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“Cloaking the Underlying Long-Range Order of Randomly Perturbed Lattices” is published in Physical Review E

“Cloaking the Underlying Long-Range Order of Randomly Perturbed Lattices” is published in Physical Review E

March 13, 2020 By jaeukk@princeton.edu

Read the full paper: here
Link to the journal: here

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 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 \(\overline{\Lambda}\). 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 \(\tau\) order metric. Therefore, while the perturbation strength \(a\) may seem to be a natural choice for an order metric of perturbed lattices, the \(\tau\) 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.

Filed Under: News Tagged With: Hyperuniform, perturbed lattice, URL, without long-range order

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The Torquato Group • Salvatore Torquato • Department of Chemistry, Princeton University
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