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arXiv 0912.3109hep-lat
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QCD中的涨落、相关性和符号问题

Fluctuations, correlations and the sign problem in QCD

M. P. Lombardo, K. Splittorff, J. J. M. Verbaarschot

摘要:

我们研究了非零夸克化学势下QCD中费米子行列式的相位角和幅值的分布以及它与手征凝聚和重子数的关联。结果是由手征微扰理论(ChPT)中的单圈阶,以及在一维欧几里德QCD中的分析和数值计算得出的。我们发现当夸克质量进入狄拉克算符的谱时,费米子行列式的相位分布发生了质的变化:从高斯分布变为洛伦兹分布。我们还探讨了一些观测量仍然弱相关的费米子行列式的相位,即使符号问题是严重的可能性。我们讨论了在非零重子化学势下我们的研究结果对QCD晶格模拟的实际意义。

英文摘要:

We study the distribution of the phase angle and the magnitude of the fermion determinant as well as its correlation with the chiral condensate and the baryon number for QCD at non-zero quark chemical potential. Results are derived to one-loop order in Chiral Perturbation Theory (ChPT), as well as by analytical and numerical calculations in QCD in one Euclidean dimension. We find a qualitative change of the distribution of the phase of the fermion determinant when the quark mass enters the spectrum of the Dirac operator: it changes from a periodicized Gaussian distribution to a periodicized Lorentzian distribution. We also explore the possibility that some observables remain weakly correlated with the phase of the fermion determinant even though the sign problem is severe. We discuss the practical implications of our findings on lattice simulations of QCD at non-zero baryon chemical potential.

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