Simplicity of eigenvalues in Anderson-type models

Details Simplicity of eigenvalues in Anderson-type models Simplicity of eigenvalues in Anderson-type models

2010-01-20

arxiv.org/abs/1001.3440v1

Physics

Mathematical Physics

20 pages

Scientific paper

We show almost sure simplicity of eigenvalues for several models of Anderson-type random Schr\"odinger 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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