Instantaneous tunneling of relativistic massive spin-0 particles

TL;DR

This paper investigates the tunneling time of relativistic spin-0 particles, showing that above-barrier energies have finite traversal times while below-barrier energies tunnel instantaneously, extending previous non-relativistic results.

Contribution

It introduces a relativistic formalism for time-of-arrival operators for spin-0 particles and analyzes tunneling times in this context, revealing energy-dependent tunneling behavior.

Findings

Above-barrier energies have finite tunneling times.

Below-barrier energies tunnel instantaneously.

Relativistic effects modify tunneling time predictions.

Abstract

The tunneling time problem earlier studied in Phys. Rev. Lett 108 170402 (2012) using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous. This raises the question on whether instantaneous tunneling time is a consequence of using a non-relativistic theory. Here, we extend the analysis by proposing a formalism on the construction of relativistic TOA-operators for spin-0 particles in the presence of an interaction potential via quantization. We then construct the corresponding barrier traversal time operator and impose the condition that the barrier height is less than the rest mass energy of the particle. We show that only the above-barrier energy components of the incident wavepacket's momentum distribution contribute to the barrier traversal time while the below-barrier components are transmitted instantaneously.