Quasiballistic transport for discrete one-dimensional quasiperiodic Schrödinger operators

• Published in: Journal of spectral theory
• Main Author: Haeming, Lian
• Format: Journal Article
• Language: English
• Published: 29.08.2025
• ISSN: 1664-039X; 1664-0403; 1664-0403
• DOI: 10.4171/jst/566

For discrete one-dimensional quasiperiodic Schrödinger operators with frequencies satisfying \beta(\alpha)>\bigl(\frac{3}{\delta}\bigr)\min_{\sigma}\gamma , 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 , where \gamma is the associated Lyapunov exponent and \sigma is the spectrum. We achieve this by obtaining a quantitative ballistic lower bound for the Abel-averaged entries of the time evolution operator associated with general periodic Schrödinger operators in terms of the bandwidths. A similar result which assumes \beta(\alpha)>\bigl(\frac{C}{\delta}\bigr)\min_{\sigma}\gamma , was obtained earlier by Jitomirskaya and Zhang, for an implicit constant C<\infty .