Simplicity of eigenvalues in Anderson-type models

Abstract

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.

20 pages

References in corpus (4)

• An Invitation to Random Schroedinger operators
• Correlations Estimates in the Lattice Anderson Model
• Simplicity of eigenvalues in the Anderson model
• A remark on an estimate by Minami

Cited by in corpus (8)

• Eigenvalue statistics for random Schrodinger operators with non rank one perturbations
• Multiplicity bound of Singular Spectrum for higher rank Anderson models
• Level Spacing for Non-Monotone Anderson Models
• Multiplicity theorem of singular Spectrum for general Anderson type Hamiltonian
• Jakšić-Last Theorem for Higher Rank Perturbations
• On multiplicity of spectrum for Anderson type operators with higher rank perturbations
• Global multiplicity bounds and Spectral Statistics Random Operators
• Protecting points from operator pencils