Time delay in tunneling: Transmission and reflection time delays

Jaworski, Wojciech; Wardlaw, David M.

doi:10.1103/physreva.37.2843

Cited by 75 publications

(37 citation statements)

References 24 publications

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“…The presence of such terms was already pointed out in the case V ℓ = V r [23] and also in a more general situation [42].…”

Section: Discussionmentioning

confidence: 92%

“…As regards the timedependent approach, the existence of the Møller wave operators was established in [21], and a complete and detailed mathematical study of the questions (i)-(iii) mentioned before can be found in a paper by Davies and Simon [22]. As far as we know, time delay has been considered only for potentials for which V ℓ = V r , e.g., in [23]; of course this special situation is also covered by our results.…”

Section: Introductionmentioning

confidence: 99%

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Time delay for one-dimensional quantum systems with steplike potentials

Amrein

Jacquet

2007

Phys. Rev. A

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This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schrödinger Hamiltonian H = −∆ + V with a potential V (x) converging to different limits V ℓ and V r as x → −∞ and x → +∞ respectively. Due to the anisotropy they exhibit a two-channel structure. We first establish the existence and properties of the channel wave and scattering operators by using the modern Mourre approach. We then use scattering theory to show the identity of two apparently different representations of time delay. The first one is defined in terms of sojourn times while the second one is given by the Eisenbud-Wigner operator. The identity of these representations is well known for systems where V (x) vanishes as |x| → ∞ (V ℓ = V r ).We show that it remains true in the anisotropic case V ℓ = V r , i.e., we prove the existence of the time-dependent representation of time delay and its equality with the time-independent EisenbudWigner representation. Finally we use this identity to give a time-dependent interpretation of the Eisenbud-Wigner expression which is commonly used for time delay in the literature.

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“…The presence of such terms was already pointed out in the case V ℓ = V r [23] and also in a more general situation [42].…”

Section: Discussionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Time delay for one-dimensional quantum systems with steplike potentials

Amrein

Jacquet

2007

Phys. Rev. A

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“…The expression for the average of the dwell time for time-dependent scattering processes in terms of the probability densities corresponds (in sharp contrast to its second moment, as shown below) to the classical expression for an ensemble of classical particles and it reads [20,21] …”

Section: Introductionmentioning

confidence: 99%

Relation between quantum dwell times and flux-flux correlations

2009

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We examine the connection between the dwell time of a quantum particle in a region of space and flux-flux correlations at the boundaries. It is shown that the first and second moments of a flux-flux correlation function which generalizes a previous proposal by Pollak and Miller [E. Pollak and W. H. Miller, Phys. Rev. Lett. 53, 115 (1984)], agree with the corresponding moments of the dwell-time distribution, whereas the third and higher moments do not. We also discuss operational approaches and approximations to measure the flux-flux correlation function and thus the second moment of the dwell time, which is shown to be characteristically quantum, and larger than the corresponding classical moment even for freely moving particles.

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“…These problems have on one hand been treated axiomatically aiming at ideal quantities relying only on the system of interest, see, e.g., Refs. [2,3,4,5]. Other approaches may be called "operational" in the sense that a sort of "measurement device" is introduced to which the system of interest is coupled; see, e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

Passage-time distributions from a spin-boson detector model

2007

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The passage-time distribution for a spread-out quantum particle to traverse a specific region is calculated using a detailed quantum model for the detector involved. That model, developed and investigated in earlier works, is based on the detected particle's enhancement of the coupling between a collection of spins (in a metastable state) and their environment. We treat the continuum limit of the model, under the assumption of the Markov property, and calculate the particle state immediately after the first detection. An explicit example with 15 boson modes shows excellent agreement between the discrete model and the continuum limit. Analytical expressions for the passage-time distribution as well as numerical examples are presented. The precision of the measurement scheme is estimated and its optimization discussed. For slow particles, the precision goes like E −3/4 , which improves previous E −1 estimates, obtained with a quantum clock model.

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Time delay in tunneling: Transmission and reflection time delays

Cited by 75 publications

References 24 publications

Time delay for one-dimensional quantum systems with steplike potentials

Time delay for one-dimensional quantum systems with steplike potentials

Relation between quantum dwell times and flux-flux correlations

Passage-time distributions from a spin-boson detector model

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