A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices

Details A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices

2009-07-24

arxiv.org/abs/0907.4195v1

Phys.Rev.E80:065201,2009

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, 5 figures

Scientific paper

10.1103/PhysRevE.80.065201

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. New 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 new results can describe data from two-colour QCD simulations with chemical potential in the symplectic class.

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