Klatt Michael A, Kim Jaeuk, Torquato Salvatore
Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Department of Chemistry, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E. 2020 Mar;101(3-1):032118. doi: 10.1103/PhysRevE.101.032118.
Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a diffuse contribution, the scattering intensity from the the resulting point pattern typically inherits the Bragg peaks (long-range order) of the original lattice. Here we demonstrate how these Bragg peaks can be hidden in the effective diffraction pattern of independent and identically distributed perturbations. All Bragg peaks vanish if and only if the sum of all probability densities of the positions of the shifted lattice points is a constant at all positions. The underlying long-range order is then "cloaked" in the sense that it cannot be reconstructed from the pair correlation function alone. On the one hand, density fluctuations increase monotonically with the strength of perturbations a, as measured by the hyperuniformity order metric Λ[over ¯]. On the other hand, the disappearance and reemergence of long-range order, depending on whether the system is cloaked as the perturbation strength increases, is manifestly captured by the τ order metric. Therefore, while the perturbation strength a may seem to be a natural choice for an order metric of perturbed lattices, the τ order metric is a superior choice. It is noteworthy that cloaked perturbed lattices allow one to easily simulate very large samples (with at least 10^{6} particles) of disordered hyperuniform point patterns without Bragg peaks.
晶格上粒子的随机、不相关位移保持了原始晶格的超均匀性，即归一化密度涨落在无限波长极限下消失。除了漫散射贡献外，所得点图案的散射强度通常继承原始晶格的布拉格峰（长程有序）。在这里，我们展示了这些布拉格峰如何能隐藏在独立同分布扰动的有效衍射图案中。当且仅当位移晶格点位置的所有概率密度之和在所有位置都是常数时，所有布拉格峰才会消失。那么潜在的长程有序在某种意义上就被“隐藏”了，即仅从对关联函数无法重构它。一方面，密度涨落随着扰动强度(a)单调增加，扰动强度由超均匀性阶度量(\overline{\Lambda})衡量。另一方面，长程有序的消失和重现，取决于随着扰动强度增加系统是否被隐藏，这明显地由(\tau)阶度量捕捉到。因此，虽然扰动强度(a)似乎是扰动晶格有序度量的自然选择，但(\tau)阶度量是更好的选择。值得注意的是，隐藏的扰动晶格允许人们轻松模拟非常大的（至少有(10^{6})个粒子）无布拉格峰的无序超均匀点图案样本。
