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Wigner surmise for Hermitian and non-Hermitian chiral random matrices

We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral random matrix theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in the microscopic large-N limit, we find an excellent agreement...

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Main Authors: Akemann, Gernot (Author) , Bittner, Elmar (Author) , Phillips, M. J. (Author) , Shifrin, L. (Author)
Format: Article (Journal)
Language:English
Published: 3 December 2009
In: Physical review. E, Statistical, nonlinear, and soft matter physics
Year: 2009, Volume: 80, Issue: 6, Pages: 1-4
ISSN:1550-2376
DOI:10.1103/PhysRevE.80.065201
Online Access:Verlag, Volltext: http://dx.doi.org/10.1103/PhysRevE.80.065201
Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevE.80.065201
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Author Notes:G. Akemann, E. Bittner, M.J. Phillips, and L. Shifrin

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520 |a We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral random matrix theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in the microscopic large-N limit, we find an excellent agreement valid for a small number of exact zero eigenvalues. Compact expressions are derived for real eigenvalues in the orthogonal and symplectic classes and at intermediate non-Hermiticity for the unitary and symplectic classes. Such individual Dirac eigenvalue distributions are a useful tool in lattice gauge theory, and we illustrate this by showing that our results can describe data from two-color quantum chromodynamics simulations with chemical potential in the symplectic class. 
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