论文标题
c^k Quasi periodic schrodinger操作员的间隙长度的多项式衰减和光谱应用
Polynomial decay of the gap length for C^k quasi-periodic Schrodinger operators and spectral application
论文作者
论文摘要
对于局部扰动状态中的准周期schrödinger算子，根据二聚体常数，频率为diophantine且电势为$ c^k $足够小，我们证明相应的光谱间隙的长度具有与其标签相对于其标签的多项型衰变上限。这是基于$ c^k $ quasi periodic $ {\ rm sl}（2，2，\ mathbb {r}）$ cocycles的精制定量可降低定理，也基于Moser-pöschel参数用于相关的SchrödingerCocycles。作为应用程序，我们能够显示频谱的同质性。
For the quasi-periodic Schrödinger operators in the local perturbative regime where the frequency is Diophantine and the potential is $C^k$ sufficiently small depending on the Diophantine constants, we prove that the length of the corresponding spectral gap has a polynomial decay upper bound with respect to its label. This is based on a refined quantitative reducibility theorem for $C^k$ quasi-periodic ${\rm SL}(2,\mathbb{R})$ cocycles, and also based on the Moser-Pöschel argument for the related Schrödinger cocycles. As an application, we are able to show the homogeneity of the spectrum.
