LOCALIZATION FOR THE ONE-DIMENSIONAL ANDERSON MODEL VIA POSITIVITY AND LARGE DEVIATIONS FOR THE LYAPUNOV EXPONENT

被引：33

作者：

Bucaj, Valmir ^{[1
]}

Damanik, David ^{[2
]}

Fillman, Jake ^{[3
]}

Gerbuz, Vitaly ^{[2
]}

Vandenboom, Tom ^{[4
]}

Wang, Fengpeng ^{[5
]}

Zhang, Zhenghe ^{[6
]}

机构：

[1] US Mil Acad, Dept Math, West Point, NY 10996 USA

[2] Rice Univ, Dept Math, Houston, TX 77005 USA

[3] Virginia Tech, Dept Math, 225 Stanger St 0123, Blacksburg, VA 24061 USA

[4] Yale Univ, Dept Math, New Haven, CT 06511 USA

[5] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Guangdong, Peoples R China

[6] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 372卷 / 05期

关键词：

SINGULAR CONTINUOUS-SPECTRUM; RANK-ONE PERTURBATIONS; ORTHOGONAL POLYNOMIALS; SCHRODINGER-OPERATORS; MULTISCALE ANALYSIS; INTEGRATED DENSITY; LARGE DISORDER; PRODUCTS; MATRICES; EQUATIONS;

D O I：

10.1090/tran/7832

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a complete and self-contained proof of spectral and dynamical localization for the one-dimensional Anderson model, starting from the positivity of the Lyapunov exponent provided by Furstenberg's theorem. That is, a Schrodinger operator in l(2)(Z) whose potential is given by independent, identically distributed (i.i.d.) random variables almost surely has pure point spectrum with exponentially decaying eigenfunctions, and its unitary group exhibits exponential off-diagonal decay, uniformly in time. We also explain how to obtain analogous statements for extended CMV matrices whose Verblunsky coefficients are i.i.d., as well as for half-line analogues of these models.

引用

页码：3619 / 3667

页数：49

共 56 条

[1] Disordered quantum walks in one lattice dimension [J].