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Localization in one-dimensional chains with Lévy-type disorder.

Sepideh S Zakeri1, Stefano Lepri2,3, Diederik S Wiersma1,4,5

  • 1European Laboratory for Non-linear Spectroscopy (LENS), University of Florence, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 15, 2015
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Summary
This summary is machine-generated.

We investigated Anderson localization in disordered lattices, finding that wave localization length scales with frequency. This reveals how wave behavior is affected by long-range correlated disorder, crucial for understanding complex optical systems.

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Area of Science:

  • Condensed matter physics
  • Wave phenomena
  • Disordered systems

Background:

  • Anderson localization describes wave confinement in disordered media.
  • Lévy glasses exhibit complex optical properties due to long-range correlated disorder.
  • Understanding wave propagation in such systems is vital for optical technologies.

Purpose of the Study:

  • To investigate Anderson localization of classical lattice waves in a disordered chain.
  • To analyze the impact of long-range correlated, power-law distributed mass impurities on wave localization.
  • To explore the small-frequency behavior of localization length in such systems.

Main Methods:

  • Theoretical analysis of wave propagation in a disordered lattice.
  • Numerical simulations to model wave packet dynamics.
  • Derivation of the localization length's frequency dependence.

Main Results:

  • Established a power-law relationship for localization length: ξ(ω)∼ω-α.
  • Demonstrated that for small frequencies, waves experience scale-dependent effective disorder.
  • Observed a characteristic inverse power-law front for localized wave packets over time.

Conclusions:

  • The study provides a theoretical and numerical framework for Anderson localization in Lévy-like disordered systems.
  • The findings offer insights into wave behavior in complex optical media.
  • The derived scaling law is crucial for designing and predicting the performance of optical devices with engineered disorder.