Dynamical Localization for Discrete and Continuous Random Schrr Odinger Operators
Dynamical Localization for Discrete and Continuous Random Schrr Odinger Operators
复制标题
离散和连续随机 Schrr Odinger 算子的动态定位
DOI：
--
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
Bi Evre
中科院分区：
文献类型：
--
作者：
F. Germinet;S. De;Bi Evre
我们证明了一大类随机薛定谔算子H！在λ 2（）和L2（）上，动力学定域成立，即对于适当的能量区间I和正真实的q，概率为1，supt r q（t）supt < PI（H！）t; jXj q PI（H！）t > < 1：这是一个快速下降的函数，t = e？iH！t和PI（H！）是H的光谱投影仪对应于间隔I。这一结果是通过控制H！在离散情况下，包括Bernouilli势（维数= 1）或奇异势（维数> 1）的安德森紧束缚模型，在连续情况下，包括安德森和随机朗道哈密顿量。
We show for a large class of random Schrr odinger operators H! on`2 () and on L 2 () that dynamical localization holds, i.e. that, with probability one, for a suitable energy interval I and for q a positive real, sup t r q (t) sup t < PI (H!)t; jXj q PI (H!)t > < 1: Here is a function of suuciently rapid decrease, t = e ?iH!t and PI (H!) is the spectral projector of H! corresponding to the interval I. The result is obtained through the control of the decay of the eigenfunc-tions of H! and covers, in the discrete case, the Anderson tight-binding model with Bernouilli potential (dimension = 1) or singular potential (> 1), and in the continuous case Anderson as well as random Landau Hamiltonians.