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

Akemann G, Bittner E, Phillips MJ, Shifrin L. A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices. Phys.Rev.E. 2009;80(6):065201.We use the idea of a Wigner surmise to compute approximate distributions ofthe first eigenvalue in chiral Random Matrix Theory, for both real and complexeigenvalues. Testing against known results for zero and maximal non-Hermiticityin the microscopic large-N limit we find an excellent agreement, valid for asmall number of exact zero-eigenvalues. New compact expressions are derived forreal eigenvalues in the orthogonal and symplectic classes, and at intermediatenon-Hermiticity for the unitary and symplectic classes. Such individual Diraceigenvalue distributions are a useful tool in Lattice Gauge Theory and weillustrate this by showing that our new results can describe data fromtwo-colour QCD simulations with chemical potential in the symplectic class