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Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
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Random walks and Anderson localization in a three-dimensional class C network model.

M Ortuño1, A M Somoza, J T Chalker

  • 1Departamento de Física, Universidad de Murcia, Murcia 30.071, Spain.

Physical Review Letters
|March 5, 2009
PubMed
Summary

We investigated disorder-induced localization in a 3D network model for superconductors. This study offers a more precise numerical analysis of Anderson transition critical behavior using a novel random walk mapping.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Superconductivity

Background:

  • Disorder-induced localization is a critical phenomenon affecting electron transport in materials.
  • Understanding Anderson transitions is key to designing novel electronic and quantum devices.
  • Symmetry class C models, relevant to unconventional superconductors, present unique theoretical challenges.

Purpose of the Study:

  • To investigate the disorder-induced localization transition in a 3D network model belonging to symmetry class C.
  • To analyze quasiparticle dynamics in a gapless spin-singlet superconductor lacking time-reversal invariance.
  • To achieve a more precise numerical study of critical behavior at an Anderson transition.

Main Methods:

  • Developed a 3D network model for quasiparticle dynamics in a gapless spin-singlet superconductor.
  • Utilized a unique mapping of conductance and density of states to averages in a classical system of dense, interacting random walks.
  • Performed a high-precision numerical study of critical behavior at the Anderson transition.

Main Results:

  • The study provides a novel and more precise numerical characterization of critical behavior at an Anderson transition.
  • The mapping to interacting random walks offers a powerful new approach for studying localization phenomena.
  • The findings are relevant for understanding transport properties in disordered, time-reversal symmetry broken superconductors.

Conclusions:

  • The network model and random walk mapping provide unprecedented accuracy for studying Anderson transitions.
  • This work advances the understanding of localization phenomena in symmetry class C systems.
  • The methodology can be extended to explore other complex quantum transport phenomena.