Hartman effect in presence of Aharanov Bohm flux

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.