论文标题
一维QuasiperiodicSchrödinger操作员的弹道运输
Ballistic transport for one-dimensional quasiperiodic Schrödinger operators
论文作者
论文摘要
在本文中，我们表明，具有光滑电势的一维多功能式schrödinger算子在一组能量上显示了弹道运动，相应的SchrödingerCocycles可以平稳地还原到恒定旋转。证明是通过在一系列疲惫的子集上建立本地版本的强弹道传输来执行的，可以通过在$ \ mathrm {c}^{\ ell} $ - norm中均匀界定的偶联来实现降低性。我们还根据共轭矩阵的规范建立了全球强大的弹道运输。后一种情况非常温和，并且在许多已知的例子中得到满足。
In this paper, we show that one-dimensional discrete multi-frequency quasiperiodic Schrödinger operators with smooth potentials demonstrate ballistic motion on the set of energies on which the corresponding Schrödinger cocycles are smoothly reducible to constant rotations. The proof is performed by establishing a local version of strong ballistic transport on an exhausting sequence of subsets on which reducibility can be achieved by a conjugation uniformly bounded in the $\mathrm{C}^{\ell}$-norm. We also establish global strong ballistic transport under an additional integral condition on the norms of conjugation matrices. The latter condition is quite mild and is satisfied in many known examples.
