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Open AccessArticle

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.
Entropy 2018, 20(4), 300; https://doi.org/10.3390/e20040300
Received: 27 December 2017 / Revised: 29 March 2018 / Accepted: 8 April 2018 / Published: 20 April 2018
(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)
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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MDPI and ACS Style

Méndez-Bermúdez, J.A.; Aguilar-Sánchez, R. Information-Length Scaling in a Generalized One-Dimensional Lloyd’s Model. Entropy 2018, 20, 300. https://doi.org/10.3390/e20040300

AMA Style

Méndez-Bermúdez JA, Aguilar-Sánchez R. Information-Length Scaling in a Generalized One-Dimensional Lloyd’s Model. Entropy. 2018; 20(4):300. https://doi.org/10.3390/e20040300

Chicago/Turabian Style

Méndez-Bermúdez, J. A.; Aguilar-Sánchez, R. 2018. "Information-Length Scaling in a Generalized One-Dimensional Lloyd’s Model" Entropy 20, no. 4: 300. https://doi.org/10.3390/e20040300

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