No classical limit of quantum decay for broad states

Kelkar, N. G.; Nowakowski, M.

doi:10.1088/1751-8113/43/38/385308

Cited by 28 publications

(59 citation statements)

References 43 publications

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“…The simplest choice is to take α = 0, l = 0, F (E) = 1 and to assume that P (E) has a Breit-Wigner form. It turns out that the decay curves obtained in this simplest case are very similar in form to the curves calculated for the above described more general ω(E) (see [18] and analysis in [6]). So to find the most typical properties of the decay curve it is sufficient to make the relevant calculations for ω(E) modeled by the the Breit-Wigner distribution of the energy density.…”

Section: The Breit-wigner Modelsupporting

confidence: 75%

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True quantum face of the “exponential” decay law

Urbanowski

2017

Eur. Phys. J. D

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Abstract.Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature of the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, "exponential" (or "canonical") described by the decay law of the exponential form, and late time characterized by the decay law having inverse-power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the "exponential" regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.

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Section: The Breit-wigner Modelsupporting

confidence: 75%

“…where ω(E) ≥ 0 and a(0) = 1 (see also: [5,6,18,19]). From this relation and from the Riemann-Lebesgue lemma it follows that |a(t)| → 0 as t → ∞.…”

Section: Preliminariesmentioning

confidence: 99%

True quantum face of the “exponential” decay law

Urbanowski

2017

Eur. Phys. J. D

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“…It turns out that the decay curves obtained in the very large class of models are very similar in form to the curves calculated for ω(µ) having a Breit-Wigner form (see [23] and analysis in [6]). So to find the most typical properties of the decay curve it is sufficient to make the relevant calculations for ω(µ) modeled by the the Breit-Wigner distribution of the energy density ω BW (µ).…”

Section: The Breit-wigner Modelsupporting

confidence: 65%

“…So the amplitude a 0 (t), and thus the decay law P 0 (t) of the unstable state |ϕ⟩, are completely determined by the density of the mass (energy) distribution ω(µ) for the system in this state [22] (see also: [5,6,[23][24][25][26][27]. From (10) and from the Riemann-Lebesque lemma it follows that |a(t)| → 0 as t → ∞.…”

Section: Preliminariesmentioning

confidence: 99%

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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“…The problem with understanding the properties of broad resonances in the scalar sector ( σ meson problem [21]) discussed in [18,22] and recently in [23] where the hypothesis was formulated that this problem could be connected with the properties of the decay amplitude in the transition time region, seems to be possible manifestations of this effect and this problem refers to the first possibility mentioned above.…”

Section: Discussion: Possible Hyphotetical Effectsmentioning

confidence: 99%

Late Time Behavior of Unstable Particles

Urbanowski¹,

Piskorski²

2012

JNPP

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Possible consequences of non-exponential behavior of the survival amplitude of an unstable particle at very late times are considered. We describe a new quantum phenomenon: Analyzing the transition time region between exponential and post-exponential form of the survival amplitude we find that the instantaneous energy of the considered unstable state can take large values, much larger than the energy of this state for t from the exponential time region. We find also that the instantaneous energy of the unstable state tends to the minimal energy of the system min E as ∞ → t which is much smaller than the energy of this state for t of the order of the lifetime of the considered state. Taking into account the results obtained for the model considered, it is hypothesized that this purely quantum mechanical effect may be responsible for the properties of broad resonances such as σ meson as well as having astrophysical consequences.

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No classical limit of quantum decay for broad states

Cited by 28 publications

References 43 publications

True quantum face of the “exponential” decay law

True quantum face of the “exponential” decay law

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

Late Time Behavior of Unstable Particles

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