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arXiv 0711.0629hep-lat
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非零化学势下QCD的个别Dirac本征值分布：RMT预测和格点结果

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

Gernot Akemann, Jacques Bloch, Leonid Shifrin, Tilo Wettig

备注：
7 pages, talk given by L. Shifrin at the XXV International Symposium on Lattice Field Theory, Regensburg, Germany, 30 Jul - 4 Aug 2007
发表信息：
PoS LAT2007:224,2007
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摘要：

对于非零化学势$μ$的QCD，Dirac本征值在复平面上是散射的。在这种情况下，我们定义了个体特征值的排序概念，并从随机矩阵理论（RMT）中推导出个体特征值的分布。我们区分两种情况下依赖于参数$α=μ^2 F^2 V$，其中$V$是体积和$F$是熟悉的手征微扰理论的低能常数。对于小的$α$，我们使用Fredholm行列式展开，并观察到前几项已经给出了很好的近似。对于大的$α$，所有的谱相关是旋转不变的，并且可以导出精确的结果。我们比较RMT预测晶格数据，并在这两种情况下发现良好的协议在拓扑部门$ν=0,1,2$。

英文摘要：

For QCD at non-zero chemical potential $μ$, 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 $α=μ^2 F^2 V$, where $V$ is the volume and $F$ is the familiar low-energy constant of chiral perturbation theory. For small $α$, we use a Fredholm determinant expansion and observe that already the first few terms give an excellent approximation. For large $α$, 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 $ν=0,1,2$.

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