Tunneling time in nanostructures

Gasparian, V.; Ortuño, M.; Schön, Günter; Simon, Ulrich

doi:10.1016/b978-012513760-7/50027-7

Cited by 10 publications

(11 citation statements)

References 99 publications

(211 reference statements)

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“…A very natural (but, as it turns out, wrong) thing to do is to then take the length of the barrier L and divide by the delay time g τ to obtain a tunneling velocity / g g v L τ = . The result of this exercise suggests that the group velocity in tunneling can become arbitrarily large as the barrier length increases while the delay stays fixed [5,10,14]. Such a result is not just an artifact arising from the use of the nonrelativistic Schrodinger equation but is also present in the fully relativistic Dirac equation [19,26].…”

Section: Introductionmentioning

confidence: 91%

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The meaning of group delay in barrier tunnelling: a re-examination of superluminal group velocities

Winful¹

2006

New J. Phys.

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We show that the group delay in tunneling is not a traversal time but a lifetime of stored energy or stored probability escaping through both ends of the barrier. Because it is a lifetime associated with both forward (transmitted) and backward (reflected) fluxes, it cannot be used to define a group velocity for forward transit in cases where a wavepacket is mostly reflected. For photonic tunneling barriers the group delay is identical to the dwell time which is also a property of an entire wave function with reflected and transmitted components. Theoretical predictions and experimental reports of superluminal group velocities in barrier tunneling are re-interpreted.

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Section: Introductionmentioning

confidence: 91%

“…Equations (14) provide one way to distribute the dwell time between the reflection and transmission channels since it follows from the conservation law…”

Section: Group Delay Flux Delays and Dwell Timementioning

confidence: 99%

The meaning of group delay in barrier tunnelling: a re-examination of superluminal group velocities

Winful¹

2006

New J. Phys.

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“…There has been considerable interest on the question of time spent by a particle (interaction time) in a scattering region or in a given region of space [1,2,3]. This problem has been approached from many different points of view, but there is no clear consensus about a simple expression for this time as there is no hermitian operator associated with it (although experimentalists have claimed to measure it [1]).…”

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confidence: 99%

Wave attenuation to clock sojourn times

Benjamin

Jayannavar

2002

Solid State Communications

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The subject of time in quantum mechanics is of perennial interest especially because there is no observable for the time taken by a particle to transmit (or reflect) from a particular region. Several methods have been proposed based on scattering phase shifts and using different quantum clocks, where the time taken is clocked by some external input or indirectly from the phase of the scattering amplitudes. In this work we give a general method for calculating conditional sojourn times based on wave attenuation. In this approach clock mechanism does not couple to the Hamiltonian of the system. For simplicity, specific case of a delta dimer is considered in detail. Our analysis re-affirms recent results based on correcting quantum clocks using optical potential methods, albeit in a much simpler way.Comment: 4 pages, 5 figures. Minor corrections made and journal reference adde

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“…Without pretending to give an exhaustive review on the theory of the traversal time problem of electromagnetic waves, we just mention that two characteristic times have arisen in many approaches (see for example, Refs. [32,33] and references therein). These times are related as a consequence of the analytical properties of the complex quantity whose real and imaginary components are the two characteristic times.…”

Section: Alternating Right and Left-handed Materials: Layered Structuresmentioning

confidence: 99%

Faraday and Kerr Effects in Right and Left-Handed Films and Layered Materials

Lofy

Gasparian

Gevorkian

et al. 2020

Reviews on Advanced Materials Science

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AbstractIn the present work, we study the rotations of the polarization of light propagating in right and left-handed films and layered structures. Through the use of complex values representing the rotations we analyze the transmission (Faraday effect) and reflections (Kerr effect) of light. It is shown that the real and imaginary parts of the complex angle of Faraday and Kerr rotations are odd and even functions for the refractive index n, respectively. In the thin film case with left-handed materials there are large resonant enhancements of the reflected Kerr angle that could be obtained experimentally. In the magnetic clock approach, used in the tunneling time problem, two characteristic time components are related to the real and imaginary portions of the complex Faraday rotation angle . The complex angle at the different propagation regimes through a finite stack of alternating right and left-handed materials is analyzed in detail. We found that, in spite of the fact that Re(θ) in the forbidden gap is almost zero, the Im(θ) changes drastically in both value and sign.

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Tunneling time in nanostructures

Cited by 10 publications

References 99 publications

The meaning of group delay in barrier tunnelling: a re-examination of superluminal group velocities

The meaning of group delay in barrier tunnelling: a re-examination of superluminal group velocities

Wave attenuation to clock sojourn times

Faraday and Kerr Effects in Right and Left-Handed Films and Layered Materials

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