Gianfausto Dell'Antonio, Lucattilio Tenuta
Quantum graphs as holonomic constraints
(95K, Latex with 3 eps figures)

ABSTRACT.  We consider the dynamics on a quantum graph as the limit of the dynamics generated by a one-particle Hamiltonian in $\field{R}{2}$ with a potential having a deep strict minimum on the graph, when the width of the well shrinks to zero. For a generic graph we prove convergence outside the vertices to the free dynamics on the edges. For a simple model of a graph with two edges and one vertex, we prove convergence of the dynamics to the one generated by the Laplacian with Dirichlet boundary conditions in the vertex.