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Effective Delocalization in the One-Dimensional Anderson Model with Stealthy Disorder.

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This study on the 1D Anderson model reveals that stealthy disorder can lead to effective delocalization. Unusual scaling of the localization length suggests potential applications for wave phenomena.

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Area of Science:

  • Condensed Matter Physics
  • Disordered Systems
  • Wave Phenomena

Background:

  • The Anderson model describes electron localization in disordered systems.
  • Stealthy disorder, with a vanishing power spectrum, presents unique theoretical challenges.
  • Understanding localization length is crucial for predicting system behavior.

Purpose of the Study:

  • To analyze the 1D Anderson model with specifically defined stealthy disorder.
  • To investigate the impact of stealthiness (χ) and disorder strength (W) on localization length (ξ).
  • To explore the applicability of findings to photonic and phononic waves.

Main Methods:

  • Perturbative expansion of the self-energy.
  • Numerical simulations to determine localization length.
  • Analysis of scaling behavior of ξ with respect to W and χ.

Main Results:

  • For small disorder (W) and specific stealthiness (χ), the system exhibits effective delocalization.
  • Localization length (ξ) exceeds large system sizes under these conditions.
  • ξ scales as W^{-2n} with large n due to systematic cancellation of leading terms.

Conclusions:

  • Stealthy disorder can induce delocalization in the 1D Anderson model.
  • The observed delocalization is a consequence of the unique properties of stealthy disorder.
  • The findings are relevant for understanding wave propagation in photonic and phononic systems.