Universality in Chiral Random Matrix Theory at {beta} = 1 and {beta} = 4
Universality in Chiral Random Matrix Theory at {beta} = 1 and {beta} = 4
复制标题
{beta} = 1 和 {beta} = 4 时手性随机矩阵理论的普遍性
DOI：
10.1103/physrevlett.81.248
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发表时间：
1998
影响因子：
8.6
通讯作者：
J. Verbaarschot
中科院分区：
文献类型：
--
作者：
M. K. Sener;J. Verbaarschot
本文将实({beta}=1)和四元数实({beta}=4)矩阵元素的不变手征随机矩阵系综谱相关函数的核表示为相应的复厄米特随机矩阵系综核({beta}=2)。这些恒等式在高斯概率分布的情况下是精确的，并且在一定的光滑性假设下，它们对于任意有限多项式势是渐近有效的。它们通过Brezin和Neuberger提出的构造得到了证明。如Akemann，Damgaard，Magnea和Nishigaki所示，所有三个手性系综本征值接近于零的普遍行为随后从微观普适性出发，即{beta}=2。{版权所有}{ital1998}{italthe American Physitive Society}
In this paper the kernel for the spectral correlation functions of invariant chiral random matrix ensembles with real ({beta}=1 ) and quaternion real ({beta}=4 ) matrix elements is expressed in terms of the kernel of the corresponding complex Hermitian random matrix ensembles ({beta}=2 ). Such identities are exact in case of a Gaussian probability distribution and, under certain smoothness assumptions, they are shown to be valid asymptotically for an arbitrary finite polynomial potential. They are proved by means of a construction proposed by Brezin and Neuberger. Universal behavior of the eigenvalues close to zero for all three chiral ensembles then follows from microscopic universality for {beta}=2 as shown by Akemann, Damgaard, Magnea, and Nishigaki. {copyright} {ital 1998} {ital The American Physical Society}