as a composition of an oscillating and exponential functions. The amplitude of these oscillations is very small for t ≪ τ and grows with increasing time and depends on the model considered. We also study the survival probability of moving relativistic unstable particles with definite momentum : It turns out that late time deviations of the survival probability of these particles from the exponential-like form of the decay law should occur much earlier than it follows from the classical standard approach resolving itself into replacing time t by t/γ (where γ is the relativistic Lorentz factor) in the formula for the survival probability \U0001d4ab(t).