Generic singular continuous spectrum for ergodic Schrödinger operators

Abstract

We consider Schrödinger operators with ergodic potential $V_{\omega }(n)=f(T^n(\omega ))$, $n\in \mathbb{Z}$, $\omega \in \Omega$, where $T:\Omega \to \Omega$ is a non-periodic homeomorphism. We show that for generic $f\in C(\Omega )$, the spectrum has no absolutely continuous component. The proof is based on approximation by discontinuous potentials which can be treated via Kotani Theory.

6 pages

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• Genericity of zero Lyapunov exponents
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Cited by in corpus (2)

• Dynamics and spectral theory of quasi-periodic Schrödinger-type operators
• Generic Continuous Spectrum for Ergodic Schr"odinger Operators