06-79 Gianfausto Dell'Antonio, Lucattilio Tenuta
Quantum graphs as holonomic constraints (95K, Latex with 3 eps figures) Mar 17, 06
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 06-79.src( 06-79.keywords , paper.tex , initialstate.eps , naphthaleneskeleton.eps , tubular2.eps )