一维宽无序量子传输的统计特性
Statistics of quantum transmission in one dimension with broad disorder
摘要：
研究了由一系列独立散射单元构成的一维无序系统中量子传输的统计特性。每个单元的特征在于其长度和其作用，其作用与通过该单元的传输概率的对数成比例。单位作用和长度是独立的随机变量，具有窄或宽的共同分布。这项调查的动机是无序系统的非平稳随机势的波动增长与距离的结果。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值，可以区分出四个阶段。样品的行动，这是成比例的对数的电导在整个样品中，被发现服从波动的标度律，因此是非自平均，在三个四个阶段。根据上述两个指数的值，样本动作通常可以随着样本长度比线性增长更慢地增长（欠定位），比线性增长更快地增长（超定位），或者线性增长但具有非平凡的样本到样本波动（波动定位）。
英文摘要：
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).
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