A New Phase Time Formula for Opaque Barrier Tunneling

TL;DR

This paper introduces a new phase time formula for opaque barrier tunneling, providing an alternative calculation method that aligns well with numerical simulations and reveals a proportional relationship between transit time and barrier width for certain wave packets.

Contribution

It proposes a novel phase time formula for opaque tunneling barriers, improving accuracy and understanding of tunneling dynamics near the barrier height.

Findings

New phase time formula agrees with numerical simulations

Transit time proportional to barrier width near barrier height

Alternative method improves tunneling time calculations

Abstract

After a brief review of the derivation of the standard phase time formula, based on the use of the stationary phase method, we propose, in the opaque limit, an alternative method to calculate the phase time. The new formula for the phase time is in excellent agreement with the numerical simulations and shows that for wave packets whose upper limit of the momentum distribution is very close to the barrier height, the transit time is proportional to the barrier width.