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Absolutely continuous spectrum of multifrequency quasiperiodic Schrödinger operator
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.jfa.2020.108632
Xuanji Hou , Jing Wang , Qi Zhou

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

中文翻译:

多频准周期薛定谔算子的绝对连续谱

在本文中,我们证明对于任何$d$-频率解析拟周期薛定谔算子,如果频率是弱Liouvillean,并且势足够小,那么对应的算子具有绝对连续谱。此外,在$d=2$的情况下,我们甚至建立了在小电位和一些超Liouvillean频率下交流频谱的存在,由于最近Avila和Jitomirskaya的反例,这个结果是最优的。
更新日期:2020-10-01
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