PUB - Publikationen an der Universität Bielefeld

The microscopic spectral density of the QCD Dirac operator at nonzero baryonchemical potential for an arbitrary number of quark flavors was derivedrecently from a random matrix model with the global symmetries of QCD. In thispaper we show that these results and extensions thereof can be obtained fromthe replica limit of a Toda lattice equation. This naturally leads to afactorized form into bosonic and fermionic QCD-like partition functions. In themicroscopic limit these partition functions are given by the static limit of achiral Lagrangian that follows from the symmetry breaking pattern. Inparticular, we elucidate the role of the singularity of the bosonic partitionfunction in the orthogonal polynomials approach. A detailed discussion of thespectral density for one and two flavors is given.