Substitution Hamiltonians with bounded trace map orbits

[摘要] We investigate discrete one-dimensional Schrodinger operators with aperiodic potentials generated by primitive invertible substitutions on a two-letter alphabet. We prove that the spectrum coincides with the set of energies having a bounded trace map orbit and show that it is a Canter set of zero Lebesgue measure. This result confirms a suggestion arising from a study of Roberts and complements results obtained by Bovier and Ghez. As an application we present a class of models exhibiting a purely singular continuous spectrum with probability one. (C) 2000 Academic Press.

[发布日期] 2000-09-15

[关键词] Schrodinger operators;invertible substitutions;trace maps