Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics

0475652 - ÚJF 2018 RIV US eng J - Journal Article
Exner, Pavel - Lipovský, J.
Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics.
Journal of Mathematical Physics. Roč. 58, č. 4 (2017), č. článku 042101. ISSN 0022-2488. E-ISSN 1089-7658
R&D Projects: GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : self-adjoint coupling * high-energy regime * resonances in quantum graphs
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 1.165, year: 2017

The aim of the paper is to investigate resonances in quantum graphs with a general self-adjoint coupling in the vertices and their trajectories with respect to varying edge lengths. We derive formulae determining the Taylor expansion of the resonance pole position up to the second order, which represent, in particular, a counterpart to the Fermi rule derived recently by Lee and Zworski for graphs with the standard coupling. Furthermore, we discuss the asymptotic behavior of the resonances in the high-energy regime in the situation where the leads are attached through delta or delta'(s) conditions, and we prove that in the case of delta'(s) coupling the resonances approach to the real axis with the increasing real parts as O (Re k)(-2).
Permanent Link: http://hdl.handle.net/11104/0272311