We obtain (up to logarithmic scaling) the power-law lower bound $M_{ p}(T_{ k})\gtrsim T_{ k}^{ (1-\delta)p}$ on a subsequence $T_{ k}\rightarrow\infty$, uniformly across $p>0$, for discrete one-dimensional quasiperiodic Schr\"odinger operators with frequencies satisfying $\beta(\alpha)>\frac{ 3}{ \delta}\min_{ \sigma}\gamma$. 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 $\beta(\alpha)>\frac{ C}{ \delta}\min_{ \sigma}\gamma$, was obtained earlier by Jitomirskaya and Zhang, for an implicit constant $C<\infty$.
Categories: math.SP