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

J A Méndez-Bermúdez1, R Aguilar-Sánchez2

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Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

This study numerically investigates eigenfunctions in 1D disordered wires with long-tailed energy distributions. It reveals a universal scaling law for information length, dependent on eigenfunction localization length and wire length.

Keywords:
Lloyd modelinformation lengthone-dimensional disordered systemsscaling laws

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Area of Science:

  • Condensed Matter Physics
  • Disordered Systems
  • Quantum Mechanics

Background:

  • Understanding electron localization in disordered materials is crucial for electronic devices.
  • Disorder in one-dimensional (1D) systems exhibits unique localization phenomena.
  • Long-tailed disorder distributions present a more complex scenario than standard models.

Purpose of the Study:

  • To numerically study the localization properties of eigenfunctions in 1D tight-binding wires.
  • To analyze systems with on-site disorder characterized by long-tailed distributions.
  • To investigate the relationship between information length and eigenfunction localization.

Main Methods:

  • Detailed numerical simulations of 1D tight-binding models.
  • Characterization of disorder using long-tailed probability distributions P(ϵ) ~ 1/ϵ^(1+α).
  • Extraction of eigenfunction localization length (ξ) from Landauer's conductance scaling.

Main Results:

  • A universal scaling law for information length (β) was found: β = γx / (1 + γx), where x = ξ/L.
  • The scaling parameter γ is dependent on the disorder tail parameter α.
  • For α = 2, the system's properties effectively reproduce the 1D Anderson model.

Conclusions:

  • The study establishes a general scaling law for eigenfunction information length in disordered 1D wires.
  • This work generalizes previous models, like the 1D Lloyd's model (α=1).
  • The findings provide insights into electron transport and localization in complex disordered systems.