Abstract:
The problem discussed in this talk comes from efforts to
understand approximation of quantum graph Hamiltonians by
Laplacians on "fat graphs". After reviewing the background and
known result in both the Neumann and Dirichlet setting we discuss
how quantum graphs with nontrivial spectral properties can be
obtained from squeezed Dirichlet networks. To illustrate the
propose strategy we work out the simplest nontrivial example, a
family of bent tubes giving a graph of one vertex and two edges,
or a two-parameter family of generalized point interactions on the
line.
