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Universal mechanism for Anderson and weak localization.

Marcel Filoche1, Svitlana Mayboroda

  • 1Physique de la Matière Condensée, Ecole Polytechnique, Centre National de la Recherche Scientifique, 91128 Palaiseau, France. marcel.filoche@polytechnique.edu

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Summary
This summary is machine-generated.

This study reveals a universal mechanism behind Anderson localization and weak localization in vibrating systems. This mechanism unifies various localization phenomena by partitioning systems into subregions based on a hidden geometric landscape.

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Area of Science:

  • Physics
  • Wave Phenomena
  • Condensed Matter Physics

Background:

  • Stationary wave localization occurs in diverse systems (mechanical, optical, quantum) due to disorder or complex geometry.
  • Anderson localization is a key example, explaining metal-insulator transitions, but a unified understanding is lacking.

Purpose of the Study:

  • To demonstrate a single, universal mechanism underlying both Anderson and weak localization.
  • To establish a unified theoretical framework for various wave localization phenomena.

Main Methods:

  • Analysis of the interplay between the wave operator and system geometry.
  • Identification of a hidden landscape partitioning the system into weakly coupled subregions.
  • Solving a specific boundary problem to characterize the landscape and coupling strengths.

Main Results:

  • Both Anderson and weak localizations stem from the same universal mechanism.
  • This mechanism partitions systems into subregions defined by the valleys of a hidden geometric landscape.
  • The landscape's properties rigorously predict localization behavior and eigenmode energies.

Conclusions:

  • Anderson localization is a specific instance of weak localization within a rough landscape.
  • The developed theory provides a unified perspective on wave localization across different systems and dimensions.
  • Geometric properties of the hidden landscape are crucial for understanding and predicting localization.