Cantor spectrum of graphene in magnetic fields
Spectral Theory
2020-01-08 v1 Mathematical Physics
math.MP
Abstract
We consider a quantum graph as a model of graphene in magnetic fields and give a complete analysis of the spectrum, for all constant fluxes. In particular, we show that if the reduced magnetic flux through a honeycomb is irrational, the continuous spectrum is an unbounded Cantor set of Lebesgue measure zero.
Cite
@article{arxiv.1803.00988,
title = {Cantor spectrum of graphene in magnetic fields},
author = {Simon Becker and Rui Han and Svetlana Jitomirskaya},
journal= {arXiv preprint arXiv:1803.00988},
year = {2020}
}
Comments
55 pages, 8 figures