Quantum tunneling from a new type of Unified Cantor Potential

Abstract

We introduce a new type of potential system that combines the families of general Cantor (fractal system) and general Smith-Volterra-Cantor (non-fractal system) potentials. We call this system as Unified Cantor Potential (UCP) system. The UCP system of total span L is characterized by scaling parameter ρ>1, stage G and two real numbers α and β. For α=1, β=0, the UCP system represents general Cantor potential while for α=0, β=1, this system represent general Smith-Volterra-Cantor (SVC) potential. We provide close-form expression of transmission probability from UCP system for arbitrary α and β by using q-Pochhammer symbol. Several new features of scattering are reported for this system. The transmission probability TG(k) shows a scaling behavior with k which is derived analytically for this potential. The proposed system also opens up the possibility for further generalization of new potential systems that encompass a large class of fractal and non-fractal systems. The analytical formulation of tunneling from this system would help to study the transmission feature at breaking threshold when a system transit from fractal to non-fractal domain. © 2023 Elsevier Inc.