Abstract: In this presentation, we will discuss resonances for a quantum graph whose compact part is attached at a vertex to an infinite lead. The transmission condition at this vertex depends on a small parameter, and we prove, under certain assumptions about the graph's geometry, the existence of a family of resonances whose imaginary part tends to infinity.
This work is motivated by a question arising from experimental physics where such families of resonances have been observed. I will show how, with elementary mathematical tools, it is possible to establish the existence and localization of these resonances.
This is an interdisciplinary work in collaboration with Maxime Ingremeau, Ulrich Kuhl, Olivier Legrand, Junjie Lu (Univ. Nice).