Hyperuniformity of quasicrystals and related structures
Erdal Oguz (Tel Aviv University)
Density fluctuations in many-body systems are of fundamental importance throughout various scientific disciplines. Hyperuniform systems, which include crystals and quasicrystals, have density fluctuations that are anomalously suppressed at long wavelengths compared to the fluctuations in typical disordered point distributions such as in ideal gases and liquids.
In this talk, I will provide the first rigorous hyperuniformity analysis of quasicrystals and related points sets, and its consequences. Most importantly, we reveal that one-dimensional quasicrystals obtained by the cut-and-project method fall into two distinct classes with respect to their large-scale density fluctuations. This distinction provides a new classification scheme of quasicrystalline systems. Furthermore, our results suggest that these two classes exhibit distinct physical properties; for instance, by employing a tight-binding model, we discover that wave localization in each class displays a qualitatively different behavior.