Random Hamiltonians with arbitrary point interactions in one dimension

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:282

Article

Damanik, David¹  Fillman, Jake²  Helman, Mark¹  Kesten, Jacob¹  Sukhtaiev, Selim³ 

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

[2] Texas State Univ, Dept Math, San Marcos, TX 78666 USA

[3] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

关键词: Anderson localization;    Laplace operator;   

DOI  :  10.1016/j.jde.2021.01.044

来源: Elsevier

【 摘 要 】

We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random selfadjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we prove the following dichotomy: Either every realization of the random operator has purely absolutely continuous spectrum or spectral and exponential dynamical localization hold. In particular, we establish Anderson localization for Schrodinger operators with Bernoulli-type random singular potential and singular density. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free