Massive partition functions and complex eigenvalue correlations in matrix models with symplectic symmetry
Massive partition functions and complex eigenvalue correlations in matrix models with symplectic symmetry
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辛对称矩阵模型中的大量配分函数和复特征值相关性
DOI：
10.1016/j.nuclphysb.2006.12.008
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
F. Basile
中科院分区：
文献类型：
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作者：
G. Akemann;F. Basile
我们计算随机矩阵辛和手征辛系综的非厄米特扩展的所有大规模配分函数或特征多项式及其复本征值相关函数。我们的结果是有效的一般重量函数没有退化的质量参数。我们导出的表达式是根据复平面上斜正交多项式的Pfweian和它们的核给出的。它们比具有真实的特征值的辛矩阵模型的相应表达式简单得多，并且我们明确地展示了如何在厄米极限下恢复这些表达式。这解释了三个不同的内核作为四元数矩阵元素的外观，这里是一个内核的导数。
We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are valid for general weight functions without degeneracies of the mass parameters. The expressions we derive are given in terms of the Pfaffian of skew orthogonal polynomials in the complex plane and their kernel. They are much simpler than the corresponding expressions for symplectic matrix models with real eigenvalues, and we explicitly show how to recover these in the Hermitean limit. This explains the appearance of three different kernels as quaternion matrix elements there in terms of derivatives of a single kernel here.