Arithmetic version of anderson localization for quasiperiodic Schr\"odinger operators with even cosine type potentials

Lingrui Ge; Jiangong You; Xin Zhao

Arithmetic version of anderson localization for quasiperiodic Schr\"odinger operators with even cosine type potentials

Spectral Theory 2021-07-20 v1 Mathematical Physics Dynamical Systems math.MP

Authors: Lingrui Ge , Jiangong You , Xin Zhao

Abstract

We propose a new method to prove Anderson localization for quasiperiodic Schr\"odinger operators and apply it to the quasiperiodic model considered by Sinai and Fr\"ohlich-Spencer-Wittwer. More concretely, we prove Anderson localization for even $C^2$ cosine type quasiperiodic Schr\"odinger operators with large coupling constants, Diophantine frequencies and Diophantine phases.

Keywords

Anderson localization quasiperiodic Schrödinger operators cosine type potentials Diophantine frequencies Diophantine phases coupling constants

Cite

@article{arxiv.2107.08547,
  title  = {Arithmetic version of anderson localization for quasiperiodic Schr\"odinger operators with even cosine type potentials},
  author = {Lingrui Ge and Jiangong You and Xin Zhao},
  journal= {arXiv preprint arXiv:2107.08547},
  year   = {2021}
}