Localization and Regularity of the Integrated Density of States for Schrodinger Operators on Zd with C2-cosine Like Quasi-Periodic Potential

被引：0

作者：

Cao, Hongyi ^{[1
]}

Shi, Yunfeng ^{[2
]}

Zhang, Zhifei ^{[1
]}

机构：

[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

[2] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2023年 / 404卷 / 01期

关键词：

ANDERSON LOCALIZATION; HOLDER CONTINUITY; EQUATION;

D O I：

10.1007/s00220-023-04847-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we study the multidimensional lattice Schrodinger operators with C2-cosine like quasi-periodic (QP) potential. We establish quantitative Green's function estimates, the arithmetic version of Anderson (and dynamical) localization, and the finite volume version of ( 1 2 -)-Holder continuity of the integrated density of states for such QP Schrodinger operators. Our proof is based on an extension of the fundamental multi-scale analysis type method of Frohlich-Spencer-Wittwer (Commun Math Phys 132(1), 5-25, 1990) to the higher lattice dimensions. We resolve the level crossing issue on eigenvalues parameterizations in the case of both higher lattice dimension and C2 regular potential.

引用

页码：495 / 561

页数：67

共 34 条

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