Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results

Akemann G, Bloch J, Shifrin L, Wettig T (2007)
In: PoS. LAT2007. .

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Abstract
For QCD at non-zero chemical potential $\mu$, the Dirac eigenvalues arescattered in the complex plane. We define a notion of ordering for individualeigenvalues in this case and derive the distributions of individual eigenvaluesfrom random matrix theory (RMT). We distinguish two cases depending on theparameter $\alpha=\mu^2 F^2 V$, where $V$ is the volume and $F$ is the familiarlow-energy constant of chiral perturbation theory. For small $\alpha$, we use aFredholm determinant expansion and observe that already the first few termsgive an excellent approximation. For large $\alpha$, all spectral correlationsare rotationally invariant, and exact results can be derived. We compare theRMT predictions to lattice data and in both cases find excellent agreement inthe topological sectors $\nu=0,1,2$.
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Akemann G, Bloch J, Shifrin L, Wettig T. Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results. In: PoS. Vol LAT2007. 2007.
Akemann, G., Bloch, J., Shifrin, L., & Wettig, T. (2007). Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results. PoS, LAT2007.
Akemann, G., Bloch, J., Shifrin, L., and Wettig, T. (2007). “Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results” in PoS, vol. LAT2007,.
Akemann, G., et al., 2007. Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results. In PoS. no.LAT2007
G. Akemann, et al., “Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results”, PoS, vol. LAT2007, 2007.
Akemann, G., Bloch, J., Shifrin, L., Wettig, T.: Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results. PoS. LAT2007, (2007).
Akemann, Gernot, Bloch, Jacques, Shifrin, Leonid, and Wettig, Tilo. “Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results”. PoS. 2007.Vol. LAT2007.
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