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Einladung zum Vortrag (Zoom) von Herrn Prof. Dr. Pavel Exner am 07.02.2024 - 15:00 Uhr im Rahmen des Forschungsseminars Analysis
[07.02.2024]Im Rahmen des Forschungsseminars Analysis hält am Mittwoch, den 7. Februar 2024, um 15:00 Uhr,
Herr Prof. Dr. Pavel Exner (Doppler Institute for Mathematical Physics and Applied Mathematics, Prag)
einen Vortrag zum Thema:
Effects of time-reversal non-invariance in quantum graphs
Abstract:
The topic of this talk are quantum graphs with the vertex coupling which does not preserve the time-reversal invariance. As a case study the simplest example with the asymmetry being maximal at a fixed energy will be analyzed. In this situation the high-energy scattering depends crucially on the vertex parity; we will demonstrate implications of this fact for spectral and transport properties in several classes of graphs, both finite and infinite periodic ones. In particular, we prove the Band-Berkolaiko universality for kagome lattices with this coupling. Furthermore, we discuss other timeasymmetric graphs and identify a class of such couplings which exhibits a nontrivial PT -symmetry despite being self-adjoint; we also illustrate the role of the Dirichlet component in the vertex coupling. Finally, we show how a square lattice with such a coupling behaves in the presence of a magnetic field when the two time-asymmetry effects compete. The results come from a common work with Marzieh Baradaran, Jiří Lipovský, and Miloš Tater.
Der Vortrag findet im Rahmen eines Zoom-Meetings statt. Bei Interesse an den Zugangsdaten bitte bei Herrn PD Dr. habil. Joachim Kerner (joachim.kerner) melden.
