The solution of a chiral random matrix model with complex eigenvalues

Details The solution of a chiral random matrix model with complex eigenvalues The solution of a chiral random matrix model with complex eigenvalues

2002-04-29

arxiv.org/abs/hep-th/0204246v1

J.Phys.A36:3363,2003

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, 4 figures

Scientific paper

10.1088/0305-4470/36/12/328

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. Applications to the Dirac operator eigenvalue spectrum in QCD with non-vanishing chemical potential are briefly discussed. This is an extended version of arXiv:hep-th/0204068.

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