PUB - Publikationen an der Universität Bielefeld

Two different matrix models for QCD with a non-vanishing quark chemicalpotential are shown to be equivalent by mapping the corresponding partitionfunctions. The equivalence holds in the phase with broken chiral symmetry. Itis exact in the limit of weak non-Hermiticity, where the chemical potentialsquared is rescaled with the volume. At strong non-Hermiticity it holds onlyfor small chemical potential. The first model proposed by Stephanov is directlyrelated to QCD and allows to analyze the QCD phase diagram. In the second modelsuggested by the author all microscopic spectral correlation functions ofcomplex Dirac operators can be calculated in the broken phase. We brieflycompare those predictions to complex Dirac eigenvalues from quenched QCDlattice simulations.