• DOI:10.1142/S0129055X14500159
• Corpus ID: 882215

Schrödinger operators with δ- and δ′-interactions on Lipschitz surfaces and chromatic numbers of associated partitions

@article{Behrndt2013SchrdingerOW,
  title={Schr{\"o}dinger operators with $\delta$- and $\delta$′-interactions on Lipschitz surfaces and chromatic numbers of associated partitions},
  author={Jussi Behrndt and Pavel Exner and Vladimir Lotoreichik},
  journal={Reviews in Mathematical Physics},
  year={2013},
  volume={26},
  pages={1450015}
}

• J. Behrndt, P. Exner, V. Lotoreichik
• Published 29 June 2013
• Mathematics
• Reviews in Mathematical Physics

We investigate Schrodinger 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 Schrodinger 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 Schrodinger operators and, in particular, it allows to transform known results for Schrodinger operators with δ-interactions to Schrodinger operators with δ′-interactions.