Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions

Abstract

The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function g2(r) or its corresponding structure factor S(k) is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density ρ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic "hyperuniform" varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms for the structure factor. This formulation enables us to devise an improved algorithm to construct systematically canonical-ensemble particle configurations with such targeted pair statistics, whenever realizable. As a proof-of-concept, we test the algorithm by targeting several different structure factors across dimensions that are known to be realizable and one hyperuniform target that is known to be nontrivially unrealizable. Our algorithm succeeds for all realizable targets and appropriately fails for the unrealizable target, demonstrating the accuracy and power of the method to numerically investigate the realizability problem. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but were heretofore not known to be realizable by disordered hyperuniform point configurations, including d-dimensional Gaussian structure factors, d-dimensional generalizations of the 2D one-component plasma (OCP), the d-dimensional Fourier duals of the previous OCP cases. Moreover, we also explore unusual nonhyperuniform targets, including "hyposurficial" and "antihyperuniform" examples. In all of these instances, the targeted structure factors were achieved with high accuracy, suggesting that they are indeed realizable by equilibrium configurations with pairwise interactions at positive temperatures. Remarkably, we also show that the structure factor of nonequilibrium "perfect glass" specified by two-, three-, and four-body interactions, can also be realized by equilibrium pair interactions at positive temperatures. Our findings lead us to the conjecture that any realizable structure factor corresponding to either a translationally invariant equilibrium or nonequilibrium system can be attained by an equilibrium ensemble involving only effective pair interactions. Our investigation not only broadens our knowledge of analytical functional forms for g2(r) and S(k) associated with disordered point configurations across dimensions but also deepens our under...

Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling

“…There have been two conceptual approaches to address various issues on computer glasses, including the structure factors that vary depending on the protocols used. 1,2,[5][6][7][8][9][10][11][12][13][14]16 One is the ensemble approach to investigate physically relevant packings based on the packing protocol selected. The other method is the geometric-structure approach for the quantitative characterization of single-packing configurations to enumerate and classify the jammed structures.…”

“…On the one hand, the ensemble approach has involved the problem that the protocol-dependency of the occurrence frequency of jammed configurations leads to the ambiguity of weighing jammed states. 1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17] Recently, however, the protocoldependency problem is theoretically tackled: the canonical ensemble method is developed for a large number of allowed configurations to resolve the configuration realizability issue. 16 The geometric-structure study, on the other hand, has distinguished three types of jamming for densely packed spheres: 1,2,11 local, collective and strict jammings.…”

“…1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17] Recently, however, the protocoldependency problem is theoretically tackled: the canonical ensemble method is developed for a large number of allowed configurations to resolve the configuration realizability issue. 16 The geometric-structure study, on the other hand, has distinguished three types of jamming for densely packed spheres: 1,2,11 local, collective and strict jammings. These types of jamming are hierarchical in that local and collective jammings are prerequisites for collective and strict ones, respectively, as follows: (i) in locally jammed states, a particle cannot translate when the positions of all other spheres in the packing are fixed; (ii) in collectively jammed states, particles prevented from translating are further stable to uniform compression; (iii) strictly jammed packings are stable against both uniform and shear deformations.…”

“…26,[84][85][86][87] The similarity in anharmonic vibrations suggests that the ensemble of configurations visited by the slow dynamics could reveal the characteristics of marginal stability associated with the free-energy landscape, even though possible configurations depend on a protocol adopted. 1,2,[5][6][7][8][9][10][11][12][13][14]16…”

“…Hyperuniformity is characterized by density fluctuations that decrease to zero at the longest scales. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] We have observed the hyperuniform states in a variety of complex soft matter systems, including foams, polymer blends, colloidal suspensions and biological tissues (see ref. 1 and 2 for reviews).…”