2023/12/16 by Vibhav Narayan Singh, Mohd. Hasan, Singh, Vibhav Narayan +8
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #FOS: Physical sciences #Fractal and DNA sequence analysis #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2312.10501
openalex publication_date 2023/12/16 · openalex created_date 2023/12/20 · openalex updated_date 2026/07/28
In this paper, we introduce and analyze the Smith-Volterra-Cantor potential of power \( n \), denoted as SVC\((ρ, n)\). Bridging the gap between the general Cantor and SVC systems, this novel potential offers a fresh perspective on Cantor-like potential systems within quantum mechanics that unify fractal and non-fractal potentials. Utilizing the Super Periodic Potential (SPP) formalism, we derive the close form expression of the transmission probability \( TG(k) \). Notably, the system exhibits exceptionally sharp transmission resonances, a characteristic that distinguishes it from other quantum systems. Furthermore, the multifaceted transmission attributes of the SVC\((ρ, n)\) are found to be critically dependent on both parameters, \( ρ\) and \( n \), offering an intricate interplay that warrants deeper exploration. Our findings highlight a pronounced scaling behavior of reflection probability with \( k \), which is underpinned by analytical derivations.