Traversal Time for Tunneling

Abstract

The time required for decay of a metastable state, through tunneling, is a well settled subject. During this lifetime of the initial state, the particle oscillates within its initial well. By contrast, questions about the duration of the actual tunneling process, when it finally occurs, have led to widely divergent answers. In recent years, Jonson, Stevens, and we, have, through independent approaches, pointed out that there is an effective barrier traversal velocity obtained by dividing the magnitude of the imaginary momentum, under the barrier, by the particle mass. Here we present a fourth approach to this earlier answer, by considering a time modulated stream incident on the barrier. At low modulation frequencies the transmitted beam reproduces the incident modulation without lag, and without change in modulation depth. As the modulation frequency is increased we eventually depart from this simple behavior, and that is taken as a measure of the transversal time. We also provide some of the details omitted in our earlier analysis.