Absolutely Continuous Spectrum of Multifrequency Quasiperiodic Schrödinger operator

Abstract

In this paper, we prove that for any $d$-frequency analytic quasiperiodic Schrödinger 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 $d=2$, 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.

References in corpus (1)

• Almost reducibility and absolute continuity I