A trace formula for scattering resonances of unbalanced quantum graphs
Spectral Theory
2022-08-05 v2 Mathematical Physics
math.MP
Abstract
Given an unbalanced open quantum graph, we derive a formula relating sums over its scattering resonances with integrals outside a strip. We deduce lower bounds on the number of resonances (in bounded regions of the complex plane),that are independent of the size of the graph. We also deduce partial results indicating that Benjamini-Schramm convergence of open quantum graphs should imply convergence of the empirical spectral measures.
Keywords
Cite
@article{arxiv.2206.12460,
title = {A trace formula for scattering resonances of unbalanced quantum graphs},
author = {Maxime Ingremeau},
journal= {arXiv preprint arXiv:2206.12460},
year = {2022}
}