Generic singular continuous spectrum for ergodic Schrödinger operators

Details Generic singular continuous spectrum for ergodic Schrödinger operators Generic singular continuous spectrum for ergodic Schrödinger operators

2004-09-06

arxiv.org/abs/math/0409061v1

Mathematics

Dynamical Systems

6 pages

Scientific paper

We consider Schr\"odinger operators with ergodic potential $V_\omega(n)=f(T^n(\omega))$, $n \in \Z$, $\omega \in \Omega$, 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.

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