Systematic approach to define and classify quantum transmission and reflection times

Brouard, S.; Sala, R.; Muga, J. G.

doi:10.1103/physreva.49.4312

Cited by 119 publications

(98 citation statements)

References 37 publications

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“…Another type of limitation on the Hartman effect is that, for large enough barriers, the above-the-barrier components with momentum p > p b = (2mV 0 ) 1/2 , V 0 being the barrier energy, start to dominate, so that the time of passage becomes "classical" and depends again on the barrier width d. This has been discussed by various authors [15,34], first of all by Hartman himself [1], but we shall present a brief review for completeness in the following section, which also introduces the Hartman effect itself from a quantitative point of view [59]. Section III presents the known causality bounds and introduces the concepts and notation to establish the bound for the absence of bound states in Section IV.…”

Section: Introductionmentioning

confidence: 99%

“…Throughout the paper we shall assume that the barrier is located between −a and a, the barrier width being thus d = 2a. The average passage time at a may be defined as follows [34],…”

Section: The Hartman Effect and Its Large-barrier-width Limitationmentioning

confidence: 99%

“…For a minimum-uncertainty wave packet, the critical width d c separating the Hartman and classical regimes may be estimated by the formula [34,35] …”

Section: The Hartman Effect and Its Large-barrier-width Limitationmentioning

confidence: 99%

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Bounds and enhancements for negative scattering time delays

et al. 2002

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The time of passage of the transmitted wave packet in a tunneling collision of a quantum particle with a square potential barrier becomes independent of the barrier width in a range of barrier thickness. This is the Hartman effect, which has been frequently associated with "superluminality". A fundamental limitation on the effect is set by non-relativistic "causality conditions". We demonstrate first that the causality conditions impose more restrictive bounds on the negative time delays (time advancements) when no bound states are present. These restrictive bounds are in agreement with a naive, and generally false, causality argument based on the positivity of the "extrapolated phase time", one of the quantities proposed to characterize the duration of the barrier's traversal. Nevertheless, square wells may in fact lead to much larger advancements than square barriers. We point out that close to thresholds of new bound states the time advancement increases considerably, while, at the same time, the transmission probability is large, which facilitates the possible observation of the enhanced time advancement.

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Section: Introductionmentioning

confidence: 99%

“…Throughout the paper we shall assume that the barrier is located between −a and a, the barrier width being thus d = 2a. The average passage time at a may be defined as follows [34],…”

Section: The Hartman Effect and Its Large-barrier-width Limitationmentioning

confidence: 99%

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Bounds and enhancements for negative scattering time delays

et al. 2002

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“…The figures combine variously the different distributions, their components, and the flux for the three points, X = −2, 5, 12, corresponding to positions before, in, and after the barrier respectively. The evaluation of the integrals requires explicit representations of the states |p ± that can be found elsewhere [31]. Fig.…”

Section: Numerical Examplementioning

confidence: 99%

Time-of-arrival distributions for interaction potentials

2001

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Several proposals for a time-of-arrival distribution of ensembles of independent quantum particles subject to an external interaction potential are compared making use of the "crossing state" concept. It is shown that only one of them has the properties expected for a classical distribution in the classical limit. The comparison is illustrated numerically with a collision of a Gaussian wave packet with an opaque square barrier.

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“…Steinberg argues that the clock presents only a "weak measurement" and that therefore complex times are permitted [18]. In quantum mechanics the questions "how much time has the transmitted particle spent in a given interval" is problematic since being in an "interval" and "to be transmitted" corresponds to noncommuting operators [19]. Reasonably, we can only speak of a time duration, if it is real and positive.…”

Section: Introductionmentioning

confidence: 99%

The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics

Büttiker

Time in Quantum Mechanics

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Abstract. Starting from the Larmor clock we introduce a hierarchy of density of states. At the bottom of this hierarchy are the partial densities of states which represent the contribution to the local density of states if both the incident and the out-going scattering channel is prescribed. We discuss the role of the partial densities of states in a number of electrical conduction problems in phase coherent mesoscopic systems: The partial densities of states play a prominent role in measurements with a scanning tunneling microscope on multiprobe conductors in the presence of current flow. The partial densities of states determine the degree of dephasing generated by a weakly coupled voltage probe. We show that the partial densities of states determine the frequency-dependent response of mesoscopic conductors in the presence of slowly oscillating voltages applied to the contacts of the sample. We introduce the off-diagonal elements of the partial density of states matrix to describe fluctuation processes. These examples demonstrate that the analysis of the Larmor clock has a wide range of applications.

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Systematic approach to define and classify quantum transmission and reflection times

Cited by 119 publications

References 37 publications

Bounds and enhancements for negative scattering time delays

Bounds and enhancements for negative scattering time delays

Time-of-arrival distributions for interaction potentials

The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics

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