Quantitative Green's function estimates for lattice quasi-periodic Schr?dinger operators

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外文摘要：In this paper,we establish quantitative Green's function estimates for some higher-dimensional lattice quasi-periodic(QP)Schrödinger operators.The resonances in the estimates can be described via a pair of symmetric zeros of certain functions,and the estimates apply to the sub-exponential-type non-resonance conditions.As the application of quantitative Green's function estimates,we prove both the arithmetic version of Anderson localization and the finite volume version of(1/2-)-Hölder continuity of the integrated density of states(IDS)for such QP Schrödinger operators.This gives an affirmative answer to Bourgain's problem in Bourgain(2000).

外文关键词：

Hölder continuity of the IDSquantitative Green's function estimatesquasi-periodic Schrödinger operatorsarithmetic Anderson localizationmulti-scale analysis

作者：

Hongyi Cao、Yunfeng Shi、Zhifei Zhang

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作者单位：

School of Mathematical Sciences,Peking University,Beijing 100871,China

School of Mathematics,Sichuan University,Chengdu 610064,China

基金：

National Natural Science Foundation of ChinaNational Key R&D ProgramNational Natural Science Foundation of ChinaNational Natural Science Foundation of China

项目编号：

122713802021YFA10016001217101012288101

出版年：

2024

DOI：

10.1007/s11425-022-2126-8

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

CSTPCD

影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(5)