 
Summary: arXiv:quantph/9610039v227Nov1996
A New TimeScale for Tunneling
E. Eisenberg and Y. Ashkenazy
Department of Physics, BarIlan University, RamatGan 52900, Israel
(July 4, 2002)
Abstract
We study the tunneling through an oscillating delta barrier. Using time peri
odicity of the model, the timedependent Schršodinger equation is reduced to
a simple but infinite matrix equation. Employing Toeplitz matrices methods,
the infinite matrix is replaces by a 3Ś3 matrix, allowing an analytical solution.
Looking at the frequency dependence of the transmission amplitudes, one ob
serves a new time scale which dominates the tunneling dynamics. This time
scale differs from the one previously introduced by Bšuttiker and Landauer.
The relation between these two is discussed.
I. INTRODUCTION
The question regarding the actual time spent during tunneling through a barrier has
been in discussion for over half a century [16]. The introduction of highspeed tunneling
based semiconductor devices in recent years [7] has brought new urgency to the problem.
However, in spite of the long history of this subject it still remains controversial.
Most of the opinions on this matter can be classified into three categories. The most
