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Scattering theory for graphs isomorphic to a regular tree at infinity. (English) Zbl 1282.81092

Summary: We describe the spectral theory of the adjacency operator of a graph which is isomorphic to a regular tree at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the adjacency operator on a regular tree. We develop this scattering theory using the classical recipes for Schrödinger operators in Euclidian spaces.{
©2013 American Institute of Physics}

MSC:

81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
81U05 \(2\)-body potential quantum scattering theory
05C05 Trees
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References:

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