Delocalization for the 3D discrete random Schrödinger operator at weak disorder
Delocalization for the 3D discrete random Schrödinger operator at weak disorder
复制标题
弱无序下 3D 离散随机薛定谔算子的离域
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
R. Kirby
中科院分区：
文献类型：
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作者：
C. Liaw;W. King;R. Kirby
我们采用了最近开发的方法(Liw 2013 J.Stat.太棒了。153 1022-38)研究了三维离散随机薛定谔算符在小无序状态下的扩张态的存在性。在小无序时离域的结论与其他数值和实验观察结果一致(例如，见(Lagendijk等人，2009Phys.今天82 24-29))。此外，这项工作还对数值方法及其实施进行了验证。这种方法不是基于标度理论，消除了该领域以往数值方法常见的边界条件问题。同时，就像任何数值实验一样，人们不能完全确定地排除有限尺寸效应。我们的工作可以被认为是对Lanczos算法的一种新的、完全不同的使用；后验检验表明，正交性损失非常小。在迭代应用离散随机薛定谔算符后，我们数值地跟踪最初位于原点的波包的‘整体分布’(这里：我们最有可能找到电子的位置的分布)。
We apply a recently developed approach (Liaw 2013 J. Stat. Phys. 153 1022–38) to study the existence of extended states for the three-dimensional discrete random Schrödinger operator at small disorder. The conclusion of delocalization at small disorder agrees with other numerical and experimental observations (see e.g. (Lagendijk et al 2009 Phys. Today 82 24–29)). Further the work furnishes a verification of the numerical approach and its implementation. Not being based on scaling theory, this method eliminates problems due to boundary conditions, common to previous numerical methods in the field. At the same time, as with any numerical experiment, one cannot exclude finite-size effects with complete certainty. Our work can be thought of as a new and quite different use of Lanczos' algorithm; a posteriori tests show that the orthogonality loss is very small. We numerically track the ‘bulk distribution’ (here: the distribution of where we most likely find an electron) of a wave packet initially located at the origin, after iterative application of the discrete random Schrödinger operator.