Related papers: Random Scalar Fields and Hyperuniformity
This survey explores the foundational theory and recent developments in the study of hyperuniformity. We present a comprehensive mathematical framework in the context of weakly stationary random measures, emphasizing spectral…
Phenomenologically interesting scalar potentials are highly atypical in generic random landscapes. We develop the mathematical techniques to generate constrained random potentials, i.e. Slepian models, which can globally represent…
Hyperuniform many-body systems in $d$-dimensional Euclidean space are characterized by completely suppressed (normalized) infinite-wavelength density fluctuations, and appear to be endowed with novel exotic physical properties. In this…
Hyperuniform point patterns are characterized by vanishing infinite wavelength density fluctuations and encompass all crystal structures, certain quasi-periodic systems, and special disordered point patterns. This article generalizes the…
Granular media such as sand and sugar are ubiquitous in nature and industry but are less well understood than fluids or solids. We consider the behavior of rapid granular flows where the transfer of momenta by collisions dominates. The…
The plethora of scalar fields participating in the formulation of a softly broken supersymmetric theory can threat the stability of the standard vacuum. The generic situation is twofold. Directions in scalar field space may exist along…
We show how gauge-invariant cosmological perturbations may be constructed by an unambiguous choice of hypersurface-orthogonal time-like vector field (i.e., time-slicing). This may be defined either in terms of the metric quantities such as…
We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…
Hyperuniformity characterizes a state of matter for which density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an experimental system is hyperuniform is experimentally…
Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information…
A variety of performance demands are being placed on material systems, including desirable mechanical, thermal, electrical, optical, acoustic and flow properties. The purpose of the present article is to review the emerging field of…
In this paper it is shown how to obtain, without ever using the background classical equations of motion, a simple second order Hamiltonian involving the Mukhanov-Sasaki variable describing quantum linear scalar perturbations for the case…
The formation of hypernuclei in hadron-induced reactions and in heavy-ion collisions within a combination of a covariant transport model and a statistical fragmentation approach is investigated. We study the applicability and limitations of…
Hyperuniform structures are spatial patterns whose fluctuations disappear on long length scales, making them effectively homogeneous when observed from afar. Mathematically, this means that their spectral density, $\tilde{\rho}({\bf k})$,…
Advancements in materials design and manufacturing have allowed for the production of ordered and disordered metamaterials with diverse and novel properties. Hyperuniform two-phase heterogeneous materials, which anomalously suppress density…
It has been shown numerically that systems of particles interacting with "stealthy" bounded, long-ranged pair potentials (similar to Friedel oscillations) have classical ground states that are, counterintuitively, disordered, hyperuniform…
Crystalline two-dimensional (2D) materials such as graphene possess unique physical properties absent in their bulk form, enabling many novel device applications. Yet, little is known about their amorphous counterparts, which can be…
We study a $\mathcal PT$-symmetric scalar Euclidean field theory with a complex action, using both theoretical analysis and lattice simulations. This model has a rich phase structure that exhibits pattern formation in the critical region.…
A supersolid is a system that presents long-range order and shear rigidity as a solid but which also supports a non-dissipative superflow as a superfluid. From an effective perspective, supersolids are identified with phases of matter that…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…