Time-of-arrival probabilities and quantum measurements. III. Decay of unstable states

Anastopoulos, Charis

doi:10.1063/1.2839920

Cited by 23 publications

(24 citation statements)

References 31 publications

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“…4.3.2 is rather similar to the classic studies of α-decay by Gamow [41] and Gurney and Condon [42]-see also, Ref. [20].…”

Section: Discussionsupporting

confidence: 84%

“…Besides time-of-arrival probabilities, the method has been applied to the modeling of particle detectors in high-energy processes [13], and to the study of temporal correlations in accelerated detectors [18]. Earlier versions of QTP [19] have been employed in studies of non-relativistic tunneling times [7], non-exponential decays [20] and time-extended measurements [21].…”

Section: Our Approach To the Tunneling-time Problemmentioning

confidence: 99%

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Quantum temporal probabilities in tunneling systems

Anastopoulos

Savvidou

2013

Annals of Physics

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We study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal probabilities in tunneling systems that (i) defines 'classical' time observables for quantum systems and (ii) applies to relativistic particles interacting through quantum fields. We show that the relevant probabilities are defined in terms of specific correlations functions of the quantum field associated with tunneling particles. We construct a probability distribution with respect to the time of particle detection that contains all information about the temporal aspects of the tunneling process. In specific cases, this probability distribution leads to the definition of a delay time that, for parity-symmetric potentials, reduces to the phase time of Bohm and Wigner. We apply our results to piecewise constant potentials, by deriving the appropriate junction conditions on the points of discontinuity. For the double square potential, in particular, we demonstrate the existence of (at least) two physically relevant time parameters, the delay time and a decay rate that describes the escape of particles trapped in the inter-barrier region. Finally, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles. We demonstrate that the idea of faster-than-light speeds in tunneling follows from an inadmissible use of classical reasoning in the description of quantum systems.

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“…4.3.2 is rather similar to the classic studies of α-decay by Gamow [41] and Gurney and Condon [42]-see also, Ref. [20].…”

Section: Discussionsupporting

confidence: 84%

Section: Our Approach To the Tunneling-time Problemmentioning

confidence: 99%

Quantum temporal probabilities in tunneling systems

Anastopoulos

Savvidou

2013

Annals of Physics

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“…where • P (x, τ ; L, +) is the probability density that a particle was recorded at the first detector at time τ and then recorded at the second detector. P (x, τ, L, +) is the post-selected probability density (17).…”

Section: A Detection and Non-detection Events In The Joint Timeof-arrmentioning

confidence: 99%

“…(x, τ ) for a particle to be found at time τ in position x, provided that it was detected on the other side of the barrier at some later time. The probability density is [17] and to relativistic quantum measurements [14,18,19]. The key idea is to distinguish between the roles of time as a parameter to Schrödingers equation and as a label of the causal ordering of events [20,21].…”

Section: Introductionmentioning

confidence: 99%

Path of a tunneling particle

Anastopoulos

Savvidou

2017

Phys. Rev. A

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“…In the relativistic context [4,5], this distinction is mirrored into one between the parameters of spacetime translations and the spacetime coordinates associated to a measurement record. The QTP method has also been applied for the temporal characterization of tunneling [6] and non-exponential decays [7], and for calculating the response and correlations of particle detectors in non-inertial motion [8].…”

Section: Introductionmentioning

confidence: 99%

Measurements on relativistic quantum fields: I. Probability assignment

Anastopoulos¹,

Savvidou²

2015

Preprint

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We present a new method for describing quantum measurements in relativistic systems that applies (i) to any QFT and for any field-detector coupling, (ii) to the measurement of any observable, and (iii) to arbitrary size, shape and motion of the detector. We explicitly construct the probabilities associated to n measurement events, while treating the spacetime coordinates of the events are random variables. These probabilities define a linear functional of a 2n unequal time correlation function of the field, and thus, they are Poincaré covariant. The probability assignment depends on the properties of the measurement apparatuses, their state of motion, intrinsics dynamics, initial states and couplings to the measured field. For each apparatus, this information is contained in a function, the detector kernel, that enters into the probability assignment. In a companion paper, we construct the detector kernel for different types of measurement.

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Time-of-arrival probabilities and quantum measurements. III. Decay of unstable states

Cited by 23 publications

References 31 publications

Quantum temporal probabilities in tunneling systems

Quantum temporal probabilities in tunneling systems

Path of a tunneling particle

Measurements on relativistic quantum fields: I. Probability assignment

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