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arXiv · 1304.2805

Absolutely continuous spectrum for limit-periodic Schr\"odinger operators

Helge Krueger
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Abstract

We show that a large class of limit-periodic Schr\"odinger operators has purely absolutely continuous spectrum in arbitrary dimensions. This result was previously known only in dimension one. The proof proceeds through the non-perturbative construction of limit-periodic extended states. An essential step is a new estimate of the probability (in quasi-momentum) that the Floquet Bloch operators have only simple eigenvalues.

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Helge Krueger. 2013-04-09. Absolutely continuous spectrum for limit-periodic Schr\"odinger operators. https://arxiv.org/abs/1304.2805

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