发帖
雷达卡
摘要翻译：
对于NxN随机矩阵(GOE，GUE，GSE)的经典高斯系综，在时间序列δ(n)中，刻画了n个展开特征值的涨落。本文用蒙特卡罗模拟方法研究了beta-Hermite系综与beta（零或正）的关系。当beta>0(1<n<n)时，delta(n)的涨落和自相关函数与n成对数变化。GOE(beta=1)和GUE(beta=2)的高阶矩delta(n)的简单对数行为对任何正β都是有效的，并由其方差线性依赖于ln(n)的高斯分布来解释。对于三个高斯系综的delta(n)级数，用小波分析证明了1/f噪声是beta和n的函数。当beta从1减小到0时，对于给定的足够大的n,从beta=1的1/f噪声到beta=0的1/f^2噪声的演化是不均匀的，在最细的尺度上是a~1/f^2噪声，在最粗的尺度上是a~1/f噪声。随着beta的减小，以a~1/f^2噪声为主的尺度范围逐渐增大。渐近地，当beta=0时为1/f^2噪声，而当beta为正时为1/f噪声。
---
英文标题：
《Spectral fluctuations of tridiagonal random matrices from the
beta-Hermite ensemble》
---
作者：
C. Male, G. Le Caer and R. Delannay
---
最新提交年份：
2007
---
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
--
---
英文摘要：
A time series delta(n), the fluctuation of the nth unfolded eigenvalue was recently characterized for the classical Gaussian ensembles of NxN random matrices (GOE, GUE, GSE). It is investigated here for the beta-Hermite ensemble as a function of beta (zero or positive) by Monte Carlo simulations. The fluctuation of delta(n) and the autocorrelation function vary logarithmically with n for any beta>0 (1<<n<<N). The simple logarithmic behavior reported for the higher-order moments of delta(n) for the GOE (beta=1) and the GUE (beta=2) is valid for any positive beta and is accounted for by Gaussian distributions whose variances depend linearly on ln(n). The 1/f noise previously demonstrated for delta(n) series of the three Gaussian ensembles, is characterized by wavelet analysis both as a function of beta and of N. When beta decreases from 1 to 0, for a given and large enough N, the evolution from a 1/f noise at beta=1 to a 1/f^2 noise at beta=0 is heterogeneous with a ~1/f^2 noise at the finest scales and a ~1/f noise at the coarsest ones. The range of scales in which a ~1/f^2 noise predominates grows progressively when beta decreases. Asymptotically, a 1/f^2 noise is found for beta=0 while a 1/f noise is the rule for beta positive.
---
PDF链接：
https://arxiv.org/pdf/704.359
京公网安备 11010802022788号
