Tunneling from general Smith–Volterra–Cantor potential

Abstract

We study the tunneling problem from the general Smith–Volterra–Cantor (SVC) potential of finite length L characterized by the scaling parameter ρ and stage G. We show that the SVC(ρ) potential of stage G is a special case of the super periodic potential (SPP) of order G. By using the SPP formalism developed by us earlier, we provide the closed form expression of the tunneling probability TG(k) with the help of the q-Pochhammer symbol. The profile of TG(k) with wave vector k is found to saturate with increasing stage G. Very sharp transmission resonances are found to occur in this system, which may find applications in the design of sharp transmission filters.