Stochastic Approach to the Tunnel Effect

Abstract

There is a growing interest in the investigation about the time required by particles to tunnel accross potential barriers, due both to important technological advances on the subject and to concerns of a conceptual nature. The fact that the various proposed versions of tunneling times are mutually inconsistent and give widely different outcomes, reveals that there is still much to be learned from such an apparently simple problem.

In this paper we approach the problem by using the phenomenological theory of stochastic quantum mechanics to obtain semi-quantitative information about the tunneling times. The results are in good agreement with recent numerical calculations performed within the framework of Nelson’s stochastic theory. In particular, the most important effect of an opaque barrier on the tunneling particles is shown to occur before they actually enter the barrier. Further, a very simple statistical approach is shown to give valuable information on the average time spent by all particles inside the barrier.

The stochasticity of the particle dynamics, combined with the obviously wavelike features exhibited in the tunnel effect, call for an analysis within the framework of stochastic electrodynamics. As a first entry to this program, we briefly discuss the possible role of the zeropoint field in determining the behavior of tunneling particles, with the purpose of ultimately obtaining a satisfactory understanding of this intriguing quantum phenomenon.