Sharp diameter bound on the spectral gap for quantum graphs
Spectral Theory
2019-05-09 v1
Abstract
We establish an upper bound on the spectral gap for compact quantum graphs which depends only on the diameter and total number of vertices. This bound is asymptotically sharp for pumpkin chains with number of edges tending to infinity.
Cite
@article{arxiv.1905.03071,
title = {Sharp diameter bound on the spectral gap for quantum graphs},
author = {David Borthwick and Livia Corsi and Kenny Jones},
journal= {arXiv preprint arXiv:1905.03071},
year = {2019}
}
Comments
11 pages, 8 figures