论文标题
光谱类型的准周期Schrödinger操作员在扰动方面的稳定性
Stability of Spectral Types of Quasi-Periodic Schrödinger Operators With Respect to Perturbations by Decaying Potentials
论文作者
论文摘要
我们考虑通过衰减电位并寻求保留各种光谱特性的衰减条件，考虑具有分析抽样函数的整数晶格上的扰动。在（几乎）可降低性方案中，我们证明，对于有限的第一瞬间扰动，基本频谱纯粹是绝对连续的，并且新创建的离散频谱必须在未扰动光谱的每个空白处都是有限的。我们还证明，对于固定期，在正lyapunov指数状态下几乎所有频率的安德森定位都在指数衰减的扰动下保留。
We consider perturbations of quasi-periodic Schrödinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under which various spectral properties are preserved. In the (almost) reducibility regime we prove that for perturbations with finite first moment, the essential spectrum remains purely absolutely continuous and the newly created discrete spectrum must be finite in each gap of the unperturbed spectrum. We also prove that for fixed phase, Anderson localization occurring for almost all frequencies in the regime of positive Lyapunov exponents is preserved under exponentially decaying perturbations.
