Space-time resolved quantum field approach to Klein tunneling dynamics across a finite barrier

TL;DR

This paper uses a space-time resolved quantum field approach to analyze Klein tunneling, revealing that no actual tunneling occurs through finite barriers, but instead pair production mediates transmission, with effects depending on barrier width and particle type.

Contribution

It introduces a space-time resolved quantum field framework to study Klein tunneling, highlighting the role of pair production and barrier width effects in relativistic quantum systems.

Findings

No actual tunneling through finite supercritical barriers.

Transmission mediated by pair production at barrier edges.

Barrier width influences pair production differently for fermions and bosons.

Abstract

We investigate Klein tunneling through finite potential barriers with space-time resolved solutions to relativistic quantum field equations. We find that no particle actually tunnels through a finite supercritical barrier, even in the case of resonant tunneling. The transmission is instead mediated by modulations in pair production rates, at each edge of the barrier, caused by the incoming electron. We further examine the effect of the barrier's width on the numbers of produced pairs in the fermionic case (characterized by saturation) and in the bosonic case (characterized by exponential superradiance). This work paves the way to precise studies of the radiating dynamics of supercritical barriers, and could be applied to certain analogs of Klein tunneling observed in systems modeled by relativistic wave equations.