强弹道输运与指数动力学局域化的关系
On the relation between strong ballistic transport and exponential dynamical localization
摘要：
我们建立了一个家庭的离散准周期薛定谔算子的强弹道输运的结果指数动力学本地化的对偶家庭。后者基本上是由Jitomirskaya和Krüger在单频率设置中以及由Ge-You-Zhou在多频率情况下所示的。在这两种情况下，我们得到了$\frac{1}{T}X(T)$到渐近速度算子$Q$的强收敛性，从而改进了最近由Zhao所作的微扰结果，并提供了已知最强的弹道运动形式.在一个频率设置，这种方法允许处理丢番图频率非微扰，也考虑弱刘维的情况下。
英文摘要：
We establish strong ballistic transport for a family of discrete quasiperiodic Schrödinger operators as a consequence of exponential dynamical localization for the dual family. The latter has been, essentially, shown by Jitomirskaya and Krüger in the one-frequency setting and by Ge--You--Zhou in the multi-frequency case. In both regimes, we obtain strong convergence of $\frac{1}{T}X(T)$ to the asymptotic velocity operator $Q$, which improves recent perturbative results by Zhao and provides the strongest known form of ballistic motion. In the one-frequency setting, this approach allows to treat Diophantine frequencies non-perturbatively and also consider the weakly Liouville case.
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