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Generic singular continuous spectrum for ergodic Schrödinger operators

Artur Avila·David Damanik
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Abstract

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

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Artur Avila, David Damanik. 2004-09-06. Generic singular continuous spectrum for ergodic Schrödinger operators. https://arxiv.org/abs/math/0409061

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