Sommaire:

In a point pattern, let the variance associated with the number of points contained in a spherical window of radius $R$ be denoted by $\sigma^2(R)$. Hyperuniform point patterns in $d$ dimensions do not possess infinite-wavelength fluctuations or, equivalently, possess a number variance $\sigma^2(R)$ that grows more slowly than the window volume, i.e., $R^d$, and thus the corresponding static structure factor $S(k)$ vanishes as $k \to 0$. Hyperuniform systems include all infinite periodic structures, aperiodic quasicrystals, and some special disordered systems. Previous investigations showed that the characteristic small-wavelength scaling of the structure factor and the number variance for large $R$ in hyperuniform systems can be thought of as a useful tool to rank order systems according to the degree to which large-scale density fluctuations are suppressed. In this talk, we investigate the hyperuniformity in one- and two-dimensional quasicrystals with a variety of different scaling factors and rotational symmetries. First, we deliver a proof of the hyperuniformity of quasicrystals. We further study how the small-wavelength scaling and the number variance depends on the intrinsic properties of the quasicrystal such as incommensurate length scales. We find that, unlike crystals, quasicrystals' small-wavelength scattering behavior crucially depends on the dimension. We compare these results to a number of different periodic systems as well as disordered hyperuniform systems.

Pour plus d'informations, merci de contacter Berthier L.