QCD at nonzero density and nontrivial topology: lattice simulations and random-matrix predictions

Predictions of Random Matrix Theory for the spectrum of the QCD Dirac operator at nonzero chemical potential and nontrivial topology will be compared to data generated by lattice QCD simulations. For this purpose, one needs to work with a lattice Dirac operator which satisfies the Ginsparg-Wilson condition. The question of how a chemical potential should be introduced in such an operator has not yet been addressed in the literature and, therefore, has to be answered in this project. In addition, several related problemes will be investigated: the applicability of Random Matrix Theory in the regime of strong nonhermiticity, the determination of the Thouless energy at nonzero density, and the extraction of the chiral condensate from the lattice data by means of random matrix predictions.