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Numerical study of eigenvector statistics for random banded matrices.

Ville Uski1, Rudolf A Römer, Michael Schreiber

  • 1Department of Physical Resource Theory, Chalmers University of Technology, SE-41296 Göteborg, Sweden. frtvu@fy.chalmers.se

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
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This study numerically investigates eigenvector amplitude statistics in random-banded-matrix ensembles. The nonlinear sigma model

Area of Science:

  • Quantum physics
  • Statistical mechanics

Background:

  • Eigenvector amplitude statistics are crucial for understanding quantum systems.
  • Random matrix theory provides a framework for analyzing disordered systems.
  • The nonlinear sigma model offers a rigorous description for random-banded-matrix ensembles.

Purpose of the Study:

  • To numerically study eigenvector amplitude statistics near the band center in random-banded-matrix ensembles.
  • To extend the predictions of the nonlinear sigma model to complex quantum systems.
  • To investigate the validity range of perturbation theory in this context.

Main Methods:

  • Numerical simulations of random-banded-matrix ensembles.
  • Application of the nonlinear sigma model framework.
  • Analysis of perturbation theory starting from random matrix theory formulas.

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Main Results:

  • Characterization of eigenvector amplitude statistics.
  • Assessment of the nonlinear sigma model's applicability to complex quantum systems.
  • Determination of the validity limits for perturbation theory.

Conclusions:

  • The nonlinear sigma model accurately describes eigenvector statistics in random-banded-matrix ensembles.
  • The study provides insights into extending these findings to more complex quantum systems.
  • The research clarifies the applicability of perturbation theory in disordered quantum systems.