随机势场中一维非线性薛定谔方程Anderson模型的统计性质
Statistical Properties of the one dimensional Anderson model relevant for the Nonlinear Schrödinger Equation in a random potential
摘要：
计算了Anderson模型的四个本征函数组的重叠和的统计性质以及四个本征能的组合。一些分布被发现是标度函数，正如预期的本地化的标度理论。这些使得能够在超出计算资源的情况下计算分布。这些分布是非常重要的探索非线性薛定谔方程（NLSE）在一个随机的潜力，因为在一些探索中，我们研究的条款被认为是噪声和目前的工作描述其统计特性。
英文摘要：
The statistical properties of overlap sums of groups of four eigenfunctions of the Anderson model for localization as well as combinations of four eigenenergies are computed. Some of the distributions are found to be scaling functions, as expected from the scaling theory for localization. These enable to compute the distributions in regimes that are otherwise beyond the computational resources. These distributions are of great importance for the exploration of the Nonlinear Schrödinger Equation (NLSE) in a random potential since in some explorations the terms we study are considered as noise and the present work describes its statistical properties.
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