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Annalen der Physik

Traversal time for Dirac particles through a potential barrier

C‐F. Li, Xi Chen

Published Dec 1, 2002• 1 citation
Publisher

Abstract

Abstract A traversal time that has no problem of superluminality was advanced for particles to tunnel through potential barriers in the non‐relativistic quantum theory in a previous paper by C.‐F. Li and Q. Wang, Physica B 296 (2001) 356. This time is generalized in this paper to Dirac's relativistic quantum theory. Both evanescent and propagating cases are considered. It is shown that the traversal time in the evanescent case has much the same properties as in the non‐relativistic quantum theory and thus has no problem of superluminality. It also gets rid of the problem of superluminality in the propagating case. Comparisons with the dwell time, the group delay, and the velocity of monochromatic front are also made.

DOI
10.1002/andp.20025141204

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Abstract A traversal time that has no problem of superluminality was advanced for particles to tunnel through potential barriers in the non‐relativistic quantum theory in a previous paper by C.‐F. Li and Q. Wang, Physica B 296 (2001) 356. This time is generalized in this paper to Dirac's relativistic quantum theory. Both evanescent and propagating cases are considered. It is shown that the traversal time in the evanescent case has much the same properties as in the non‐relativistic quantum theory and thus has no problem of superluminality. It also gets rid of the problem of superluminality in the propagating case. Comparisons with the dwell time, the group delay, and the velocity of monochromatic front are also made.
A traversal time that has no problem of superluminality was advanced for particles to tunnel through potential barriers in the non-relativistic quantum theory in a previous paper by C.-F. Li and Q. Wang, Physica B 296 (2001) 356. This time is generalized in this paper to Dirac's relativistic quantum theory. Both evanescent and propagating cases are considered. It is shown that the traversal time in the evanescent case has much the same properties as in the non-relativistic quantum theory and thus has no problem of superluminality. It also gets rid of the problem of superluminality in the propagating case. Comparisons with the dwell time, the group delay, and the velocity of monochromatic front are also made.
We study the relativistic quantum mechanical problem of a Dirac particle tunneling through two successive electrostatic barriers. Our aim is to study the emergence of the so-called generalized Hartman effect, an effect observed in the context of nonrelativistic tunneling as well as in its electromagnetic counterparts and which is often associated with the possibility of superluminal velocities in the tunneling process. We discuss the behavior of both the phase (or group) tunneling time and the dwell time, and show that in the limit of opaque barriers the relativistic theory also allows the emergence of the generalized Hartman effect. We compare our results with the nonrelativistic ones and discuss their interpretation.
Abstract Starting out with the dwell time approach by Smith for stationary one‐dimensional tunneling problems, we introduce the notion of the minimum tunneling time required for traversal through an arbitrary potential barrier. The newly devised time scale is based on a simple variational principle and presents a strictly local quantity not depending on the asymptotics of the potential distribution. Its properties are illustrated using the customary square barrier as an example. The minimum tunneling time approach cannot support the existence of superluminal velocities in barrier penetration.
The tunneling of particles is in direct analogy with the transmission of evanescent electromagnetic waveguide modes as has been shown quite recently. We compare experimental data of an electromagnetic wave packet traversing an evanescent waveguide region with theoretical values derived for particle tunneling through a rectangular potential barrier. The transmission time was deduced by transformation of the experimental frequency data to the time domain. The data are in agreement and reveal superluminal wave-packet velocities for opaque evanescent regions.