TY - RPRT
T1 - Dynamics on a graph as the limit of the dynamics on a "fat graph"
Y1 - 2014
A1 - Gianfausto Dell'Antonio
A1 - Alessandro Michelangeli
AB - We discuss how the vertex boundary conditions for the dynamics of a quantum particle constrained on a graph emerge in the limit of the dynamics of a particle in a tubular region around the graph (\fat graph") when the transversal section of this region shrinks to zero. We give evidence of the fact that if the limit dynamics exists and is induced by the Laplacian on the graph with certain self-adjoint boundary conditions, such conditions are determined by the possible presence of a zero energy resonance on the fat graph. Pictorially, one may say that in the shrinking limit the resonance acts as a bridge connecting the boundary values at the vertex along the different rays.
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/7485
U1 - 7598
ER -