ar X iv : q ua nt - p h / 96 10 03 9 v 1 2 5 O ct 1 99 6 A New Time - Scale for Tunneling

We study the tunneling through an oscillating delta barrier. Using time peri-odicity of the model, the time-dependent Schrödinger equation is reduced to a simple but infinite matrix equation. Employing Toeplitz matrices methods, the infinite matrix is replaces by a 3×3 matrix, allowing an analytical solution. Looking at the frequency dependence of the transmission amplitudes, one observes a new time scale which dominates the tunneling dynamics. This time scale differs from the one previously introduced by Büttiker and Landauer. The relation between these two is discussed.