On the relation between strong ballistic transport and exponential dynamical localization
Spectral Theory
2020-01-14 v2 Mathematical Physics
math.MP
Abstract
We establish strong ballistic transport for a family of discrete quasiperiodic Schr\"odinger operators as a consequence of exponential dynamical localization for the dual family. The latter has been, essentially, shown by Jitomirskaya and Kr\"uger in the one-frequency setting and by Ge--You--Zhou in the multi-frequency case. In both regimes, we obtain strong convergence of to the asymptotic velocity operator , 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.
Cite
@article{arxiv.2001.01314,
title = {On the relation between strong ballistic transport and exponential dynamical localization},
author = {Ilya Kachkovskiy},
journal= {arXiv preprint arXiv:2001.01314},
year = {2020}
}
Comments
Fixed a mistake in the proof of Lemma 3.1. Other minor corrections