Relativistic Tunneling Through Two Successive Barriers

TL;DR

This paper investigates relativistic quantum tunneling through two barriers, demonstrating the emergence of the Generalized Hartman Effect and comparing relativistic and nonrelativistic results to understand tunneling times.

Contribution

It extends the study of tunneling times to the relativistic regime, showing the Hartman effect persists and analyzing its implications.

Findings

The Hartman effect appears in relativistic tunneling with opaque barriers.

Relativistic tunneling times can be independent of barrier width.

Comparison shows similarities and differences with nonrelativistic tunneling results.

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.