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Periodic and limit-periodic discrete Schr\"odinger operators

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arxiv 1108.1584 v1 pith:IIED22EL submitted 2011-08-07 math.SP

Helge Krueger This is my paper · ORCID
classification math.SP
keywords limit-periodicdiscretefurthermoreodingeroperatorsperiodicperiodspotential
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The theory of discrete periodic and limit-periodic Schr\"odinger operators is developed. In particular, the Floquet--Bloch decomposition is discussed. Furthermore, it is shown that an arbitrarily small potential can add a gap for even periods. In dimension two, it is shown that for coprime periods small potential terms don't add gaps thus proving a Bethe--Sommerfeld type statement. Furthermore limit-periodic potentials whose spectrum is an interval are constructed.

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  1. Absence of flat bands for discrete periodic graph operators with generic potentials

    math.SP 2025-09 conditional novelty 8.0 of 10

    Generic potentials on any connected periodic graph produce no flat bands.

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