Spectral analysis for adjacency operators on graphs
Mathematical Physics
2009-11-11 v1 math.MP
Abstract
We put into evidence graphs with adjacency operator whose singular subspace is prescribed by the kernel of an auxiliary operator. In particular, for a family of graphs called admissible, the singular continuous spectrum is absent and there is at most an eigenvalue located at the origin. Among other examples, the one-dimensional XY model of solid-state physics is covered. The proofs rely on commutators methods.
Cite
@article{arxiv.math-ph/0603020,
title = {Spectral analysis for adjacency operators on graphs},
author = {M. Mantoiu and S. Richard and R. Tiedra de Aldecoa},
journal= {arXiv preprint arXiv:math-ph/0603020},
year = {2009}
}
Comments
16 pages, 9 figures