论文标题
计算$ l^2 $本地化景观的随机方法
A stochastic method to compute the $L^2$ localisation landscape
论文作者
论文摘要
L. Herviou和J. H. Bardarson的$ l^2 $本地化景观是对M. Filoche和S. Mayboroda的本地化景观的概括。我们提出了一种随机方法来计算$ l^2 $本地化景观，该景观可以使用稀疏矩阵方法计算景观。我们还提出了$ L^2 $景观的能量过滤，该景观可用于在任何选择的能源范围内的能量。我们通过将$ l^2 $景观应用于安德森（Anderson）在一个和二维中的本地化模型，以及在量子霍尔效应模型中的本地化中，将这些建议的实用性。
The $L^2$ localisation landscape of L. Herviou and J. H. Bardarson is a generalisation of the localisation landscape of M. Filoche and S. Mayboroda. We propose a stochastic method to compute the $L^2$ localisation landscape that enables the calculation of landscapes using sparse matrix methods. We also propose an energy filtering of the $L^2$ landscape which can be used to focus on eigenstates with energies in any chosen range of the energy spectrum. We demonstrate the utility of these suggestions by applying the $L^2$ landscape to Anderson's model of localisation in one and two dimensions, and also to localisation in a model of the quantum Hall effect.
