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摘要翻译：
用Monte Carlo方法研究了beta-Hermite系综（beta-HE）随机矩阵展开谱最近邻能级间的间距分布。在本征值的经典静电解释中，β-He的随机矩阵是实对称和三对角的，其中β可以取任意正值，是温度的倒数。广义gamma分布是最近邻间距(NNS)分布的极好近似，但仍然是简单的。它们既解释了s趋于零时的能级排斥，又解释了s范围内NNS分布的整体形状，这对于实验或大多数数值模拟都是可行的。GOE(beta=1)的精确NNS分布用广义gamma分布比用Wigner推测更好地描述，而当β大于~2时，最佳广义gamma近似基本上与Wigner推测一致。由beta-HE得到的矩阵特征值之间的最小NN间距分布，无论是由计算的特征值还是由展开的特征值都是Brody分布。
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英文标题：
《Nearest-neigbor spacing distributions of the beta-Hermite ensemble of
random matrices》
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作者：
G. Le Caer, C. Male and R. Delannay
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：Disordered Systems and Neural Networks 无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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英文摘要：
The distributions of the spacing s between nearest-neighbor levels of unfolded spectra of random matrices from the beta-Hermite ensemble (beta-HE) is investigated by Monte Carlo simulations. The random matrices from the beta-HE are real-symmetric and tridiagonal where beta, which can take any positive value, is the reciprocal of the temperature in the classical electrostatic interpretation of eigenvalues. Generalized gamma distributions are shown to be excellent approximations of the nearest-neighbor spacing (NNS) distributions for any beta while being still simple. They account both for the level repulsion when s tends to zero and for the whole shape of the NNS distributions in the range of s which is accessible to experiment or to most numerical simulations. The exact NNS distribution of the GOE (beta=1) is in particular significantly better described by a generalized gamma distribution than it is by the Wigner surmise while the best generalized gamma approximation coincides essentially with the Wigner surmise for beta larger than ~2. The distributions of the minimum NN spacing between eigenvalues of matrices from the beta-HE, obtained both from as-calculated eigenvalues and from unfolded eigenvalues are Brody distributions.
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PDF链接：
https://arxiv.org/pdf/704.3261
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