ISSN:
1434-6036
Keywords:
PACS. 73.40.Gk Tunneling - 03.65.Bz Foundations, theory of measurement, miscellaneous theories (including Aharonov Bohm effect, Bell inequalities, Berry's phase) - 05.60.Gg Quantum transport
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract: This paper is concerned with the transmission time of an incident Gaussian wave packet through a symmetric rectangular barrier. Following Hartman (J. Appl. Phys. 33, 3427 (1962)), the transmission time is usually taken as the difference between the time at which the peak of the transmitted packet leaves the barrier of thickness and the time at which the peak of the incident Gaussian wave packet arrives at the barrier. This yields a corresponding transmission velocity which appears under certain conditions as a supervelocity, i.e. becomes larger than the corresponding propagation velocity in free space which is the group velocity for electrons or the velocity of light for photons, respectively. By analysing the propagation of a broadband wave packet (which leads in free space to an extremely concentrated wave packet at a certain time) we obtain the pulse response function of the barrier and show that the insertion of the barrier is physically unable to produce a supervelocity. Therefore, the peak of an incident Gaussian wave packet and the peak of the transmitted wave packet are in no causal relationship. The shape of the transmitted wave packet is produced from the incident wave by convolution with the pulse response of the barrier. This yields a distortion of the shape of the wave packet which includes also the observed negative time shift of the peak. We demonstrate further that the phenomenon of Hartman's supervelocities is not restricted to barriers with their exponentially decaying fields but occurs for instance also in transmission lines with an inserted LCR circuit.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s100510050988
