Arkiv för Matematik
- Ark. Mat.
- Volume 51, Number 1 (2013), 157-183.
Simplicity of eigenvalues in Anderson-type models
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.
S. N. was supported by Russian research grant RFBR 09-01-00515a.
G. S. was supported in part by NSF grant DMS-0653374.
Ark. Mat., Volume 51, Number 1 (2013), 157-183.
Received: 22 October 2010
First available in Project Euclid: 31 January 2017
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Naboko, Sergey; Nichols, Roger; Stolz, Günter. Simplicity of eigenvalues in Anderson-type models. Ark. Mat. 51 (2013), no. 1, 157--183. doi:10.1007/s11512-011-0155-3. https://projecteuclid.org/euclid.afm/1485907198