English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The aim of the paper is to investigate resonances in quantum graphs with ageneral self-adjoint coupling in the vertices and their trajectories withrespect to varying edge lengths. We derive formulae determining the Taylorexpansion of the resonance pole position up to the second order whichrepresent, in particular, a counterpart to the Fermi rule derived recently byLee and Zworski for graphs with the standard coupling. Furthermore, we discussthe asymptotic behavior of the resonances in the high-energy regime in thesituation where the leads are attached through $\delta$ or $\delta_\mathrm{s}'$conditions, and we prove that in the case of $\delta_\mathrm{s}'$ coupling theresonances approach to the real axis with the increasing real parts as$\mathcal{O}\big((\mathrm{Re\,}k)^{-2}\big)$.

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