0433710 - ÚJF 2015 RIV SG eng J - Článek v odborném periodiku
Behrndt, J. - Exner, Pavel - Lotoreichik, V.
Schrodinger operators with delta- and delta '-interactions on Lipschitz surfaces and chromatic numbers of associated partitions.
[BEHRNDT, Jussi; EXNER, Pavel; LOTOREICHIK, Vladimir.: Schrödinger operators with delta-interactions supported on conical surfaces, Journal of Physics A: Mathematical and Theoretical 47, 355202 Read More: http://www.worldscientific.com/doi/abs/10.1142/S0129055X14500159]. Reviews in Mathematical Physics. Roč. 26, č. 8 (2014), s. 1450015. ISSN 0129-055X. E-ISSN 1793-6659
Grant CEP: GA ČR(CZ) GA14-06818S; GA MŠMT 7AMB13AT010
Institucionální podpora: RVO:61389005
Klíčová slova: Schrödinger operator * delta-potential * delta'-potential * singular potential * Lipschitz domain * chromatic number * operator inequality * eigenvalue inequality * compact perturbation * essential spectrum * geometrically induced bound state * star-graph
Kód oboru RIV: BE - Teoretická fyzika
Impakt faktor: 1.329, rok: 2014 ; AIS: 1.057, rok: 2014

We investigate Schrodinger operators with delta- and delta'-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 delta- and delta'-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 delta-interactions to Schrodinger operators with delta'-interactions.
Trvalý link: http://hdl.handle.net/11104/0237870