Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2007-11-05
PoS LAT2007:224,2007
Physics
High Energy Physics
High Energy Physics - Lattice
7 pages, talk given by L. Shifrin at the XXV International Symposium on Lattice Field Theory, Regensburg, Germany, 30 Jul - 4
Scientific paper
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 $\nu=0,1,2$.
Akemann Gernot
Bloch Jacques
Shifrin Leonid
Wettig Tilo
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