English

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