论文标题
绝对连续的多频准式Schrödinger操作员
Absolutely Continuous Spectrum of Multifrequency Quasiperiodic Schrödinger operator
论文作者
论文摘要
在本文中，我们证明，对于任何$ d $ - 频率分析的quasiperiodicschrödinger运算符，如果频率较弱，并且电势足够小，则相应的操作员具有绝对连续的频谱。此外，在$ d = 2 $的情况下，我们甚至确定了在较小的潜力和一些超级频率下的交流光谱的存在，并且由于最近对Avila和Jitomirskaya的反例，该结果是最佳的。
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.
