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Localization, anomalous diffusion, and slow relaxations: a random distance matrix approach.

Ariel Amir1, Yuval Oreg, Yoseph Imry

  • 1Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

We analyzed random matrices with elements dependent on point distances. Our findings reveal eigenvalue distributions and localization properties, offering insights into particle diffusion and material relaxation.

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Random matrix theory

Background:

  • Random matrix models are crucial for understanding complex systems.
  • Matrix elements depending on inter-particle distance are relevant to diffusion and localization phenomena.

Purpose of the Study:

  • To investigate the spectral properties of random matrices with exponentially distance-dependent elements.
  • To determine eigenvalue distributions and eigenmode localization for this class of matrices.

Main Methods:

  • Renormalization group procedure
  • Direct moment calculation
  • Analysis of low-density regimes and arbitrary dimensions

Main Results:

  • Derived the eigenvalue distribution density (spectrum) for low densities.
  • Characterized the localization properties of eigenmodes in arbitrary dimensions.
  • Established a connection between matrix properties and physical phenomena like diffusion and phonon localization.

Conclusions:

  • The study provides a theoretical framework for understanding spectral properties in systems with spatially correlated disorder.
  • Results have implications for modeling diffusion, glass dynamics, and wave localization in disordered media.