Magnetic sparseness and Schr\"odinger operators on graphs
Spectral Theory
2017-11-29 v1 Functional Analysis
Abstract
We study magnetic Schr\"odinger operators on graphs. We extend the notion of sparseness of graphs by including a magnetic quantity called the frustration index. This notion of magnetic sparse turn out to be equivalent to the fact that the form domain is an space. As a consequence, we get criteria of discreteness for the spectrum and eigenvalue asymptotics.
Keywords
Cite
@article{arxiv.1711.10418,
title = {Magnetic sparseness and Schr\"odinger operators on graphs},
author = {Michel Bonnefont and Sylvain Golénia and Matthias Keller and Shiping Liu and Florentin Münch},
journal= {arXiv preprint arXiv:1711.10418},
year = {2017}
}