García-García Antonio M, Osborn James C
Laboratoire de Physique Théorique et Modèles Statistiques, Bâtiment 100, Université de Paris-Sud, 91405 Orsay Cedex, France.
Phys Rev Lett. 2004 Sep 24;93(13):132002. doi: 10.1103/PhysRevLett.93.132002. Epub 2004 Sep 22.
We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the dimensionless Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.
我们将量子色动力学（QCD）狄拉克算子建模为具有适当手征对称性的幂律随机带状矩阵（RBM）。我们的动机源于狄拉克算子在瞬子零模基下的形式以及相应的瞬子规范背景。我们将该模型的谱关联与瞬子液体模型（ILM）的谱关联进行比较，发现二者在远超 Thouless 能量的情况下具有一致性。在谱的主体部分，RBM 的无量纲 Thouless 能量与系统大小的平方根成比例，这与 ILM 和手征微扰理论一致。在原点附近，RBM 的标度与主体部分相同，这与手征微扰理论相符，但与 ILM 不符。最后，我们讨论了应如何修改此 RBM，以便描述有限温度手征恢复转变时 QCD 狄拉克算子的谱关联。
