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超统计中的随机矩阵理论。

Random matrix theory within superstatistics.

作者信息

Abul-Magd A Y

机构信息

Department of Mathematics, Faculty of Science,Zagazig University, Zagazig, Egypt.

出版信息

Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Dec;72(6 Pt 2):066114. doi: 10.1103/PhysRevE.72.066114. Epub 2005 Dec 13.

DOI:10.1103/PhysRevE.72.066114
PMID:16486017
Abstract

We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable. We illustrate the method by calculating the level density, the nearest-neighbor-spacing distributions, and the two-level correlation functions for systems in transition from order to chaos. The calculated spacing distribution fits the resonance statistics of random binary networks obtained in a recent numerical experiment.

摘要

我们根据最近提出的超统计概念的基本规定,提出了随机矩阵理论的一种推广。假设平均能级间距本身是一个随机变量,那么具有混合规则-混沌动力学系统的谱特征表示为标准理论中相应量的加权平均值。我们通过计算从有序到混沌转变过程中系统的能级密度、最近邻间距分布和两能级关联函数来说明该方法。计算得到的间距分布与最近数值实验中获得的随机二元网络的共振统计结果相符。

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