一类双参数拟周期算子的局域化问题
Localization for Quasi-Periodic Operators with Two Parameters
DOI: 10.12677/AAM.2019.86122, PDF,   
作者: 王 均：河海大学(常州)，基础学部数理部，江苏 常州
关键词: 局域化；Lyapunov指数；拟周期；Localization； Lyapunov Index； Quasi-Periodic
摘要: 本文考虑了一类双参数拟周期算子：(H(θ,λ,ω)u)(n)=a(n)u(n+1)+a(n-1)u(n-1)+v(n)u(n)其中，ω是Diophantine数，利用改进的局域化方法证明了，当，对全测的θ∈T，该算子Hθ,λ,ω有Anderson局域化。
Abstract: The main purpose of this paper is to prove localization for a kind of quasi-periodic operators , where , Diophantine num-ber ω, full measured θ∈T and , .
文章引用：王均. 一类双参数拟周期算子的局域化问题[J]. 应用数学进展, 2019, 8(6): 1064-1071. https://doi.org/10.12677/AAM.2019.86122

参考文献

[1] Last, Y. (1993) Almost Everything about the Almost Mathieu Operator I. Proceedings of the 11th International Con-gress of Mathematical Physics, 151, 183-192. [Google Scholar] [CrossRef] 
[2] Germinet, F. (1999) Dy-namical Localization II with an Application to the Almost Mathieu Operator. Journal of Statistical Physics, 95, 273-286.
[3] Jitomirskaya, S. and Last, Y. (1996) Dimensional Hausdorffproperties of Singular Continuous Spectra. Physical Review Letters, 76, 1765-1769. [Google Scholar] [CrossRef] 
[4] Last, Y. (1993) A Relation between Absolutely Continuous Spectrum of Ergodic Jacobi Matrices and the Spectra of Periodic Approximants. Communications in Mathematical Physics, 151, 183-192. [Google Scholar] [CrossRef] 
[5] Aubry, S. and Andre, G. (1980) Analyticity Breaking and Anderson Localization in Incommensurate Lattices. Annals of the Israel Physical Society, 3, 133-140.
[6] Avron, J. and Simon, B. (1983) Almost Periodic Schrodinger Operators II. The IDS. Duke Mathematical Journal, 50, 369-391. [Google Scholar] [CrossRef] 
[7] Bourgain, J. and Jitomirskaya, S. (2002) Continuity of the Lyapunov Exponent for Quasiperiodic Operators with Analytic Potential. Journal of Statistical Physics, 108, 1203-1208. [Google Scholar] [CrossRef] 
[8] Jitomirskaya, S. (1999) Metal-Insulator Transition for the Almost Mathieu Operator. Annals of Mathematics, 150, 1159-1175. [Google Scholar] [CrossRef] 

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