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    Anomalous Diffusion in One-Dimensional Disordered Systems: A Discrete Fractional Laplacian Method (Part I)

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    Date
    2020-04-03
    Author
    Padgett, J.
    Kostadinova, E.
    Liaw, C.
    Busse, K.
    Matthews, L.
    Hyde, T.
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    Abstract
    This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous dffusion. Herein, we investigate the transport properties of a one dimensional disordered system that employs the discrete fractional Laplacian, (-Δ)^s, s ∈(0,2), in combination with results from spectral and measure theory. It is a classical mathematical result that the standard Anderson model exhibits localization of energy states for all nonzero disorder in one-dimensional systems. Numerical simulations utilizing our proposed model demonstrate that this localization effect is enhanced for sub-diffusive realizations of the operator, s ∈(1,2), while the super-diffusive realizations of the operator, s ∈(0,1) can exhibit energy states with less localized features. These results suggest that the proposed method can be used to examine anomalous diffusion in physical systems where strong correlations, structural defects, and nonlocal effects are present.
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    https://hdl.handle.net/2104/11775
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    Copyright © Baylor® University All rights reserved. Legal Disclosures.
    Baylor University Waco, Texas 76798 1-800-BAYLOR-U
    Baylor University Libraries | One Bear Place #97148 | Waco, TX 76798-7148 | 254.710.2112 | Contact: libraryquestions@baylor.edu
    If you find any errors in content, please contact librarywebmaster@baylor.edu
    DSpace software copyright © 2002-2016  DuraSpace
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