Hybrid Quasicrystals, Transport and Localization in Products of Minimal Sets

TL;DR

This paper introduces hybrid quasicrystals formed from convex combinations of almost periodic sequences, exploring their spectral properties and transport behaviors in one-dimensional models, revealing a spectrum from localization to transport.

Contribution

It demonstrates that these hybrid sequences are almost periodic and studies their impact on quantum transport, linking minimality of hulls to diverse dynamical behaviors.

Findings

Sequences are almost periodic.

Transport varies from localization to extended states.

Rich dynamical behaviors depend on sequence combinations.

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 {\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.