Gevrey势能的离散拟周期 Schrodinger算子的非扰动Anderson局域化

考虑一类具有Gevrey势能的离散拟周期Schrodinger算子, 其中其势能可写成一维环面上的大值解析函数加上Gevrey小扰动. 用大偏差定理和半代数理论证明在大系数下, 对任意的固定相位以及对几乎所有的频率, 该算子满足非扰动的Anderson局域化.

Non-perturbative Anderson Localization of Discrete Quasi-periodic Schrodinger Operators of Gevrey Potential Energy

We considered a class of discrete quasi-periodic Schrodinger operators with some Gevrey potential energy, in which the potential energy could be written as a large valued analytical function having a Gevrey small perturbation on the one-dimensional torus. By using large deviation theorem and semi-algebraic theory, we proved that the operator satisfied the non-perturbative Anderson localization for any fixed phase and almost all frequencies under large coefficients.