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Absolutely continuous spectrum for limit-periodic Schrödinger operators

We show that a large class of limit-periodic Schrödinger 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.

preprint2013arXivOpen access
Helge Krueger
math.SP
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Helge Krueger

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