Magnetic sparseness and Schrödinger operators on graphs
Abstract
We study magnetic Schrödinger 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 $\ell^{2}$ space. As a consequence, we get criteria of discreteness for the spectrum and eigenvalue asymptotics.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2017
- DOI:
- 10.48550/arXiv.1711.10418
- arXiv:
- arXiv:1711.10418
- Bibcode:
- 2017arXiv171110418B
- Keywords:
-
- Mathematics - Spectral Theory;
- Mathematics - Functional Analysis;
- 47A10;
- 34L20;
- 05C63;
- 47B25;
- 47A63