Approximation of a general singular vertex coupling in quantum graphs

0341394 - ÚJF 2010 RIV US eng J - Článek v odborném periodiku
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
Grant CEP: GA MŠMT LC06002
Výzkumný záměr: CEZ:AV0Z10480505
Klíčová slova: Quantum graphs * Boundary conditions * Singular vertex coupling
Kód oboru RIV: BE - Teoretická fyzika
Impakt faktor: 2.919, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0184398