Hybrid Quasicrystals, Transport and Localization in Products of Minimal Sets

Abstract

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 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. * CRdO thanks the partial support by CNPq.