A New Time-Scale for Tunneling
E. Eisenberg and Y. Ashkenazy
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
(July 4, 2002)
We study the tunneling through an oscillating delta barrier. Using time peri-
odicity of the model, the time-dependent 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.
The question regarding the actual time spent during tunneling through a barrier has
been in discussion for over half a century . The introduction of high-speed tunneling-
based semiconductor devices in recent years  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