Delone measures of finite local complexity and applications to spectral theory of one-dimensional continuum models of quasicrystals
Delone measures of finite local complexity and applications to spectral theory of one-dimensional continuum models of quasicrystals
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有限局部复杂性的 Delone 测度及其在准晶一维连续介质模型谱理论中的应用
DOI：
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发表时间：
2010
期刊：
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通讯作者：
P. Stollmann
中科院分区：
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作者：
Steffen Klassert;D. Lenz;P. Stollmann
我们研究实线上的度量，并提出各种版本来说明这种度量仅取有限多个值的含义。然后我们通过这些措施来研究拉普拉斯算子的扰动。使用 Kotani-Remling 理论，我们表明如果测量不是周期性的，则所得算子具有空的绝对连续谱。当与戈登型论证相结合时，这使我们能够证明准晶体的某些连续介质模型的纯奇异连续谱。
We study measures on the real line and present various versions of what it means for such a measure to take only finitely many values. We then study perturbations of the Laplacian by such measures. Using Kotani-Remling theory, we show that the resulting operators have empty absolutely continuous spectrum if the measures are not periodic. When combined with Gordon type arguments this allows us to prove purely singular continuous spectrum for some continuum models of quasicrystals.