The magnetic Laplacian acting on discrete cusps
Spectral Theory
2017-06-12 v3 Mathematical Physics
Functional Analysis
math.MP
Abstract
We introduce the notion of discrete cusp for a weighted graph. In this context, we provethat the form-domain of the magnetic Laplacian and that of thenon-magnetic Laplacian can be different. We establish the emptiness of the essential spectrum and compute theasymptotic of eigenvalues for the magnetic Laplacian.
Keywords
Cite
@article{arxiv.1507.02638,
title = {The magnetic Laplacian acting on discrete cusps},
author = {Sylvain Golénia and Françoise Truc},
journal= {arXiv preprint arXiv:1507.02638},
year = {2017}
}
Comments
In this new version we correct some mistakes and we provide more detailed proofs. Some results are also improved