Dresden 2017 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 44: Statistical Physics (general)

DY 44.3: Talk

Thursday, March 23, 2017, 10:30–10:45, ZEU 147

Hyperuniformity of Quasicrystals — •Erdal C. Oğuz — School of Mechanical Engineering and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Israel

Density fluctuations in many-body systems are of fundamental importance throughout various scientific disciplines, including physics, materials science, number theory and biology. 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. Quantitatively speaking, hyperuniform systems are characterized by a local number variance of points within a spherical window of radius R that grows more slowly than the window volume in the large-R limit.

In this talk, we provide the first rigorous hyperuniformity analyses of quasicrystals by employing a new criterion for hyperuniformity to quantitatively characterize quasicrystalline point sets. We reveal that one-dimensional quasicrystals produced by projection from a two-dimensional lattice fall into two distinct classes with respect to their large-scale density fluctuations. Depending on the width of the projection window, the number variance is either uniformly bounded in the one class for large R, or it scales like ln R in the other class. This distinction provides a new classification of one-dimensional quasicrystalline systems and suggests that measures of hyperuniformity may define new classes of quasicrystals in higher dimensions as well.