中文

Generic singular continuous spectrum for ergodic Schr\"odinger operators

动力系统 2015-02-24 v1 数学物理 math.MP

摘要

We consider Schr\"odinger operators with ergodic potential Vω(n)=f(Tn(ω))V_\omega(n)=f(T^n(\omega)), nZn \in \Z, ωΩ\omega \in \Omega, where T:ΩΩT:\Omega \to \Omega is a non-periodic homeomorphism. We show that for generic fC(Ω)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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引用

@article{arxiv.math/0409061,
  title  = {Generic singular continuous spectrum for ergodic Schr\"odinger operators},
  author = {Artur Avila and David Damanik},
  journal= {arXiv preprint arXiv:math/0409061},
  year   = {2015}
}

备注

6 pages