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arXiv · 1305.0656

Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees

Pavel Exner·Christian Seifert·Peter Stollmann
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Abstract

In this paper we prove that the existence of absolutely continuous spectrum of the Kirchhoff Laplacian on a radial metric tree graph together with a finite complexity of the geometry of the tree implies that the tree is in fact eventually periodic. This complements the results by Breuer and Frank in \cite{BreuerFrank2009} in the discrete case as well as for sparse trees in the metric case.

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Pavel Exner, Christian Seifert, Peter Stollmann. 2013-05-03. Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees. https://doi.org/10.1007/s00023-013-0274-4

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