Multifractality and scaling in disordered mesoscopic systems
Multifractality and scaling in disordered mesoscopic systems
复制标题
无序介观系统中的多重分形和缩放
DOI：
10.1007/bf01324339
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
M. Janssen
中科院分区：
文献类型：
--
作者：
W. Pook;M. Janssen
本文提出了一种新的方法来研究介观观测量的标度性质及其在无序金属-绝缘体相变系统中的分布。在这类系统中，量子干涉效应导致本征态的多重分形结构，其尺度远小于跃迁的关联长度，可以用一组指数f（α）谱来描述。对（α）谱的分析可以推广到任何尺度变量。多重分形表示这些变量的广泛分布。如果跃迁仅由一个关联长度决定，则归一化标度变量的f（α）谱必定是普适的。相关长度的临界指数v由α（0）和归一化标度指数x ∶v−1=α（0）+x确定，其中f（α）取其最大值。作为一个说明性的例子，我们数值计算了强磁场中二维无序电子系统临界区本征态的f（α）谱。我们发现相似（α）谱表明标度变量的普遍对数正态分布。
We suggest a new method for investigating scaling properties of mesoscopic observables and their distributions in disordered systems showing metal-insulator transition. In such systems quantum interference effects lead to multifractal structure of eigenstates on scales much smaller than the correlation length of the transition which can be described by a set of exponents, thef(α) spectrum. The analysis off(α) spectra can be extended to any scaling variable. Multifractality is an indication for broad distributions of these variables. If the transition is governed by one correlation length only then thef(α) spectra of normalized scaling variables must be universal. The critical exponentvof the correlation length is determined by the value α(0) wheref(α) takes its maximum and the scaling exponent of normalizationx∶v−1=α(0)+x. As an illustrative example we calculate numerically thef(α) spectra of eigenstates in the critical regime of 2ddisordered electron systems in high magnetic fields. We find similarf(α) spectra indicating universal log-normal distributions of scaling variables.