Decay law of relativistic particles: Quantum theory meets special relativity

Urbanowski, K.

doi:10.1016/j.physletb.2014.08.073

Cited by 32 publications

(98 citation statements)

References 31 publications

(78 reference statements)

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“…We also show that even in the case of a single component unstable system the decay curve has an oscillatory form with a smaller or a large amplitude of oscillations depending on the model considered. Next it will also be shown that the relativistic treatment of the problem within the Stefanovich-Shirokov theory [16,17] yields decay curves tending to zero as t → ∞ much slower than one would expect using classical time dilation relation which confirms and generalizes some conclusions drawn in [19]. Our results shows that conclusions relating to the quantum decay processes of moving particles based on the use of the classical physics time dilation relation need not be universally valid.…”

Section: Introductionsupporting

confidence: 80%

“…The above derivation of the expression for a p (t) is similar to that of [19]. It is based on [37] and it is reproduced here for the convenience of readers.…”

Section: Epj Web Of Conferencesmentioning

confidence: 99%

“…For the proper interpretation of many accelerator experiments with high energy unstable particles as well as of results of observations of astrophysical processes in which a huge numbers of elementary particles (including unstable one) are produced we should be sure that this belief is supported by theoretical analysis of quantum models of decay processes. The problem seems to be extremely important because from some theoretical studies it follows that in the case of quantum decay processes this relation is valid to a sufficient accuracy only for not more than a few lifetimes τ 0 = /Γ 0 [16][17][18][19]. On the other hand all known tests of the relation P p (t) = exp [− Γ 0 t γ ] were performed for times of the order of τ 0 (see, eg.…”

Section: Introductionmentioning

confidence: 99%

“…In these considerations the basis of such an analysis will be the formalism developed in [16,17] where within the quantum field theory the formula for the survival amplitude of moving particles was derived. We will follow the method used in [19] and we will analyze numerically properties survival probability for a model of the unstable particle based on the Breit-Wigner mass distribution and considered therein.…”

Section: Introductionmentioning

confidence: 99%

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

Urbanowski

2017

EPJ Web Conf.

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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.

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Section: Introductionsupporting

confidence: 80%

“…The above derivation of the expression for a p (t) is similar to that of [19]. It is based on [37] and it is reproduced here for the convenience of readers.…”

Section: Epj Web Of Conferencesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Urbanowski

2017

EPJ Web Conf.

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“…People are convinced that this equality being classical physics relation is valid also for any t in the case of quantum decay processes. The problem seems to be extremely important because from some theoretical studies it follows that in the case of quantum decay processes this relation is valid to a sufficient accuracy only for not more than a few lifetimes τ 0 = /Γ 0 [8,9,10]. All these problems require a deeper analysis, elements of which will be presented below.…”

Section: Introductionmentioning

confidence: 99%

Nonclassical face of quantum decay processes

Urbanowski

2017

J. Phys.: Conf. Ser.

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Abstract. A detailed analysis of the quantum decay processes shows the survival probability P(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 P(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 p = 0: 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 P(t). IntroductionSince the discovery of radioactivity and the formulation of the radioactive decay law by Rutheford and Sody [1] there is a conviction that the decay law has the exponential form, N (t) = N 0 exp [−λt], where λ > 0 is a constant, N (t) is the number of atoms of the radioactive element at the instant t ≥ 0 and N 0 = N (0). Wesisskopf-Wigner theory of spontaneous emission [2] has extended this belief on the quantum decay processes: They found that to a good approximation the quantum mechanical non-decay probability of the exited atomic levels is a decreasing function of time having exponential form. Further theoretical studies of the quantum decay process [3,4] showed that such processes seem to have three stages: the early time (initial), exponential (or "canonical"), and late time having inverse-power law form [5]. Results of these theoretical studies were the reason that there is rather widespread belief that a universal feature of the quantum decay process is the presence of these three time regimes. In this situation, each experimental evidence of oscillating decay curve at times of the order of life times is considered as an anomaly: The so-called GSI-anomaly [6,7] is an example. The question arises, if indeed in the case of one component quantum unstable systems such oscillations of the decay process at the "exponential" regime are an anomaly. The another question is: Whether and how such a possible oscillations depend on the motion of the unstable quantum system. So we need also to know how to describe the decay process of unstable quantum systems in motion.Studying text books one finds that if the decay law of the unstable particle in rest has the following form P(t) = exp [− Γ 0 t ] ≡ P c (t), then in the case of the moving particle with

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Quantum decay in renormalizable field theories: Quasiparticle formation, Zeno and anti-Zeno effects

Boyanovsky

2019

Annals of Physics

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In a renormalizable theory the survival probability of an unstable quantum state features divergences as a consequence of the rapid growth of the density of states with energy. Introducing a high energy cutoff Λ, the transient dynamics during a time scale ≃ 1/Λ describes the renormalization of the bare into a "quasiparticle" state which decays on longer time scales. During this early transient the decay law features Zeno behavior e −(t/tZ ) 2 with the Zeno time-scale t Z ∝ 1/Λ 3/2 . We introduce a dynamical renormalization framework that allows to separate consistently the dynamics of formation of the quasiparticle state and its decay on longer time scales by introducing a renormalization time scale along with alternative "schemes". The survival probability obeys a renormalization group equation with respect to this scale. We find a transient suppression of the decay law for large Lorentz factor as a consequence of the narrowing of the phase space for decay different from the usual time dilation. In presence of higher mass thresholds, the energy uncertainty associated with transient dynamics leads to an anti Zeno enhancement with a transient acceleration of the decay into heavier particles. There remains memory of the transient effects in the survival probability even at long time. We discuss possible consequences of these effects in cosmology.

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Decay law of relativistic particles: Quantum theory meets special relativity

Cited by 32 publications

References 31 publications

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

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

Nonclassical face of quantum decay processes

Quantum decay in renormalizable field theories: Quasiparticle formation, Zeno and anti-Zeno effects

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