Giorgio Cipolloni, Ron Peled, Jeffrey Schenker, Jacob Shapiro
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引用次数: 0
摘要
我们证明，当 \(W \ll N^{1/4}\) 时，带宽为 W 的一大类高斯随机带矩阵在所有能量下都表现出动态的安德森定位。证明使用了分数矩方法（Aizenman 和 Molchanov 在 Commun Math Phys 157(2):245-278, 1993. https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-157/issue-2/Localizationat-large-disorder-and-at-extreme-energies-an/cmp/1104253939.full）和自适应 Mermin-Wagner 式偏移。
Dynamical Localization for Random Band Matrices Up to $$W\ll N^{1/4}$$
We prove that a large class of \(N\times N\) Gaussian random band matrices with band width W exhibits dynamical Anderson localization at all energies when \(W \ll N^{1/4}\). The proof uses the fractional moment method (Aizenman and Molchanov in Commun Math Phys 157(2):245–278, 1993. https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-157/issue-2/Localizationat-large-disorder-and-at-extreme-energies–an/cmp/1104253939.full) and an adaptive Mermin–Wagner style shift.
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