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On geometric perturbations of critical Schrodinger operators with a surface interaction
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SYSNO ASEP 0336857 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On geometric perturbations of critical Schrodinger operators with a surface interaction Title O geometrických poruchách kritických Schrödingerových operátorů s povrchovou interakcí Author(s) Exner, Pavel (UJF-V) RID, ORCID, SAI
Fraas, Martin (UJF-V)Source Title Journal of Mathematical Physics. - : AIP Publishing - ISSN 0022-2488
Roč. 50, č. 11 (2009), 112101/1-112101/12Number of pages 12 s. Language eng - English Country US - United States Keywords Schrodinger operators Subject RIV BE - Theoretical Physics R&D Projects LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10480505 - UJF-V (2005-2011) UT WOS 000272755100001 DOI 10.1063/1.3243826 Annotation We study singular Schrodinger operators with an attractive interaction supported by a closed smooth surface A subset of R-3 and analyze their behavior in the vicinity of the critical situation where such an operator has empty discrete spectrum and a threshold resonance. In particular, we show that if A is a sphere and the critical coupling is constant over it, any sufficiently small smooth area-preserving radial deformation gives rise to isolated eigenvalues. On the other hand, the discrete spectrum may be empty for general deformations. We also derive a related inequality for capacities associated with such surfaces. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2010
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