Quasiballistic transport for discrete one-dimensional quasiperiodic Schrödinger operators
Year: 2025
Type: article
Abstract: 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 .
Source: Journal of Spectral Theory
DOI: 10.4171/jst/566
Author: Lian Haeming
Institution: Queen Mary University of London
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413827555