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arXiv 2102.02839math.SPmath-phmath.MP
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具有平坦片的Maryland型拟周期算子的扰动对角化

Perturbative diagonalisation for Maryland-type quasiperiodic operators with flat pieces

Ilya Kachkovskiy, Stanislav Krymski, Leonid Parnovski, Roman Shterenberg

摘要:

我们考虑$\mathbb Z^d$上具有无界单调采样函数(“Maryland型”)的拟周期算子,它不要求是严格单调的,并且允许有平坦段.在几个几何条件下的频率,长度的部分,和他们的位置,我们表明,这些运营商享受安德森本地化在大混乱。

英文摘要:

We consider quasiperiodic operators on $\mathbb Z^d$ with unbounded monotone sampling functions ("Maryland-type"), which are not required to be strictly monotone and are allowed to have flat segments. Under several geometric conditions on the frequencies, lengths of the segments, and their positions, we show that these operators enjoy Anderson localization at large disorder.

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