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 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.
Akemann
G
G
Department of Mathematical Sciences and BURSt Research Centre, Brunel University West London, Uxbridge, United Kingdom.
Bittner
E
E
Phillips
M J
MJ
Shifrin
L
L
D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D010825:Physics / Q000379:methods*; D011789:Quantum Theory