Condensed Matter Seminar: Hyperuniformity of quasicrystals and related structures
Dr. Erdal C. Oğuz, TAU
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. Such systems are characterized by a local number variance associated with points within a spherical observation window of radius R that grows more slowly than the window volume in the large-R limit.
In this talk, we will provide the first rigorous hyperuniformity analysis of quasicrystals obtained by cut-and-projection method and related points sets derived from substitution tilings. Most importantly, we reveal that one-dimensional quasicrystals produced by projection from a two-dimensional lattice fall into two distinct classes determined by the width of the projection window. The number variance is either uniformly bounded in the one class for large R, or it scales logarithmically in R in the other class. This distinction provides a new classification of one-dimensional quasicrystalline systems and, as we show, the two classes exhibit distinct physical properties. Our analysis further suggests that measures of hyperuniformity may define new classes of quasicrystals in higher dimensions as well.
Event Organizer: Prof. Sasha Gerber