Semiclassical tunneling through opaque barriers, external interactions and the traversal time wavefunction

Abstract

We show how semiclassical scattering (tunneling) can be analysed in terms of traversal times. Real or complex valued saddle points are associated with the traversal time wavefunction and they determine the semiclassical traversal times. For free particle motion, there is a real saddle point located at the classical traversal time, τ 0. For tunneling through an opaque rectangular barrier, the saddle point lies at - iτ BL, where τ BL is the Büttiker-Landauer time. As a result, although physically significant, τ BL does not have the physical interpretation as the actual duration for tunneling. Rather, τ BL provides an estimate for the range of traversal times of those Feynman paths which contribute significantly to the tunneling. We also find the complex semiclassical traversal times and transmission probabilities for tunneling in the presence of absorption and for interaction with a slow oscillatory mode.