On the relation between strong ballistic transport and exponential dynamical localization

Abstract

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.

Fixed a mistake in the proof of Lemma 3.1. Other minor corrections

References in corpus (1)

• Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems

Cited by in corpus (1)

• Ballistic transport for one-dimensional quasiperiodic Schrödinger operators