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math.SP2013★ 13 cited
Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators
Pavel Exner, Stepan Manko
We investigate approximations of the vertex coupling on a star-shaped graph by families of operators with singularly scaled rank-one interactions. We find a family of vertex coupli…
math.SP2013★ 7 cited
Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees
Pavel Exner, Christian Seifert, Peter Stollmann
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 geomet…