13-38 Pavel Exner, Christian Seifert, Peter Stollmann

Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees (365K, pdf) May 6, 13

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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

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