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Absolutely Continuous Spectrum of Multifrequency Quasiperiodic Schrodinger operator

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 نشر من قبل Zhou Qi
 تاريخ النشر 2020
  مجال البحث
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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.



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