- 95-456 Bovier A., Ghez J.-M.
- Schr\"odinger operators generated by substitutions
Oct 12, 95
(auto. generated ps),
of related papers
Abstract. In the framework of the theoretical study of quasi-crystals, we
consider one-dimensional Schr\"odinger operators with potentials generated by
primitive substitutions. First, we give the general construction of the trace
map of their associated transfer matrices. Then, under an algorithmically
verifiable hypothesis, we prove that their spectrum is singular continuous
and supported on a Cantor set of zero Lebesgue measure. Finally, we apply
this result to some examples.