SISSA Open Science

Dynamics on a graph as the limit of the dynamics on a "fat graph"

 dc.contributor.author Dell'Antonio, Gianfausto dc.contributor.author Michelangeli, Alessandro dc.date.accessioned 2014-12-12T13:16:30Z dc.date.available 2014-12-12T13:16:30Z dc.date.issued 2014 dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/7485 dc.description.abstract 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. en_US 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. dc.language.iso en_US en_US dc.publisher SISSA en_US dc.relation.ispartofseries SISSA;69/2014/MATE dc.title Dynamics on a graph as the limit of the dynamics on a "fat graph" en_US dc.type Preprint en_US
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