Relativistic Tunneling Through Two Successive Barriers

Abstract

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 \emph{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.

7 pages, 3 figures. Revised version, with a new appendix added. Slightly changes in the styles and captions of Figures 1 and 2. To appear in Physical Review A

References in corpus (4)

• The meaning of group delay in barrier tunneling: A re-examination of superluminal group velocities
• Barrier Paradox in the Klein Zone
• Dirac Equation Studies in the Tunnelling Energy Zone
• Small Corrections to the Tunneling Phase Time Formulation

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• Superluminal tunneling times without superluminal signaling: Fading of the MacColl-Hartman effect at early times
• From a 1D completed scattering and double slit diffraction to the quantum-classical problem for isolated systems
• Perfect transmission of a Dirac particle in one-dimension double square barrier
• From a 1D completed scattering and double slit diffraction to the quantum-classical problem: A new approach