English

Absence of singular continuous spectrum for perturbed discrete Schr\"odinger operators

Mathematical Physics 2019-04-10 v1 math.MP Spectral Theory

Abstract

We show that the spectral measure of discrete Schr\"odinger operators (Hu)(n)=u(n+1)+u(n1)+V(n)u(n) (Hu)(n)= u({n+1})+u({n-1})+V(n)u(n) does not have singular continuous component if the potential V(n)=O(n1)V(n)=O(n^{-1}).

Keywords

Cite

@article{arxiv.1809.07884,
  title  = {Absence of singular continuous spectrum for perturbed discrete Schr\"odinger operators},
  author = {Wencai Liu},
  journal= {arXiv preprint arXiv:1809.07884},
  year   = {2019}
}