Some Results on Absolutely Continuous Spectrum for Laplacians on Radial Metric Tree Graphs

26.07.2023  –  Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie

Dr. Christian Seifert (TUHH)

Abstract: Given a radial metric tree graph, we consider Laplacians with self-adjoint coupling conditions at the vertices. We consider the questions whether presence of absolutely continuous spectrum has consequences on the geometry of the graph.
Indeed, we will show that, for a large class of coupling conditions, under a suitable finite complexity condition the graph (as well as the couplings) have to be eventually periodic.

The talk is based on joint works with Pavel Exner, Jonathan Rohleder, and Peter Stollmann.