论文标题
无界单调准二级算子的扰动系列的收敛系
Convergence of perturbation series for unbounded monotone quasiperiodic operators
论文作者
论文摘要
We consider a class of unbounded quasiperiodic Schrödinger-type operators on $\ell^2(\mathbb Z^d)$ with monotone potentials (akin to the Maryland model) and show that the Rayleigh--Schrödinger perturbation series for these operators converges in the regime of small kinetic energies, uniformly in the spectrum.结果，我们比此类运营商的类别更一般地获得了安德森本地化的新证明，并为特征值和特征向量提供了明显的收敛串联扩展。如果电势仅局部单调并且一对一，则可以将此结果限制在能量窗口中。对这种方法的修改还允许在频率的其他限制下具有非刻痕单调的潜力并具有平坦的片段。
We consider a class of unbounded quasiperiodic Schrödinger-type operators on $\ell^2(\mathbb Z^d)$ with monotone potentials (akin to the Maryland model) and show that the Rayleigh--Schrödinger perturbation series for these operators converges in the regime of small kinetic energies, uniformly in the spectrum. As a consequence, we obtain a new proof of Anderson localization in a more general than before class of such operators, with explicit convergent series expansions for eigenvalues and eigenvectors. This result can be restricted to an energy window if the potential is only locally monotone and one-to-one. A modification of this approach also allows the potential to be non-strictly monotone and have a flat segment, under additional restrictions on the frequency.
