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The distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and Lattice results

Presenter: Leonid Shifrin — Brunel University West London

Gernot Akemann, Jacques Bloch, Leonid Shifrin, Tilo Wettig

For QCD at non-zero chemical potential mu, Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalue distributions in the general case of complex eigenvalues. In our Random Matrix Theory (RMT) predictions we distinguish 2 cases. At small mu<<1 (weak non-hermiticity) we use a Fredholm determinant expansion where already the first few terms give an excellent approximation. For mu=1 (maximally strong non-hermiticity) case, all spectral correlations are rotational invariant and exact distributions are derived. When comparing RMT predictions and Lattice data we find agreement at weak non-hermiticity for several values of mu and topological sectors nu=0,1. For the largest mu the data show an excellent agreement with our strong non-hermiticity predictions at nu=0 and 1.