论小耦合机制下有界类型的斯图尔米安哈密顿频谱

Alexandro Luna
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引用次数: 0

摘要

我们证明了一个离散薛定谔(Schr "oddinger)算子的谱的豪斯多夫维度(Hausdorff dimension),该算子具有有界类型的斯图尔绵势能(Sturmian potential),当耦合趋于零时,其谱的豪斯多夫维度趋于一。证明基于迹图形式主义。
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On the spectrum of Sturmian Hamiltonians of bounded type in a small coupling regime
We prove that the Hausdorff dimension of the spectrum of a discrete Schr\"odinger operator with Sturmian potential of bounded type tends to one as coupling tends to zero. The proof is based on the trace map formalism.
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