A multi-scale analysis proof of the power-law localization for random operators on Zd

被引：9
作者：
Shi, Yunfeng [1 ]
机构：
[1] Sichuan Univ, Coll Math, Chengdu 610064, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 297卷
关键词：
Power-law localization; Multi-scale analysis; Random operators; Polynomial long-range hopping; LARGE DISORDER; ANDERSON LOCALIZATION; DIFFUSION; BERNOULLI; SPECTRUM; SYSTEMS; ABSENCE; MODEL;
D O I：
10.1016/j.jde.2021.06.028
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we give a multi-scale analysis proof of the power-law localization for random operators on Z(d) for arbitrary d >= 1. (C) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页码：201 / 225
页数：25
相关论文
共 24 条
[1]   LOCALIZATION AT LARGE DISORDER AND AT EXTREME ENERGIES - AN ELEMENTARY DERIVATION [J].
AIZENMAN, M ;
MOLCHANOV, S .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1993, 157 (02) :245-278
[2]   LOCALIZATION AT WEAK DISORDER - SOME ELEMENTARY BOUNDS [J].
AIZENMAN, M .
REVIEWS IN MATHEMATICAL PHYSICS, 1994, 6 (5A) :1163-1182
[3]   ABSENCE OF DIFFUSION IN CERTAIN RANDOM LATTICES [J].
ANDERSON, PW .
PHYSICAL REVIEW, 1958, 109 (05) :1492-1505
[4]  
[Anonymous], 2015, Random operators
[5]   Quasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential [J].
Berti, Massimiliano ;
Bolle, Philippe .
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2013, 15 (01) :229-286
[6]   On localization in the continuous Anderson-Bernoulli model in higher dimension [J].
Bourgain, J ;
Kenig, CE .
INVENTIONES MATHEMATICAE, 2005, 161 (02) :389-426
[7]   CONTINUOUS SINGULAR MEASURES WITH SMALL FOURIER-STIELTJES TRANSFORMS [J].
BROWN, G ;
HEWITT, E .
ADVANCES IN MATHEMATICS, 1980, 37 (01) :27-60
[8]   ANDERSON LOCALIZATION FOR BERNOULLI AND OTHER SINGULAR POTENTIALS [J].
CARMONA, R ;
KLEIN, A ;
MARTINELLI, F .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1987, 108 (01) :41-66
[9]   ANDERSON LOCALIZATION FOR MULTI-DIMENSIONAL SYSTEMS AT LARGE DISORDER OR LARGE ENERGY [J].
DELYON, F ;
LEVY, Y ;
SOUILLARD, B .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1985, 100 (04) :463-470
[10]   Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice [J].
Ding, Jian ;
Smart, Charles K. .
INVENTIONES MATHEMATICAE, 2020, 219 (02) :467-506
123