Simplicity of eigenvalues in Anderson-type models release_rev_278a7b3a-418f-42fc-8187-329445b7d1b6

by Sergey Naboko, Roger Nichols, G√ľnter Stolz

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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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Type  article
Stage   submitted
Date   2010-01-20
Version   v1
Language   en ?
arXiv  1001.3440v1
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Revision: 278a7b3a-418f-42fc-8187-329445b7d1b6