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Title: Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results
Authors: Akemann, G
Bloch, J
Shifrin, L
Wettig, T
Keywords: Random Matrices;Lattice Gauge Theory
Issue Date: 2007
Publisher: Proceedings of Science PoS(LATTICE 2007)224
Citation: , Oct 2007
Abstract: For QCD at non-zero chemical potential $\mu$, the Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalues in this case and derive the distributions of individual eigenvalues from random matrix theory (RMT). We distinguish two cases depending on the parameter $\alpha=\mu^2 F^2 V$, where $V$ is the volume and $F$ is the familiar low-energy constant of chiral perturbation theory. For small $\alpha$, we use a Fredholm determinant expansion and observe that already the first few terms give an excellent approximation. For large $\alpha$, all spectral correlations are rotationally invariant, and exact results can be derived. We compare the RMT predictions to lattice data and in both cases find excellent agreement in the topological sectors $\nu=0,1,2$.
Appears in Collections:Mathematical Physics
Dept of Mathematics Research Papers
Mathematical Sciences

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