4.5 Article

Quantum tunneling from a new type of Unified Cantor Potential

Journal

ANNALS OF PHYSICS
Volume 458, Issue -, Pages -

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2023.169485

Keywords

Quantum tunneling; Cantor potential; Factal system; Transmission probability; Scaling law

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This study introduces a new type of potential system, which combines fractal and non-fractal potentials. The close-form expression of transmission probability is derived, and new scattering features are reported for this system.
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 rho > 1, stage G and two real numbers a and fi. For a = 1, fi = 0, the UCP system represents general Cantor potential while for a = 0, fi = 1, this system represent general Smith-Volterra-Cantor (SVC) potential. We provide close-form expression of transmission probability from UCP system for arbitrary a and fi by using q-Pochhammer symbol. Several new features of scattering are reported for this system. The transmission probability T-G(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.

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