Multifractal analysis with the probability density function at the three-dimensional anderson transition.
Multifractal analysis with the probability density function at the three-dimensional anderson transition.
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使用三维安德森转变处的概率密度函数进行多重分形分析。
DOI：
10.1103/physrevlett.102.106406
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发表时间：
2008
影响因子：
8.6
通讯作者：
R. Römer
中科院分区：
文献类型：
--
作者：
Alberto Rodríguez;L. J. Vasquez;R. Römer
在三维Anderson模型中，研究了临界波函数振幅的概率密度函数。我们给出了PDF和多重分形谱f(α)之间的形式表达式，其中适当地分析了有限尺寸修正的作用。我们证明了PDF的非高斯性和对称关系的存在。从PDF中，我们提取关于f(α)在临界点的信息，例如负分维的存在和可能存在终止点。基于PDF的多重分形分析被证明是一种有效的替代基于逆参与率比例的标准方法。
The probability density function (PDF) for critical wave function amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of finite-size corrections is properly analyzed. We show the non-Gaussian nature and the existence of a symmetry relation in the PDF. From the PDF, we extract information about f(alpha) at criticality such as the presence of negative fractal dimensions and the possible existence of termination points. A PDF-based multifractal analysis is shown to be a valid alternative to the standard approach based on the scaling of inverse participation ratios.