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

Akemann G, Bittner E, Phillips MJ, Shifrin L (2009)
Phys.Rev.E 80(6).

Journal Article | Published | English

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Abstract
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.
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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).
Akemann, G., Bittner, E., Phillips, M. J., & Shifrin, L. (2009). A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices. Phys.Rev.E, 80(6).
Akemann, G., Bittner, E., Phillips, M. J., and Shifrin, L. (2009). A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices. Phys.Rev.E 80.
Akemann, G., et al., 2009. A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices. Phys.Rev.E, 80(6).
G. Akemann, et al., “A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices”, Phys.Rev.E, vol. 80, 2009.
Akemann, G., Bittner, E., Phillips, M.J., Shifrin, L.: A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices. Phys.Rev.E. 80, (2009).
Akemann, Gernot, Bittner, E., Phillips, M. J., and Shifrin, L. “A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices”. Phys.Rev.E 80.6 (2009).
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