English

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 2\ell^{2} 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}
}