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
收藏
页数：18
相关论文
共 50 条
  • [1] KAM THEORY FOR QUASI-PERIODIC EQUILIBRIA IN ONE-DIMENSIONAL QUASI-PERIODIC MEDIA
    Su, Xifeng
    de la Llave, Rafael
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2012, 44 (06) : 3901 - 3927
  • [2] LOCALIZATION IN OPTICS - QUASI-PERIODIC MEDIA
    KOHMOTO, M
    SUTHERLAND, B
    IGUCHI, K
    PHYSICAL REVIEW LETTERS, 1987, 58 (23) : 2436 - 2438
  • [3] RESONANT EQUILIBRIUM CONFIGURATIONS IN QUASI-PERIODIC MEDIA: KAM THEORY
    de la Llave, Rafael
    Su, Xifeng
    Zhang, Lei
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2017, 49 (01) : 597 - 625
  • [4] LOCALIZATION OF MODES IN MEDIA WITH A SIMPLE QUASI-PERIODIC MODULATION
    SALAT, A
    PHYSICAL REVIEW A, 1992, 45 (02): : 1116 - 1121
  • [5] LOCALIZATION PROBLEM IN OPTICS - NONLINEAR QUASI-PERIODIC MEDIA
    GUPTA, SD
    RAY, DS
    PHYSICAL REVIEW B, 1990, 41 (12): : 8047 - 8053
  • [6] KAM theory for quasi-periodic equilibria in 1D quasi-periodic media: II. Long-range interactions
    Su, Xifeng
    de la Llave, Rafael
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (45)
  • [7] HERMAN'S APPROACH TO QUASI-PERIODIC PERTURBATIONS IN THE REVERSIBLE KAM CONTEXT 2
    Sevryuk, Mikhail B.
    MOSCOW MATHEMATICAL JOURNAL, 2017, 17 (04) : 803 - 823
  • [8] Quasi-periodic swing via weak KAM theory
    Niu, Xun
    Wang, Kaizhi
    Li, Yong
    PHYSICA D-NONLINEAR PHENOMENA, 2025, 474
  • [9] KAM quasi-periodic solutions for the dissipative standard map
    Calleja, Renato C.
    Celletti, Alessandra
    de la Llave, Rafael
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2022, 106
  • [10] Construction of Quasi-Periodic Breathers¶via KAM Technique
    Xiaoping Yuan
    Communications in Mathematical Physics, 2002, 226 : 61 - 100
12345