Quantitative Green's function estimates for lattice quasi-periodic Schrodinger operators  

作　　者：Hongyi Cao Yunfeng Shi Zhifei Zhang 

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing 100871,China [2]School of Mathematics,Sichuan University,Chengdu 610064,China

出　　处：《Science China Mathematics》2024年第5期1011-1058,共48页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.12271380);supported by National Natural Science Foundation of China(Grant Nos.12171010 and 12288101);National Key R&D Program(Grant No.2021YFA1001600)。

摘　　要：In this paper,we establish quantitative Green’s function estimates for some higher-dimensional lattice quasi-periodic(QP)Schrodinger 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-)-Holder continuity of the integrated density of states(IDS)for such QP Schrodinger operators.This gives an affirmative answer to Bourgain’s problem in Bourgain(2000).

关 键 词：Holder continuity of the IDS quantitative Green's function estimates quasi-periodic Schrodinger operators arithmetic Anderson localization multi-scale analysis 

分 类 号：O177[理学—数学]