The KAM approach to the localization in "haarsch" quasi-periodic media

被引：2

作者：

Chulaevsky, Victor ^{[1
]}

机构：

[1] Univ Reims, Dept Math Moulin Housse, BP 1039, F-51687 Reims 2, France

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2018年 / 59卷 / 01期

关键词：

TIGHT-BINDING MODEL; ANDERSON LOCALIZATION; SCHRODINGER-OPERATORS; LARGE DISORDER; POTENTIALS;

D O I：

10.1063/1.4995024

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We propose a Kolmogorov-Arnold-Moser type approach to the spectral analysis of lattice Schrodinger operators with quasi-periodic potentials. In the strong disorder regime, we prove uniform exponential localization and establish measure-theoretic bounds on the "resonant" sets which are substantially stronger than in prior studies on localization in deterministic disordered environments. Published by AIP Publishing.

引用

页数：18

共 50 条

[21] Anderson localization for quasi-periodic lattice schrodinger operators on zd, d arbitrary [J].

Bourgain, Jean .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2007, 17 (03) :682-706

[22] Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications [J].

Jiangong You ;

Qi Zhou .

Communications in Mathematical Physics, 2013, 323 :975-1005

[23] Anderson localization for one-frequency quasi-periodic block Jacobi operators [J].

Klein, Silvius .

JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 273 (03) :1140-1164

[24] POSITIVE LYAPUNOV EXPONENT FOR A CLASS OF QUASI-PERIODIC COCYCLES [J].

Liang, Jinhao .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (03) :1361-1387

[25] The localization of light in a 2D quasi-periodic coherently prepared atomic medium [J].

Wang, C. F. ;

Cheng, J. ;

Chen, B. .

OPTICS COMMUNICATIONS, 2015, 336 :34-39

[26] ON LOCALIZATION AND HOMOGENEITY FOR ANALYTIC QUASI-PERIODIC SCHRO<spacing diaeresis>DINGER <spacing diaeresis> DINGER OPERATORS WITH GEVREY PERTURBATION [J].

Tao, Kai .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2024, 23 (09) :1216-1239

[27] Localization for Lipschitz Monotone Quasi-periodic Schrodinger Operators on Zd via Rellich Functions Analysis [J].

Cao, Hongyi ;

Shi, Yunfeng ;

Zhang, Zhifei .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2025, 406 (05)

[28] The Dynamics of a Class of Quasi-Periodic Schrodinger Cocycles [J].

Bjerklov, Kristian .

ANNALES HENRI POINCARE, 2015, 16 (04) :961-1031

[29] Quantization of Conductance in Quasi-periodic Quantum Wires [J].

Koma, Tohru ;

Morishita, Toru ;

Shuya, Taro .

JOURNAL OF STATISTICAL PHYSICS, 2019, 174 (05) :1137-1160

[30] Quantitative reducibility of Ck quasi-periodic cocycles [J].

Cai, Ao ;

Lv, Huihui ;

Wang, Zhiguo .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2025, 45 (06) :1649-1672

← 1 2 3 4 5 →