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Approximation of a general singular vertex coupling in quantum graphs
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SYSNO ASEP 0341394 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Approximation of a general singular vertex coupling in quantum graphs Author(s) Cheon, T. (JP)
Exner, Pavel (UJF-V) RID, ORCID, SAI
Turek, O. (CZ)Source Title Annals of Physics. - : Elsevier - ISSN 0003-4916
Roč. 325, č. 3 (2010), s. 548-578Number of pages 31 s. Language eng - English Country US - United States Keywords Quantum graphs ; Boundary conditions ; Singular vertex coupling 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 000274970300004 DOI 10.1016/j.aop.2009.11.010 Annotation The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a delta potential and a vector potential coupled to the "loose" edges by a delta Coupling. It is shown that if the lengths of the connecting edges shrink to zero and the potentials are properly scaled, the limit can yield any prescribed Singular vertex coupling, and moreover, that Such an approximation converges in the norm-resolvent sense. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2010
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