Particle characteristics of conventional and resonant tunneling

Abstract

The dynamics of particle tunneling is characterized by the concept of a tunneling time. The various times suggested in the literature are considered in order to characterize the complementary features of the tunneling process. Explicit calculations show how to find the particle and the wave aspects of different tunneling times. We also expose the physics behind the various definitions and their interrelations. We show that in the classical limit the particle properties dominate and in the opaque limit the wave aspects do. The complementary analysis helps in the interpretation of the tunneling process and eliminates some of the controversies found in the literature. All tunneling times are found to be special cases of a universal tunneling time definition relating to parameter derivatives of the phases of the wave functions. We propose that these relations can be used to extract the tunneling times for any general potential by integrating the wave packet through the tunneling process and extracting the derivatives numerically from these results. Furthermore, we investigate the particle properties of resonant tunneling. They are shown to dominate the dynamics inside the well regions.