Statistics of quantum transmission in one dimension with broad disorder
Statistics of quantum transmission in one dimension with broad disorder
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宽无序一维量子传输统计
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
J. Luck
中科院分区：
文献类型：
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作者：
D. Boose;J. Luck
我们研究了由一系列独立的散射单元模拟的一维无序系统的量子传输统计特性。每个单元的特征在于其长度和作用，这与通过该单元的传输概率的对数成正比。单位动作和长度是独立的随机变量，具有或窄或宽的共同分布。这项研究的动机是关于具有非平稳随机势的无序系统的结果，该无序系统的涨落随距离增长。在固定总样本长度的统计系综中，根据表征单位作用和长度分布的指数的值，可以区分四个阶段。在四个阶段中的三个阶段中，样品的作用与样品上电导的对数成正比，遵循波动的标度定律，因此是非自平均的。根据上述两个指数的值，样本作用通常可能随着样本长度而不是线性增长(欠局部化)，而是比线性增长(超局部化)更快，或者随着样本之间的非平凡波动(波动局部化)而线性增长。
We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by its length and by its action, which is proportional to the logarithm of the transmission probability through this unit. Unit actions and lengths are independent random variables, with a common distribution that is either narrow or broad. This investigation is motivated by results on disordered systems with non-stationary random potentials whose fluctuations grow with distance. In the statistical ensemble at fixed total sample length four phases can be distinguished, according to the values of the indices characterizing the distribution of the unit actions and lengths. The sample action, which is proportional to the logarithm of the conductance across the sample, is found to obey a fluctuating scaling law, and therefore to be non-self-averaging, in three of the four phases. According to the values of the two above-mentioned indices, the sample action may typically grow less rapidly than linearly with the sample length (underlocalization), more rapidly than linearly (superlocalization), or linearly but with non-trivial sample-to-sample fluctuations (fluctuating localization).