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Updated: May 27, 2026

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
10:35

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Hyperbolic disordered ensembles of random matrices.

O Bohigas1, M P Pato

  • 1CNRS, Université Paris-Sud, UMR8626, LPTMS, Orsay Cedex, F-91405, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 9, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for generating random matrices, revealing a transition in their statistical properties from semicircle to Gaussian-like behavior. This transition impacts spectral density and local fluctuations, offering insights into complex systems.

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Last Updated: May 27, 2026

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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Area of Science:

  • Random matrix theory
  • Statistical physics
  • Probability theory

Background:

  • Gaussian matrices are fundamental in random matrix theory.
  • Understanding spectral properties and statistical fluctuations is crucial for various scientific domains.

Purpose of the Study:

  • To investigate the statistical behavior of a novel family of random matrices.
  • To analyze the evolution of spectral density and local fluctuations.
  • To characterize long-range statistics in these ensembles.

Main Methods:

  • Generation of random matrices by dividing Gaussian matrices by a positive random variable.
  • Analysis of spectral density using established theoretical frameworks.
  • Examination of local fluctuations and number variance statistics.

Main Results:

  • A family of random matrices exhibiting generalized hyperbolic distribution behavior was generated.
  • Spectral density transitions from semicircle law to Gaussian-like.
  • Local fluctuations shift from Wigner-Dyson to Poisson statistics.
  • Long-range statistics show large fluctuations characteristic of nonergodic ensembles.

Conclusions:

  • The simple division procedure generates complex random matrix ensembles.
  • The study reveals a clear transition in statistical properties.
  • Findings provide insights into nonergodic behavior and statistical physics models.