P. Exner – séminaire GOMS

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Date(s) - 18 avril 2012

Catégories Pas de Catégories

It is a longstanding problem how to understand the coupling in vertices of a quantum graph using approximations, either by a family of appropriate \fat graphs” or by operators on the graph itself. In particular, within an approximation by Neumann Laplacians on a tube network the squeezing limit yields only the free (or Kirchho-) boundary conditions. In this talk I will report -rst a recent result coming from a common work with Olaf Post: it will be shown that adding families of suitably scaled potentials to those Laplacians one can get spectrally nontrivial vertex couplings, including those with wave functions discontinuous at the vertices. Furthermore, I will describe another result obtained together with Taksu Cheon and Ondrej Turek on approximations by Schrodinger opearators on graphs which shows a way how the problem can be solved in full generality.