Hartman effect in presence of Aharanov Bohm flux

TL;DR

This paper extends the understanding of the Hartman effect by demonstrating that in a quantum ring with Aharonov-Bohm flux, the tunneling delay time remains independent of barrier thickness and flux magnitude, indicating a generalized phenomenon.

Contribution

It shows that the Hartman effect persists in a quantum ring geometry with Aharonov-Bohm flux, extending previous one-dimensional results to more complex systems.

Findings

Group delay time is independent of barrier width for opaque barriers.

The effect persists regardless of the magnitude of the Aharonov-Bohm flux.

The Hartman effect is extended beyond one-dimensional systems.

Abstract

The Hartman effect for the tunneling particle implies the independence of group delay time on the opaque barrier width, with superluminal velocities as a consequence. This effect is further examined on a quantum ring geometry in the presence of Aharonov-Bohm flux. We show that while tunneling through an opaque barrier the group delay time for given incident energy becomes independent of the barrier thickness as well as the magnitude of the flux. The Hartman effect is thereby extended beyond one dimension and in the presence of Aharonov-Bohm flux.