Almost Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre Eigenvalue Statistics

Journal Article · Tue Jul 01 04:00:00 EDT 1997 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.79.557· OSTI ID:527047

Fyodorov, Y V; Sommers, H ^[1]; Khoruzhenko, B A ^[2]

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1. Fachbereich Physik, Universitaet-GH Essen, D-45117 Essen (Germany)
2. School of Mathematical Sciences, Queen Mary Westfield College, University of London, London E1 4NS (United Kingdom)

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){proportional_to}s{sup 5/2} for some parameter values. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 527047
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 4 Vol. 79; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CORRELATIONS
EIGENVALUES
FORM FACTORS
HERMITIAN MATRIX
POLYNOMIALS
RANDOMNESS
STATISTICS