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Approximation of quantum graph vertex couplings by scaled Schrodinger operators on thin branched manifolds
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SYSNO ASEP 0330854 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Approximation of quantum graph vertex couplings by scaled Schrodinger operators on thin branched manifolds Title Aproximace vazeb ve vrcholech kvantových grafů škálovanými Schrödingerovými operátory na tenkých rozvětvených varietách Author(s) Exner, Pavel (UJF-V) RID, ORCID, SAI
Post, O. (DE)Source Title Journal of Physics A-Mathematical and Theoretical. - : Institute of Physics Publishing - ISSN 1751-8113
Roč. 42, č. 41 (2009), 415305/1-415305/22Number of pages 22 s. Language eng - English Country GB - United Kingdom Keywords convergence ; scattering ; spectra 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 000270303300021 DOI 10.1088/1751-8113/42/41/415305 Annotation We discuss approximations of vertex couplings of quantum graphs using families of thin branched manifolds. We show that if a Neumann-type Laplacian on such manifolds is amended by suitable potentials, the resulting Schrodinger operators can approximate non-trivial vertex couplings. The latter include not only the delta-couplings but also those with wavefunctions discontinuous at the vertex. We work out the example of the symmetric delta'-couplings and make a conjecture that the same method can be applied to all couplings invariant with respect to the time reversal. We conclude with a result that certain vertex couplings cannot be approximated by a pure Laplacian. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2010
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