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Solid State Communications

Superluminal velocity, tunneling traversal time and causality

M. Ya. Azbel

Published Aug 1, 1994• 15 citations
Publisher
DOI
10.1016/0038-1098(94)90781-1

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Recent papers suggest that tunneling wave packets traverse the region of allowed propagation between two potential barriers with superluminal group velocity and in a time independent of barrier separation. This phenomenon has been termed the "generalized Hartman effect" and extended to multiple barriers. Here we show that this delay time is not a transit time but a cavity lifetime. It does not imply superluminal velocity. Reported experimental verifications of this effect are reinterpreted.
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.