Related papers: A Density-Based Continuous Local Symmetry Measure
The spontaneous symmetry breaking of a local chiral symmetry to its diagonal vector symmetry naturally realizes a complete geometrical structure more general than that of Yang-Mills (YM) theory, rather similar to that of gravity. A good…
We consider the use of the energy density for describing a localization of relativistic particles. This method is consistent with the causality requirements. The related positive operator valued measure is presented. The probability…
Electrostatic correlations between ions dissolved in water are known to impact their transport properties in numerous ways, from conductivity to ion selectivity. The effects of these correlations on the solvent itself remain, however, much…
The structure and degree of order in soft matter and other materials is intimately connected to the nature of the interactions between the particles. One important research goal is to find suitable control mechanisms, to enhance or suppress…
Localization by a broken particle-hole symmetry in a random system of non-interacting quantum particles is studied on a $d$--dimensional lattice. Our approach is based on a chiral symmetry argument and the corresponding invariant measure,…
Molecular chirality leads to a wonderful variety of equilibrium structures, from the simple cholesteric phase to the twist-grain-boundary phases, and it is responsible for interesting and technologically important materials like…
Chamfer Distance (CD) and Earth Mover's Distance (EMD) are two broadly adopted metrics for measuring the similarity between two point sets. However, CD is usually insensitive to mismatched local density, and EMD is usually dominated by…
The use of the absolute measure of local chirality is championed since it has a uniform distribution for randomly reshuffled chiral components so that any deviations from uniformity in the associated "X-distribution" are directly…
We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The…
Complex systems have become a popular lens for analyzing cities and complexity theory has many implications for urban performance and resilience. This paper develops a typology of measures and indicators for assessing the physical…
Sphericity and roundness are fundamental measures used for assessing object uniformity in 2D and 3D images. However, using their strict definition makes computation costly. As both 2D and 3D microscopy imaging datasets grow larger, there is…
We analytically calculate the contribution to the local density of states due to thermal sources in a disk-like patch within the framework of fluctuational electrodynamics. We further introduce a wavevector cutoff method to approximate this…
In an earlier article, we have "derived" space, as a part of the Random Dynamics project. In order to get locality we need to obtain reparametrization symmetry, or equivalently, diffeomorphism symmetry. There we sketched a procedure for how…
Parametric correlations are studied in several classes of covariant density functional theories (CDFTs) using a statistical analysis in a large parameter hyperspace. In the present manuscript, we investigate such correlations for two…
We propose a fully ab initio theory to compute the electron density response under the perturbation in the local field. This method is based on our recently developed local dielectric response theory [Phys. Rev. B 92, 241107(R), 2015],…
In addition to being the core quantity in density functional theory, the charge density can be used in many tertiary analyses in materials sciences from bonding to assigning charge to specific atoms. The charge density is data-rich since it…
The common notion suggests that metallic glasses (MGs) are a homogeneous solid at the macroscopic scale; however, recent experiments and simulations indicate that MGs contain nano-scale elastic heterogeneities. Despite the fundamental…
In the current density functional theory of linear and nonlinear time-dependent phenomena, the treatment of exchange and correlation beyond the level of the adiabatic local density approximation is shown to lead to the appearance of…
The role of inhomegeneity in determining the properties of correlated electron systems is poorly understood because of the dearth of structural probes of disorder at the nanoscale. Advances in both neutron and x-ray scattering…
We review the results of our recent numerical investigations on the electronic properties of disordered two dimensional systems with chiral unitary, chiral orthogonal, and chiral symplectic symmetry. Of particular interest is the behavior…