Vol. 4, No. 1, 2022

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Scattering resonances of large weakly open quantum graphs

Maxime Ingremeau

Vol. 4 (2022), No. 1, 49–83
Abstract

We consider a sequence of open quantum graphs, with uniformly bounded data, and we are interested in the asymptotic distribution of their scattering resonances. Supposing that the number of leads in our quantum graphs is small compared to the total number of edges, we show that most resonances are close to the real axis. More precisely, the asymptotic distribution of resonances of our open quantum graphs is the same as the asymptotic distribution of the square root of the eigenvalues of the closed quantum graphs obtained by removing all the leads.

Keywords
quantum graphs, scattering resonances, scattering theory
Mathematical Subject Classification
Primary: 35P20, 58J50, 81Q35
Milestones
Received: 15 December 2020
Revised: 10 July 2021
Accepted: 9 October 2021
Published: 29 April 2022
Authors
Maxime Ingremeau
Université Côte d’Azur
Laboratoire J. A. Dieudonné UMR CNRS 7351
Nice
France