Studying the Bell-Steinberger relation

Urbanowski, K.

doi:10.1140/epjc/s2004-01992-0

Cited by 10 publications

(41 citation statements)

References 24 publications

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“…However, positive-definiteness as it is used forΓ in Refs. [20,45] is not justified in general as a decaying quantum system can have non-decaying subspaces. For a positive semi-definite Hermitian form the Cauchy-Schwarz inequality holds, see, e.g., [46],…”

Section: A Derivation Of the Lee-wolfenstein Inequalitymentioning

confidence: 99%

Nonorthogonality constraints in open quantum and wave systems

Wiersig

2019

Phys. Rev. Research

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It is known that the overlap of two energy eigenstates in a decaying quantum system is bounded from above by a function of the energy detuning and the individual decay rates. This is usually traced back to the positive definiteness of an appropriately defined decay operator. Here, we show that the weaker and more realistic condition of positive semi-definiteness is sufficient. We prove also that the bound becomes an equality for the case of single-channel decay. However, we show that the condition of positive semi-definiteness can be spoiled by quantum backflow. Hence, the overlap of quasibound quantum states subjected to outgoing-wave conditions can be larger than expected from the bound. A modified and less stringent bound, however, can be introduced. For electromagnetic systems, it turns out that a modification of the bound is not necessary due to the linear free-space dispersion relation. Finally, a geometric interpretation of the nonorthogonality bound is given which reveals that in this context the complex energy space can seen as a surface of constant negative curvature.

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Section: A Derivation Of the Lee-wolfenstein Inequalitymentioning

confidence: 99%

Nonorthogonality constraints in open quantum and wave systems

Wiersig

2019

Phys. Rev. Research

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“…In the rest reference frame S 0 of the moving unstable quantum system, the survival amplitude at rest A 0 (t) is given by the following form, A 0 (t) = φ|e −ıHt |φ , where ı is the imaginary unit. The completeness of the eigenstates of the Hamiltonian leads to the following integral expression of the survival amplitude at rest [16,13,22,23,29],…”

Section: Moving Unstable Quantum Systems and Oscillating Decay Ratementioning

confidence: 99%

“…(32), of the survival probability transform according to the same scaling law, Eqs. (22) and (23) and Eqs. (41) and (42), respectively.…”

Section: Transformation Of Times and Relativistic Time Dilation In Dementioning

confidence: 99%

“…Recent analysis has shown that the long-time inverse-power-law decays at rest of moving unstable quantum systems transform in the laboratory reference frame, approximately, according to a scaling relation [21]. The scaling factor is determined by the (non-vanishing) lower bound of the mass spectrum and by the linear momentum, and consists in the ratio of the asymptotic value of the instantaneous mass and of the instantaneous mass at rest of the moving unstable quantum system [13,16,22,23,24,25]. The scaling relation reproduces, approximately, the relativistic dilation of times if the (non-vanishing) lower bound of the mass spectrum is considered to be the effective mass at rest of the moving unstable quantum system.…”

Section: Introductionmentioning

confidence: 99%

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

Giraldi

2019

Eur. Phys. J. D

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Decay laws of moving unstable quantum systems with oscillating decay rates are analyzed over intermediate times. The transformations of the decay laws at rest and of the intermediate times at rest, which are induced by the change of reference frame, are obtained by decomposing the modulus of the survival amplitude at rest into purely exponential and exponentially damped oscillating modes. The mass distribution density is considered to be approximately symmetric with respect to the mass of resonance. Under determined conditions, the modal decay widths at rest, Γ j , and the modal frequencies of oscillations at rest, Ω j , reduce regularly, Γ j /γ and Ω j /γ, in the laboratory reference frame. Consequently, the survival probability at rest, the intermediate times at rest and, if the oscillations are periodic, the period of the oscillations at rest transform regularly in the laboratory reference frame according to the same time scaling, over a determined time window. The time scaling reproduces the relativistic dilation of times if the mass of resonance is considered to be the effective mass at rest of the moving unstable quantum system with relativistic Lorentz factor γ.

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“…In literature, the MDD is usually represented by the Breit-Wigner form, which is a truncated Lorentzian function [10,5,13,23,15,17,18,24]. A more general form of MDDs is represented as the product of a function with a simple pole, a threshold factor and a form factor.…”

Section: Introductionmentioning

confidence: 99%

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

Giraldi¹

2019

J. Phys. A: Math. Theor.

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The transformation of canonical decay laws of moving unstable quantum systems is studied by approximating, over intermediate times, the decay laws at rest with superpositions of exponential modes via the Prony analysis. The survival probability P p (t), which is detected in the laboratory reference frame where the unstable system moves with constant linear momentum p, is represented by the transformed form P 0 (ϕ p (t)) of the survival probability at rest P 0 (t). The transformation of the intermediate times, which is induced by the change of reference frame, is obtained by evaluating the function ϕ p (t). Under determined conditions, this function grows linearly and the survival probability transforms, approximately, according to a scaling law over an estimated time window. The relativistic dilation of times holds, approximately, over the time window if the mass of resonance of the mass distribution density is considered to be the effective mass at rest of the moving unstable quantum system.

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Studying the Bell-Steinberger relation

Cited by 10 publications

References 24 publications

Nonorthogonality constraints in open quantum and wave systems

Nonorthogonality constraints in open quantum and wave systems

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

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

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