PUB - Publikationen an der Universität Bielefeld

A chiral random matrix model with complex eigenvalues is solved as aneffective model for QCD with non-vanishing chemical potential. We derive newmatrix model correlation functions which predict the local fluctuations ofcomplex Dirac operator eigenvalues at zero virtuality. The parameter whichmeasures the non-Hermiticity of the Dirac matrix is identified with thechemical potential. In the phase with broken chiral symmetry all spectralcorrelations of the Dirac eigenvalues are calculated as functions of quarkflavors and chemical potential. The derivation uses the orthogonality of theLaguerre polynomials in the complex plane. Explicit results are given for anyfinite matrix size N as well in the large-N limit for weak and strongnon-Hermiticity.