PUB - Publikationen an der Universität Bielefeld

In the presence of a non-vanishing chemical potential the eigenvalues of theDirac operator become complex. We calculate spectral correlation functions ofcomplex eigenvalues using a random matrix model approach. Our results apply tonon-Hermitian Dirac operators in three-dimensional QCD with broken flavorsymmetry and in four-dimensional QCD in the bulk of the spectrum. Thederivation follows earlier results of Fyodorov, Khoruzhenko and Sommers forcomplex spectra exploiting the existence of orthogonal polynomials in thecomplex plane. Explicit analytic expressions are given for all microscopick-point correlation functions in the presence of an arbitrary even number ofmassive quarks, both in the limit of strong and weak non-Hermiticity. In thelatter case the parameter governing the non-Hermiticity of the Dirac matricesis identified with the influence of the chemical potential.