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Correlations of eigenvectors for non-Hermitian random-matrix models.

R A Janik1, W Nörenberg, M A Nowak

  • 1Service de Physique Théorique, CEA Saclay, F-91191 Gif-Sur-Yvette, France.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

We found a general relationship between eigenvector properties and spectral Green's functions in complex random matrix theory. This finding is validated by numerical simulations for non-Hermitian models.

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Area of Science:

  • * Physics
  • * Mathematics
  • * Quantum Mechanics

Background:

  • * Non-Hermitian random-matrix models are crucial for understanding complex systems.
  • * The behavior of eigenvectors and spectral properties is key to analyzing these models.

Purpose of the Study:

  • * To establish a general relationship between the diagonal correlator of eigenvectors and the spectral Green's function.
  • * To apply this general relation to specific non-Hermitian random-matrix models.
  • * To validate the theoretical findings with numerical results.

Main Methods:

  • * Derivation of a general analytical relation in the large-N limit.
  • * Application of the derived relation to various non-Hermitian random-matrix models.
  • * Numerical simulations to verify the theoretical predictions.

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Main Results:

  • * A general formula connecting the diagonal correlator of eigenvectors and the spectral Green's function was established.
  • * The derived relation accurately describes the behavior of non-Hermitian random-matrix models.
  • * Theoretical predictions show good agreement with numerical data.

Conclusions:

  • * The established relation provides a powerful tool for analyzing non-Hermitian random-matrix models.
  • * The findings offer new insights into the spectral properties of complex quantum systems.
  • * The agreement with numerical results validates the theoretical framework.