Resonant-state expansions and the long-time behavior of quantum decay

García–Calderón, Gastón; Maldonado, I. K. A. Romero; Villavicencio, Jorge

doi:10.1103/physreva.76.012103

Cited by 46 publications

(75 citation statements)

References 33 publications

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“…The characteristic feature of all these decay curves is the presence of sharp and frequent oscillations at the transition times region (see Figs (1), (2), (4), (5)) (see also, eg. [9], [15] - [20]). So derivatives of the amplitude ( ) a t may reach extremely large values for some times from the transition time region and the modulus of these derivatives is much larger than the modulus of ( ) a t , which is very small for these times.…”

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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Section: Discussion: Possible Hyphotetical Effectsmentioning

confidence: 99%

Late Time Behavior of Unstable Particles

Urbanowski¹,

Piskorski²

2012

JNPP

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“…More recently, a derivation of the t −3/2 behaviour for the wave function was reported in ref. 7. The derivation in ref.…”

Section: Introductionmentioning

confidence: 98%

“…Finally, the long-time probability of finding the particle inside the well is examined when bound states are included and we find that the long-time dependence is different. Bound states associated with the potential well were not explicitly considered in previous works [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

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Long-time behaviour of an initially localized quantum state

Shegelski¹,

Hnybida²

2008

Can. J. Phys.

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The long-time behaviour of an initially localized quantum state is shown to decay as t −3/2 for any potential well and any potential barrier. An example using a delta barrier is also calculated fully. The result is general yet the proof uses a simple method that is clear and accessible to a wide audience. The effect of bound states on the long-time behaviour is also considered. When there are bound states the long-time behaviour is different. PACS Nos.: 03.65.−w, 03.65.Xp Résumé : Nous montrons qu'un état quantique initialement localisé s'étale avec un comportement temporel asymptotique en t −3/2 pour tout potentiel et toute barrière. Nous faisons le calcul au complet pour la barrière en fonction delta. Les résultats sont généraux, mais la preuve utilise une méthode simple qui est claire et accessible à une vaste audience. Nous étudions l'effet des états liés sur le comportement asymptotique. La présence d'états liés affecte le comportement asymptotique.[Traduit par la Rédaction]

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“…It is not possible to follow the decay process numerically. Analytical expressions are then of the utmost importance [1,5,6]. The method and formulas presented here aim at contributing in this direction.…”

Section: Introductionmentioning

confidence: 99%

Assisted tunneling of a wave packet between square barriers

Kälbermann

2009

Phys. Rev. C

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The assisted tunneling of a wave packet between square one dimensional barriers is treated analytically. The survival probability is calculated exactly for a potential mimicking a constant electric field with arbitrary time dependence. The pole spectrum of the properly normalized unperturbed wavefunctions determines the decay time. The tunneling probability is enhanced by the perturbation. The results are exemplified for a simplified model of nuclear α decay.

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Resonant-state expansions and the long-time behavior of quantum decay

Cited by 46 publications

References 33 publications

Late Time Behavior of Unstable Particles

Late Time Behavior of Unstable Particles

Long-time behaviour of an initially localized quantum state

Assisted tunneling of a wave packet between square barriers

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