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：

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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。