Jeffrey H. Schenker, Michael Aizenman
The Creation of Spectral Gaps by Graph Decoration
(158K, AMS-LaTeX)

ABSTRACT.  We present a mechanism for the creation of gaps in the 
spectra of self-adjoint operators defined over a Hilbert space of 
functions on a graph, which is based on the process of 
graph decoration. The resulting Hamiltonians 
can be viewed as associated with discrete models exhibiting a repeated 
local structure and a certain bottleneck in the hopping amplitudes.