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

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dc.contributor.authorDell'Antonio, Gianfausto
dc.contributor.authorMichelangeli, Alessandro
dc.date.accessioned2014-12-12T13:16:30Z
dc.date.available2014-12-12T13:16:30Z
dc.date.issued2014
dc.description.abstractWe 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.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/7485
dc.language.isoen_USen_US
dc.publisherSISSAen_US
dc.relation.ispartofseriesSISSA;69/2014/MATE
dc.titleDynamics on a graph as the limit of the dynamics on a "fat graph"en_US
dc.typePreprinten_US
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