Simplicity of eigenvalues in Anderson-type models

Sergey Naboko Department of Mathematical Physics, Institute of Physics, St. Petersburg State University Roger Nichols Department of Mathematics, University of Missouri Günter Stolz Department of Mathematics, University of Alabama at Birmingham

Algebraic Topology and General Topology mathscidoc:1701.02006

Arkiv for Matematik, 51, (1), 157-183, 2010.10
We show almost sure simplicity of eigenvalues for several models of Anderson-type random Schrödinger operators, extending methods introduced by Simon for the discrete Anderson model. These methods work throughout the spectrum and are not restricted to the localization regime. We establish general criteria for the simplicity of eigenvalues which can be interpreted as separately excluding the absence of local and global symmetries, respectively. The criteria are applied to Anderson models with matrix-valued potential as well as with single-site potentials supported on a finite box.
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@inproceedings{sergey2010simplicity,
  title={Simplicity of eigenvalues in Anderson-type models},
  author={Sergey Naboko, Roger Nichols, and Günter Stolz},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203634381046034},
  booktitle={Arkiv for Matematik},
  volume={51},
  number={1},
  pages={157-183},
  year={2010},
}
Sergey Naboko, Roger Nichols, and Günter Stolz. Simplicity of eigenvalues in Anderson-type models. 2010. Vol. 51. In Arkiv for Matematik. pp.157-183. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203634381046034.
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