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Approximation of a general singular vertex coupling in quantum graphs
- 1.0341394 - ÚJF 2010 RIV US eng J - Journal Article
Cheon, T. - Exner, Pavel - Turek, O.
Approximation of a general singular vertex coupling in quantum graphs.
Annals of Physics. Roč. 325, č. 3 (2010), s. 548-578. ISSN 0003-4916. E-ISSN 1096-035X
R&D Projects: GA MŠMT LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : Quantum graphs * Boundary conditions * Singular vertex coupling
Subject RIV: BE - Theoretical Physics
Impact factor: 2.919, year: 2010
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.
Permanent Link: http://hdl.handle.net/11104/0184398
Number of the records: 1