Hermitian Wilson Dirac算子的随机矩阵理论和chGUE-GUE跃迁
Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
摘要：
本文引入了一个随机双矩阵模型，该模型在一个手征厄米特（2n +nu）x（2n+nu）矩阵和一个无对称性的厄米矩阵之间插值.这些分别取自手性高斯酉包络（chGUE）和高斯酉包络（GUE）。在chGUE附近的微观大n极限（我们称之为弱非手征极限）中，该理论与Wilson手征微扰理论中的配分函数一一对应，如文献[1]中介绍的相关的双矩阵模型. [20，21]。对于一般数量的味道和矩形块矩阵中的chGUE部分，我们推导出的配分函数显示Pfweian结构的特征值表示。在猝灭的情况下，nu= 0，1，我们推导出所有的频谱相关函数在我们的模型有限n，斜正交多项式。后者表示为标准拉盖尔多项式上的高斯积分。在弱非手征的微观极限，这产生了所有相应的淬火本征值关联函数的埃尔米特威尔逊运营商。
英文摘要：
We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit) this theory is in one to one correspondence to the partition function of Wilson chiral perturbation theory in the epsilon regime, such as the related two matrix-model previously introduced in refs. [20,21]. For a generic number of flavours and rectangular block matrices in the chGUE part we derive an eigenvalue representation for the partition function displaying a Pfaffian structure. In the quenched case with nu=0,1 we derive all spectral correlations functions in our model for finite-n, given in terms of skew-orthogonal polynomials. The latter are expressed as Gaussian integrals over standard Laguerre polynomials. In the weakly non-chiral microscopic limit this yields all corresponding quenched eigenvalue correlation functions of the Hermitian Wilson operator.
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