The solution of a chiral random matrix model with complex eigenvalues

Author: Akemann G.

Source: Journal of Physics A: Mathematical and General, Volume 36, Number 12, 2003 , pp. 3363-3378(16)

Publisher: Institute of Physics Publishing

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Abstract:

We describe in detail the solution of the extension of the chiral Gaussian unitary ensemble (chGUE) into the complex plane. The correlation functions of the model are first calculated for a finite number of N complex eigenvalues, where we exploit the existence of orthogonal Laguerre polynomials in the complex plane. When taking the large-N limit we derive new correlation functions in the case of weak and strong non-Hermiticity, thus describing the transition from the chGUE to a generalized Ginibre ensemble. We briefly discuss applications to the Dirac operator eigenvalue spectrum in quantum chromodynamics with non-vanishing chemical potential. This is an extended version of hep-th/0204068.

Language: English

Document Type: Miscellaneous

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