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Open AccessArticle

Tempered Fractional Equations for Quantum Transport in Mesoscopic One-Dimensional Systems with Fractal Disorder

1
Laboratory of Diffusion Processes, Ulyanovsk State University, 42 Leo Tolstoy Street, 432017 Ulyanovsk, Russia
2
Scientific-Manufacturing Complex “Technological Centre”, 1-7 Shokin Square, Zelenograd, 124498 Moscow, Russia
3
Institute of Hydraulics and Fluid Mechanics, Hohai University, 1 Xikang Road, Nanjing 210098, China
*
Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(4), 47; https://doi.org/10.3390/fractalfract3040047
Received: 13 June 2019 / Revised: 13 October 2019 / Accepted: 17 October 2019 / Published: 19 October 2019
New aspects of electron transport in quantum wires with Lévy-type disorder are described. We study the weak scattering and the incoherent sequential tunneling in one-dimensional quantum systems characterized by a tempered Lévy stable distribution of spacing between scatterers or tunneling barriers. The generalized Dorokhov–Mello–Pereyra–Kumar equation contains the tempered fractional derivative on wire length. The solution describes the evolution from the anomalous conductance distribution to the Dorokhov function for a long wire. For sequential tunneling, average values and relative fluctuations of conductance and resistance are calculated for different parameters of spatial distributions. A tempered Lévy stable distribution of spacing between barriers leads to a transition in conductance scaling. View Full-Text
Keywords: fractal; quantum wire; anomalous diffusion; tempered fractional equation; stable law; weak scattering; tunneling; conductance fractal; quantum wire; anomalous diffusion; tempered fractional equation; stable law; weak scattering; tunneling; conductance
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Sibatov, R.T.; Sun, H. Tempered Fractional Equations for Quantum Transport in Mesoscopic One-Dimensional Systems with Fractal Disorder. Fractal Fract 2019, 3, 47.

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