1. The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials
- Author
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Avila, Artur, Damanik, David, Gorodetski, Anton, University of Zurich, and Damanik, David
- Subjects
10123 Institute of Mathematics ,510 Mathematics ,2603 Analysis ,Almost sure spectrum ,FOS: Mathematics ,FOS: Physical sciences ,2608 Geometry and Topology ,Analysis Random Schrödinger operator ,Mathematical Physics (math-ph) ,Geometry and Topology ,Rotation number ,Spectral Theory (math.SP) ,Analysis - Abstract
We consider Schrödinger operators in $\ell^2(\mathbb{Z})$ whose potentials are given by the sum of an ergodic term and a random term of Anderson type. Under the assumption that the ergodic term is generated by a homeomorphism of a connected compact metric space and a continuous sampling function, we show that the almost sure spectrum arises in an explicitly described way from the unperturbed spectrum and the topological support of the single-site distribution. In particular, assuming that the latter is compact and contains at least two points, this explicit description of the almost sure spectrum shows that it will always be given by a finite union of non-degenerate compact intervals. The result can be viewed as a far reaching generalization of the well known formula for the spectrum of the classical Anderson model., 11 pages
- Published
- 2023