Quantum probabilities for time-extended alternatives

Anastopoulos, Charis; Savvidou, Ntina

doi:10.1063/1.2713078

Cited by 12 publications

(8 citation statements)

References 31 publications

(33 reference statements)

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“…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%

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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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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“…Path integral constructions have for many years played an important role in quantum cosmology and quantum gravity [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. They have also been particularly useful in addressing issues concerning time in nonrelativistic quantum mechanics, for example in studies of the arrival time [23][24][25][26][27][28][29][30][31][32][33][34], dwell time and tunneling time [35][36][37][38][39]. Path integrals are also useful ways of formulating continuous quantum measurement theory [40,41] Many of these applications of path integrals are in the specific framework of the decoherent histories approach to quantum theory [43][44][45][46][47][48][49][50]…”

Section: Introductionmentioning

confidence: 99%

Pitfalls of path integrals: Amplitudes for spacetime regions and the quantum Zeno effect

Halliwell

Yearsley

2012

Phys. Rev. D

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Path integrals appear to offer natural and intuitively appealing methods for defining quantummechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time interval is typically defined by summing over all paths between given initial and final points but restricting them to pass through the region at any time.We argue that there is, however, under very general conditions, a significant complication in such constructions. This is the fact that the concrete implementation of the restrictions on paths over an interval of time corresponds, in an operator language, to sharp monitoring at every moment of time in the given time interval. Such processes suffer from the quantum Zeno effect -the continual monitoring of a quantum system in a Hilbert subspace prevents its state from leaving that subspace.As a consequence, path integral amplitudes defined in this seemingly obvious way have physically and intuitively unreasonable properties and in particular, no sensible classical limit. In this paper we describe this frequently-occurring but little-appreciated phenomenon in some detail, showing clearly the connection with the quantum Zeno effect. We then show that it may be avoided by implementing the restriction on paths in the path integral in a "softer" way. The resulting amplitudes then involve a new coarse graining parameter, which may be taken to be a timescale ǫ, describing the softening of the restrictions on the paths. We argue that the complications arising from the Zeno effect are then negligible as long as ǫ ≫ 1/E, where E is the energy scale of the incoming state.

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“…The decoherence functional contains sufficient information for the construction of POVMs for the probabilities of measurement outcomes for magnitudes that have an explicit time-dependence. In particular, the probabilities for the measurement outcomes for single-time, sequential and extended-in-time measurements (obtained through the standard formalism) can be identified with suitable diagonal elements of the decoherence functional-see [24,25]. In other words, one can define POVMs by suitable smearing of the decoherence functional and in the cases above, these POVMs coincide with ones obtained from the standard methods in quantum measurement theory.…”

Section: Construction Of the Povmmentioning

confidence: 98%

“…The decoherence functional contains sufficient information for the construction of POVMs for measurements that involve variables that refer to more than one instant of time. This has been established for sequential measurements [24] and for time-extended measurements [25]. In these cases one can compare the results to ones obtained from single-time quantum mechanics, but for the time-of-arrival, there is no analogous construction without the use of histories.…”

Section: Our Approachmentioning

confidence: 99%