2020/01/05 by Kachkovskiy, Ilya
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2001.01314
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 (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.