论文标题
通过Bernoulli随机化为DelONO操作员的本地化
Localisation for Delone operators via Bernoulli randomisation
论文作者
论文摘要
Delone操作员是多维欧几里得空间中的Schrödinger运算符，其潜力由以Delone集合点为中心的给定“单位势”的所有翻译总和。在本文中，我们使用随机化来研究DeLone操作员家族的动态定位。我们通过适当地为DeLone集合添加更多积分并引入I.I.D.来做到这一点。 Bernoulli随机变量作为附加点的耦合常数。最新版本的多尺度分析可以访问由此产生的非毒性连续体安德森模型。这里的新成分是初始长度尺度估计值，由于非周期背景潜力，其证明受到阻碍。它是通过使用定量独特延续原理获得的。作为应用，我们获得了有关动态定位的概率和拓扑陈述。除其他外，我们还表明，在频谱底部，相关的Delone运算符在Delone集合的空间中表现出动态定位的DeLone集。
Delone operators are Schrödinger operators in multi-dimensional Euclidean space with a potential given by the sum of all translates of a given "single-site potential" centred at the points of a Delone set. In this paper, we use randomisation to study dynamical localisation for families of Delone operators. We do this by suitably adding more points to a Delone set and by introducing i.i.d. Bernoulli random variables as coupling constants at the additional points. The resulting non-ergodic continuum Anderson model with Bernoulli disorder is accessible to the latest version of the multiscale analysis. The novel ingredient here is the initial length-scale estimate whose proof is hampered due to the non-periodic background potential. It is obtained by the use of a quantitative unique continuation principle. As applications we obtain both probabilistic and topological statements about dynamical localisation. Among others, we show that Delone sets for which the associated Delone operators exhibit dynamical localisation at the bottom of the spectrum are dense in the space of Delone sets.
