%0 Journal Article
%T A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds
%A Pavel Exner
%A Olaf Post
%J Mathematics
%D 2012
%I arXiv
%R 10.1007/s00220-013-1699-9
%X We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at it. The procedure involves a local change of graph topology in the vicinity of the vertex; the approximation scheme constructed on the graph is subsequently `lifted' to the manifold. For the corresponding operator a norm-resolvent convergence is proved, with the natural identification map, as the tube diameters tend to zero.
%U http://arxiv.org/abs/1205.5129v2