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arXiv · 0907.4195

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

G. Akemann·E. Bittner·M. J. Phillips·L. Shifrin
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Abstract

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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G. Akemann, E. Bittner, M. J. Phillips, L. Shifrin. 2009-07-24. A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices. https://doi.org/10.1103/physreve.80.065201

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