Tunneling from general Smith-Volterra-Cantor potential

Abstract

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