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.

25 pages, 10 figures

References in corpus (3)

• Wave propagation through Cantor-set media: Chaos, scaling, and fractal structures
• Strong Resonance of Light in a Cantor Set
• A new type of solution of the Schrödinger equation on a self-similar fractal potential