Dual landscapes in Anderson localization on discrete lattices
Dual landscapes in Anderson localization on discrete lattices
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DOI：
10.1209/0295-5075/109/47001
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发表时间：
2015-02-01
期刊：
影响因子：
1.8
通讯作者：
Filoche, M.
中科院分区：
文献类型：
--
作者：
Lyra, M. L.;Mayboroda, S.;Filoche, M.
最近证明，连续无序介质中驻波的局部化子区域是由隐藏景观控制的，该隐藏景观是用波算子表示的狄利克雷问题的解。在这个理论中，安德森局域约束的强度是由这种景观决定的，并且随着能量的增加而不断减小。然而，这种情况必须在离散晶格中改变，其中靠近第一布里渊区边缘的本征模与低能模一样局域化。在这里，我们证明在一维离散晶格中，低能模式和高能模式的局域化由两种不同的景观控制，高能景观是使用哈密顿量的对称性从低能问题推导出来的对偶狄利克雷问题的解。我们使用具有随机现场势的一维紧束缚哈密顿量作为原型模型来说明此特征。此外，我们表明，除了揭示安德森局域化的子区域之外，这些双重景观还提供了能谱上局域化长度的准确总体估计，特别是在弱无序状态下。编辑精选 版权所有 (C) EPLA，2015
The localization subregions of stationary waves in continuous disordered media have been recently demonstrated to be governed by a hidden landscape that is the solution of a Dirichlet problem expressed with the wave operator. In this theory, the strength of Anderson localization confinement is determined by this landscape, and continuously decreases as the energy increases. However, this picture has to be changed in discrete lattices in which the eigenmodes close to the edge of the first Brillouin zone are as localized as the low energy ones. Here we show that in a 1D discrete lattice, the localization of low and high energy modes is governed by two different landscapes, the high energy landscape being the solution of a dual Dirichlet problem deduced from the low energy one using the symmetries of the Hamiltonian. We illustrate this feature using the one-dimensional tight-binding Hamiltonian with random on-site potentials as a prototype model. Moreover we show that, besides unveiling the subregions of Anderson localization, these dual landscapes also provide an accurate overall estimate of the localization length over the energy spectrum, especially in the weak-disorder regime. editor's choice Copyright (C) EPLA, 2015