Asymptotic of gaps at small coupling and applications of the skew-shift Schrödinger operator
Helge Krüger
Conference Publications 2011, 2011(Special): 874-880 doi: 10.3934/proc.2011.2011.874
I derive an asymptotic formula for the gaps of periodic discrete Schrödinger operators. An application to the skew-shift Schrödinger operator is discussed.
keywords: Spectrum Schrödinger operator.
Schrödinger operators defined by interval-exchange transformations
Jon Chaika David Damanik Helge Krüger
Journal of Modern Dynamics 2009, 3(2): 253-270 doi: 10.3934/jmd.2009.3.253
We discuss discrete one-dimensional Schrödinger operators whose potentials are generated by an invertible ergodic transformation of a compact metric space and a continuous real-valued sampling function. We pay particular attention to the case where the transformation is a minimal interval-exchange transformation. Results about the spectral type of these operators are established. In particular, we provide the first examples of transformations for which the associated Schrödinger operators have purely singular spectrum for every nonconstant continuous sampling function.
keywords: continuous spectrum singular spectrum interval-exchange transformations. Ergodic Schrödinger operators

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