arXiv subjects
Publications and source records attributed to Tulio O. Carvalho.
It is shown that there exits a lower bound $α>0$ to the Hausdorff dimension of the spectral measures of the one-dimensional period doubling substitution Schrödinger operator, and, generically in the hull of such sequence, $α$ is also a lower bound to the upper packing dimension of spectral measures.
We consider convex combinations of finite-valued almost periodic sequences (mainly substitution sequences) and put them as potentials of one-dimensional tight-binding models. We prove that these sequences are almost periodic. We call such combinations {\em hybrid quasicrystals} and these studies are related to the minimality, under the shift on both coordinates, of the product space of the respective (minimal) hulls. We observe a rich variety of behaviors on the quantum dynamical transport ranging from localization to transport.