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Entropy 2018, 20(4), 300; https://doi.org/10.3390/e20040300

Information-Length Scaling in a Generalized One-Dimensional Lloyd’s Model

1
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico
2
Facultad de Ciencias Químicas, Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico
*
Author to whom correspondence should be addressed.
Received: 27 December 2017 / Revised: 29 March 2018 / Accepted: 8 April 2018 / Published: 20 April 2018
(This article belongs to the Special Issue News Trends in Statistical Physics of Complex Systems)
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Abstract

We perform a detailed numerical study of the localization properties of the eigenfunctions of one-dimensional (1D) tight-binding wires with on-site disorder characterized by long-tailed distributions: For large ϵ , P ( ϵ ) 1 / ϵ 1 + α with α ( 0 , 2 ] ; where ϵ are the on-site random energies. Our model serves as a generalization of 1D Lloyd’s model, which corresponds to α = 1 . In particular, we demonstrate that the information length β of the eigenfunctions follows the scaling law β = γ x / ( 1 + γ x ) , with x = ξ / L and γ γ ( α ) . Here, ξ is the eigenfunction localization length (that we extract from the scaling of Landauer’s conductance) and L is the wire length. We also report that for α = 2 the properties of the 1D Anderson model are effectively reproduced. View Full-Text
Keywords: Lloyd model; scaling laws; information length; one-dimensional disordered systems Lloyd model; scaling laws; information length; one-dimensional disordered systems
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Méndez-Bermúdez, J.A.; Aguilar-Sánchez, R. Information-Length Scaling in a Generalized One-Dimensional Lloyd’s Model. Entropy 2018, 20, 300.

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