论文标题
随机矩阵应用到软光谱
Random matrices applications to soft spectra
论文作者
论文摘要
最近发现，光谱的统计理论的方法可以是远离汉密尔顿系统水平的光谱的有用工具。几个例子来自定量语言学和聚合物等区域。本研究的目的是通过执行更全面的光谱分析来加深这种方法，以衡量局部和远程统计。我们发现，作为一个常见的特征，这种光谱可以表现出一种情况，在这种情况下，局部统计数据相对淬火，而远程统计数据显示出很大的波动。通过结合标准随机矩阵理论（RMT）的扩展并考虑长光谱，我们证明了这种现象是在RMT频谱中引入弱混乱或在Poisson制度中起作用时会发生这种现象。我们表明，远程统计数据遵循泰勒定律，这表明在这种光谱中存在波动缩放（FS）机制。
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics and polymers. The purpose of the present study is to deepen this kind of approach by performing a more comprehensive spectral analysis that measures both the local and long-range statistics. We have found that, as a common feature, spectra of this kind can exhibit a situation in which local statistics are relatively quenched while the long range ones show large fluctuations. By combining extensions of the standard Random Matrix Theory (RMT) and considering long spectra, we demonstrate that this phenomenon occurs when weak disorder is introduced in a RMT spectrum or when strong disorder acts in a Poisson regime. We show that the long-range statistics follow the Taylor law, which suggests the presence of a fluctuation scaling (FS) mechanism in this kind of spectra.
