A New Time-Scale for Tunneling

We study the tunneling through an oscillating delta barrier. Using time periodicity of the model, the time-dependent Schrödinger equation is reduced to a simple but infinite matrix equation. Employing Toeplitz matrix methods, the infinite matrix is replaced 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 preriously introduced by Büttiker and Landauer. The relation between these two is discussed.