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

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dc.contributor.authorPadgett, J.
dc.contributor.authorKostadinova, E.
dc.contributor.authorLiaw, C.
dc.contributor.authorBusse, K.
dc.contributor.authorMatthews, L.
dc.contributor.authorHyde, T.
dc.date.accessioned2022-03-21T19:27:17Z
dc.date.available2022-03-21T19:27:17Z
dc.date.issued2020-04-03
dc.description.abstractThis 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.en_US
dc.description.keywordsAnderson localizationen_US
dc.description.keywordsanomalous diffusionen_US
dc.description.keywordsdiscrete Fractional Laplacianen_US
dc.description.keywordsspectral approachen_US
dc.description.keywordsdisordered systemen_US
dc.identifier.citationJournal of Physics A, 53, 135205, April 3 2020en_US
dc.identifier.doi10.1088/1751-8121/ab7499
dc.identifier.urihttps://hdl.handle.net/2104/11775
dc.language.isoenen
dc.publisherIOP Publishingen_US
dc.titleAnomalous Diffusion in One-Dimensional Disordered Systems: A Discrete Fractional Laplacian Method (Part I)en_US
dc.typeArticleen

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