Delay time computation for relativistic tunneling particles

TL;DR

This paper investigates relativistic tunneling times and transmission probabilities for particles described by the Dirac and Klein-Gordon equations, revealing conditions for accelerated tunneling and overcoming analytical challenges.

Contribution

It provides analytical solutions for relativistic tunneling times and transmission probabilities, including conditions for accelerated tunneling, addressing previous methodological difficulties.

Findings

Identification of conditions for accelerated tunneling

Analytical solutions for phase and dwell times

Overcoming stationary phase method limitations

Abstract

We study the tunneling zone solutions of a one-dimensional electrostatic potential for the relativistic (Dirac to Klein-Gordon) wave equation when the incoming wave packet exhibits the possibility of being almost totally transmitted through the barrier. The transmission probabilities, the phase times and the dwell times for the proposed relativistic dynamics are obtained and the conditions for the occurrence of accelerated tunneling transmission are all quantified. We show that, in some limiting cases, the analytical difficulties that arise when the stationary phase method is employed for obtaining phase (traversal) tunneling times are all overcome. Lessons concerning the phenomenology of the relativistic tunneling suggest revealing insights into condensed-matter experiments using electrostatic barriers for which the accelerated tunneling effect can be observed.