Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics

Details Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics

1997-03-14

arxiv.org/abs/cond-mat/9703152v1

Phys.Rev.Lett.79:557-560,1997

Physics

Condensed Matter

4 pages, RevTEX

Scientific paper

10.1103/PhysRevLett.79.557

By using the method of orthogonal polynomials we analyze the statistical properties of complex eigenvalues of random matrices describing a crossover from Hermitian matrices characterized by the Wigner- Dyson statistics of real eigenvalues to strongly non-Hermitian ones whose complex eigenvalues were studied by Ginibre. Two-point statistical measures (as e.g. spectral form factor, number variance and small distance behavior of the nearest neighbor distance distribution $p(s)$) are studied in more detail. In particular, we found that the latter function may exhibit unusual behavior $p(s)\propto s^{5/2}$ for some parameter values.

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