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Anderson Localization in the Subwavelength Regime.

Habib Ammari1, Bryn Davies2, Erik Orvehed Hiltunen3

  • 1Department of Mathematics, ETH Zürich, Zürich, Switzerland.

Communications in Mathematical Physics
|January 18, 2024
PubMed
Summary
This summary is machine-generated.

This study reveals how resonator mode hybridization explains Anderson localization phenomena, including energy level repulsion and phase transitions in random media. This offers new insights into wave scattering and strong localization mechanisms.

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Area of Science:

  • Physics
  • Wave Phenomena
  • Materials Science

Background:

  • Anderson localization in random media is complex, especially in multi-dimensional systems with long-range interactions.
  • Understanding the fundamental mechanisms of strong localization remains a challenge.

Purpose of the Study:

  • To investigate the mechanisms behind Anderson localization using coupled subwavelength resonator systems.
  • To provide a new framework for understanding wave scattering and localization phenomena.

Main Methods:

  • Utilizing breakthroughs in coupled subwavelength resonator systems.
  • Analyzing the scattering of time-harmonic waves by high-contrast resonators with random material parameters.
  • Employing asymptotic expansions in terms of the material contrast parameter.

Main Results:

  • Demonstrated that resonator mode hybridization drives Anderson localization features.
  • Observed energy level repulsion and a phase transition where eigenmode symmetries swap.
  • Characterized localized modes using generalized capacitance matrices.

Conclusions:

  • Hybridization of subwavelength resonant modes is key to Anderson localization.
  • The developed model captures long-range interactions and explains exotic phenomena.
  • This work provides a concise framework for understanding strong localization in random systems.