Seminario Fismat | Cantor Spectrum of a Model of Graphene in Magnetic Field (Svetlana Jitomirskaya, Universidad de California, Irvine)

We consider a quantum graph as a model of graphene in magnetic fi elds 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 and Hausdorff dimension bounded by 1/2.