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

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.