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Title:
Vertex coupling effects in quantum graph spectra
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Abstract:
The main topic of this talk are quantum graphs with the vertex coupling violating the time-reversal invariance. As a case study we analyze a simple example in which the asymmetry is maximal at a fixed energy. This has an interesting consequence, namely that high-energy scattering dependscrucially 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. We will also discuss other time-asymmetric graphs and identify a class of such couplings which exhibits a nontrivial PT-symmetry despite being self-adjoint. The results come from a common work with Marzieh Baradaran, Jiˇr ́ı Lipovsk ́y, and Miloˇs Tater.
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