Time scale of forerunners in quantum tunneling

Abstract

The forerunners preceding the main tunneling signal of the wave created by a source with a sharp onset or by a quantum shutter have been generally associated with over-the-barrier (nontunneling) components. We demonstrate that, while this association is true for distances that are larger than the penetration length, for smaller distances the forerunner is dominated by under-the-barrier components. We find that its characteristic arrival time is inversely proportional to the difference between the barrier energy and the incidence energy, a tunneling time scale different from both the phase time and the Buttiker-Landauer time.