Quantum graphs: time-reversal non-invarianceand PT-symmetry

by Prof. Pavel Exner (Doppler Institute for Mathematical Physicsand Applied Mathematics, Prague)

Thursday 1 Jul 2021, 10:00 → 12:00 Europe/Kiev

https://zoom.us/j/91749209940?pwd=N2VZYUdFcm1ZdmhkTlkrK2tnVGEwZz09 (ONLINE)

Abstract:
The talk concerns effects coming from a violation of time-reversal symmetry in the vertex coupling of quantum graphs, focusing on the situation when theasymmetry is maximal at a fixed energy. It is shown that such a coupling hasa topological property: scattering at the vertex in the high-energy regimedepends substantially on the vertex parity. We explore implications of thisfact for spectral and transport properties in several classes of graphs, bothfinite and infinite periodic ones. We also identify a class of vertex couplingexhibiting a nontrivialPT-symmetry despite being self-adjoint. The resultscome from a common work with Marzieh Baradaran, Jiří Lipovský, and Miloš Tater..

Attendees can participate in the seminar using the following link:

https://zoom.us/j/91749209940?pwd=N2VZYUdFcm1ZdmhkTlkrK2tnVGEwZz09

Meeting ID: 917 4920 9940
Passcode: 061376