Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Density of states for almost-diagonal random matrices.

Oleg Yevtushenko1, Vladimir E Kravtsov

  • 1The Abdus Salam ICTP, Strada Costiera 11, 34100 Trieste, Italy. bom@ictp.trieste.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2004
PubMed
Summary

This study investigates the density of states in disordered systems using random matrix theory. It calculates corrections to the Poissonian density of states for Gaussian ensembles, offering insights into spectral statistics.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Renormalization group for Anderson localization on high-dimensional lattices.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Renormalization group analysis of the Anderson model on random regular graphs.

Proceedings of the National Academy of Sciences of the United States of America·2024
Same author

Horizon in random matrix theory, the Hawking radiation, and flow of cold atoms.

Physical review letters·2009
Same author

Jumps in current-voltage characteristics in disordered films.

Physical review letters·2009

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Chaos

Background:

  • Disordered systems exhibit complex spectral statistics.
  • Random matrix theory provides a framework for understanding these statistics.
  • The density of states (DOS) is a key property of disordered systems.

Purpose of the Study:

  • To calculate the leading correction to the Poissonian DOS in disordered systems.
  • To analyze spectral statistics using Gaussian ensembles of random matrices.
  • To apply theoretical methods to specific models like power-law banded matrices.

Main Methods:

  • Utilizing a virial expansion method for interacting energy levels.
  • Employing Gaussian orthogonal and unitary ensembles for random matrices.

Related Experiment Videos

  • Analyzing matrices with small off-diagonal elements relative to diagonal elements.

    • Main Results:

    • Derived the leading correction to the Poissonian DOS.
    • Calculated DOS for critical power-law banded random matrices.
    • Compared DOS for different random matrix models, including the Moshe-Neuberger-Shapiro model.

    Conclusions:

    • The study provides a theoretical framework for understanding deviations from Poissonian DOS in disordered systems.
    • The virial expansion method is effective for calculating spectral properties.
    • The findings offer insights into the spectral statistics of specific random matrix models.