Absolutely Continuous Spectrum of Multifrequency Quasiperiodic Schr\"odinger operator
Dynamical Systems
2020-04-10 v1 Spectral Theory
Abstract
In this paper, we prove that for any -frequency analytic quasiperiodic Schr\"odinger operator, if the frequency is weak Liouvillean, and the potential is small enough, then the corresponding operator has absolutely continuous spectrum. Moreover, in the case , we even establish the existence of ac spectrum under small potential and some super-Liouvillean frequency, and this result is optimal due to a recent counterexample of Avila and Jitomirskaya.
Keywords
Cite
@article{arxiv.2004.04409,
title = {Absolutely Continuous Spectrum of Multifrequency Quasiperiodic Schr\"odinger operator},
author = {Xuanji Hou and Jing Wang and Qi Zhou},
journal= {arXiv preprint arXiv:2004.04409},
year = {2020}
}