Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice
Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice
复制标题
二维晶格上安德森伯努利模型边缘附近的局域化
DOI：
10.1007/s00222-019-00910-4
复制
发表时间：
2018
影响因子：
3.1
通讯作者：
Charles K. Smart
中科院分区：
文献类型：
--
作者：
Jian Ding;Charles K. Smart
我们考虑二维晶格上由拉普拉斯加伯努利势给出的哈密顿量。我们证明了，对于足够接近谱边缘的能量，大平方上的预解很可能呈指数衰减。这意味着几乎可以肯定安德森局域化的能量足够接近光谱的边缘。我们的证明遵循Bourain-Kenig的程序，使用Buhovsky-Logunov-Malinnikova-Sodin的Liouville定理启发的一个新的唯一延拓结果。
We consider a Hamiltonian given by the Laplacian plus a Bernoulli potential on the two dimensional lattice. We prove that, for energies sufficiently close to the edge of the spectrum, the resolvent on a large square is likely to decay exponentially. This implies almost sure Anderson localization for energies sufficiently close to the edge of the spectrum. Our proof follows the program of Bourgain–Kenig, using a new unique continuation result inspired by a Liouville theorem of Buhovsky–Logunov–Malinnikova–Sodin.