2013
DOI: 10.1016/j.aop.2013.06.003
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Quantum temporal probabilities in tunneling systems

Abstract: 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… Show more

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Cited by 14 publications
(23 citation statements)
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“…where γ = λa quantifies the opacity of the barrier and = (i) Since β k (a) = 0, a detector placed at the barrier's exit, records τ 1 = t ph (k 0 ) for all values of γ and . This is compatible with the idea that the phase time is the time it takes for a particle to cross the barrier, at least as far as time-of-arrival measurements are concerned [1].…”
Section: Tunnelling In the Square Barriersupporting
confidence: 79%
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“…where γ = λa quantifies the opacity of the barrier and = (i) Since β k (a) = 0, a detector placed at the barrier's exit, records τ 1 = t ph (k 0 ) for all values of γ and . This is compatible with the idea that the phase time is the time it takes for a particle to cross the barrier, at least as far as time-of-arrival measurements are concerned [1].…”
Section: Tunnelling In the Square Barriersupporting
confidence: 79%
“…This apparent superluminality is an artifact of the chain of approximations involved in deriving (45), and, in particular, the consideration of non-relativistic particles. The probability densities in the QTP method are obtained from the correlation functions of a local relativistic quantum field theory that fully respect causal propagation of signals [1].…”
Section: Tunnelling In the Square Barriermentioning
confidence: 99%
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“…For a derivation, see Refs. [14,16,21], and also the appendix. This construction originates from the treatment of spacetime coarse-grainings in the decoherent histories approach to quantum mechanics [28,33].…”
Section: The Qtp Probability Formulamentioning
confidence: 99%
“…In recent years, we developed a new method [6][7][8][9] for describing QFT measurements that shares the above property with Glauber's theory. We call this method the Quantum Temporal Probabilities (QTP) method, as its original motivation was to provide a general framework for temporally extended quantum observables [26][27][28].…”
Section: Multi-time Measurements In Qftmentioning
confidence: 99%