Generic Singular Spectrum For Ergodic Schrödinger Operators
Generic Singular Spectrum For Ergodic Schrödinger Operators
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遍历薛定谔算子的通用奇异谱
DOI：
10.1215/s0012-7094-05-13035-6
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发表时间：
2005
影响因子：
2.5
通讯作者：
D. Damanik
中科院分区：
文献类型：
--
作者：
A. Avila;D. Damanik
我们考虑具有遍历势 V_ω(n) = f(T^n(ω)), n Є Z, ω Є Ω 的薛定谔算子，其中 T : Ω → Ω 是非周期同胚。我们证明，对于一般的 f Є C(Ω)，频谱没有绝对连续的分量。该证明基于不连续势的近似，可以通过 Kotani 理论进行处理。
We consider Schrodinger operators with ergodic potential V_ω(n) = f(T^n(ω)), n Є Z, ω Є Ω, where T : Ω → Ω is a nonperiodic homeomorphism. We show that for generic f Є 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.