Schrödinger operators with delta and delta'-interactions on Lipschitz surfaces and chromatic numbers of associated partitions

Jussi Behrndt, Vladimir Lotoreichik, Pavel Exner

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate Schrödinger operators with δ- and δ′-interactions supported on hypersurfaces, which separate the Euclidean space into finitely many bounded and unbounded Lipschitz domains. It turns out that the combinatorial properties of the partition and the spectral properties of the corresponding operators are related. As the main result, we prove an operator inequality for the Schrödinger operators with δ- and δ′-interactions which is based on an optimal coloring and involves the chromatic number of the partition. This inequality implies various relations for the spectra of the Schrödinger operators and, in particular, it allows to transform known results for Schrödinger operators with δ-interactions to Schrödinger operators with δ′-interactions.
Original languageEnglish
Pages (from-to)1450015-1450058
JournalReviews in Mathematical Physics
Volume26
DOIs
Publication statusPublished - 2014

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

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