# A New Time-Scale for Tunneling Academic Article

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### abstract

• We study the tunneling through an oscillating delta barrier. Using time periodicity of the model, the time-dependent Schr\"odinger equation is reduced to a simple but infinite matrix equation. Employing Toeplitz matrices methods, the infinite matrix is replaces by a $3\times 3$ matrix, allowing an analytical solution. Looking at the frequency dependence of the transmissionamplitudes, one observes a new time scale which dominates the tunneling dynamics. This time scale differs from the one previously introduced by B\"uttiker and Landauer. The relation between these two is discussed. Comment: 12 pages + 6 figures, RevTex

### publication date

• January 1, 1997