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Related Experiment Videos

Localization in band random matrix models with and without increasing diagonal elements.

Wen-ge Wang1

  • 1Department of Physics, Southeast University, Nanjing 210096, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 22, 2002
PubMed
Summary

Localization of eigenfunctions in Wigner random matrix models can be linked to band random matrix models. This connection is established using generalized Brillouin-Wigner perturbation theory and intermediate basis states for improved analysis.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Random matrix theory

Background:

  • Understanding eigenfunction localization is crucial in various physical systems.
  • Wigner band random matrix models and band random matrix models are used to study localization phenomena.

Purpose of the Study:

  • To establish a relationship between eigenfunction localization in Wigner band random matrix models with increasing diagonal elements and band random matrix models with random diagonal elements.
  • To introduce a method for analyzing nonperturbative parts of eigenfunctions using reduced Hamiltonian matrices.

Main Methods:

  • Generalization of Brillouin-Wigner perturbation theory.
  • Introduction of reduced Hamiltonian matrices with smaller dimensions.
  • Employment of intermediate basis states to enhance the reduced Hamiltonian matrix method.

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Main Results:

  • A clear relationship is demonstrated between localization in the two considered random matrix models.
  • The study shows that reduced Hamiltonian matrices can effectively represent nonperturbative eigenfunction components.
  • The proposed method improves the analysis of eigenfunction localization.

Conclusions:

  • The findings provide a novel approach to understanding eigenfunction localization in complex random matrix systems.
  • The generalized perturbation theory and reduced Hamiltonian matrices offer a powerful tool for theoretical analysis.
  • This work contributes to the broader understanding of localization phenomena in disordered systems.