Distinguishing co-spectral quantum graphs by scattering
Spectral Theory
2023-03-08 v1 Mathematical Physics
math.MP
Abstract
We propose a simple method for resolution of co-spectrality of Schr\"odinger operators on metric graphs. Our approach consists of attaching a lead to them and comparing the -functions of the corresponding scattering problems on these (non-compact) graphs. We show that in several cases -- including general graphs on at most 6 vertices, general trees on at most 9 vertices, and general fuzzy balls -- eigenvalues and scattering data are together sufficient to distinguish co-spectral metric graphs.
Cite
@article{arxiv.2211.05465,
title = {Distinguishing co-spectral quantum graphs by scattering},
author = {Delio Mugnolo and Vyacheslav Pivovarchik},
journal= {arXiv preprint arXiv:2211.05465},
year = {2023}
}