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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.
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.
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.
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.