Non-classical Behavior of Moving Relativistic Unstable Particles

Abstract

We study the survival probability of moving relativistic unstable particles with definite momentum p = 0. The amplitude of the survival probability of these particles is calculated using its integral representation. We found decay curves of such particles for the quantum mechanical models considered. These model studies show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-exponential form of the survival probability, 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 and that the survival probabilities should tend to zero as t → ∞ much slower than one would expect using classical time dilation relation. Here we show also that for some physically admissible models of unstable states the computed decay curves of the moving particles have fluctuating form at relatively short times including times of order of the lifetime.

Transformation of intermediate times in the decays of moving unstable quantum systems via the exponential modes

“…In summary, we have described the transformation of times in the decay laws of moving unstable quantum systems, which are induced by the change of reference frame, via relations (33)-(35), and we have found that, under determined conditions, the relativistic dilation of times, Eqs. (36) and (37), holds, approximately, over the time window (26), in the laboratory reference frame, and over the time window (38), in rest reference frame. These descriptions and properties constitute the last of the two main results of the paper.…”

“…For the sake of clarity, we describe below the decay laws in the laboratory frame S p , where the unstable system moves with constant linear momentum p, by following Ref. [36]. Let H be the Hilbert space of the quantum states of the unstable system.…”

“…In the rest reference frame S 0 of the unstable system, the survival amplitude A 0 (t) is referred to as the survival amplitude at rest and reads A 0 (t) = φ|e −ıHt |φ , where ı is the imaginary unit. By considering the completeness of the eigenstates of the Hamiltonian, the survival amplitude at rest is expressed via the following integral form [36,33,17,18,5],…”

Regularities in the transformation of the oscillating decay rate in moving unstable quantum systems

“…The description is performed by following Ref. [16]. Let the state kets |m, p belong to the Hilbert space H of the quantum states of the unstable system and be the common eigenstates of the linear momentum P and of the Hamiltonian H self-adjoint operator.…”

Time dilation in the oscillating decay laws of moving two-mass unstable quantum states

“…In the present notation, 0, m| and p, m| are the bras of the state kets |m, 0 and |m, p , respectively. In the rest reference frame of the unstable system the survival amplitude reads A 0 (t) = φ|e −ıHt |φ , where ı is the imaginary unit, and is given by the following integral expression [8,7,11,12,10],…”