Quasiballistic Transport for Discrete One-Dimensional Quasiperidic Schr\"odinger Operators

We obtain (up to logarithmic scaling) the power-law lower bound Mₚ(Tₖ) Tₖ(1-δ)p on a subsequence Tₖ→∞, uniformly across $p>0$, for discrete one-dimensional quasiperiodic Schr\"odinger operators with frequencies satisfying β(α)>3/δminσγ. We achieve this by obtaining a quantitative ballistic lower bound for the Abel-averaged time evolution of general periodic Schr\"odinger operators in terms of the bandwidths. A similar result without uniformity, which assumes β(α)>C/δminσγ, was obtained earlier by Jitomirskaya and Zhang, for an implicit constant C<∞.