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This chapter provides a comprehensive review of fundamental concepts related to approximate natural orbital functionals (NOFs), emphasizing their significance in quantum chemistry and physics. Focusing on fermions, the discussion excludes…
A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for…
As a fundamental information fusion approach, the arithmetic average (AA) fusion has recently been investigated for various random finite set (RFS) filter fusion in the context of multi-sensor multi-target tracking. It is not a…
We benchmark the ground state energies and the density profiles of atomic repulsive Fermi gases in optical lattices computed via Density Functional Theory (DFT) against the results of diffusion Monte Carlo (DMC) simulations. The main focus…
The DArk Matter Particle Explorer (DAMPE) is a space-based instrument for detecting GeV-TeV cosmic rays and gamma rays. High-energy cosmic rays could be emitted from several dark matter candidates theoretically, such as the heavy dark…
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…
We study here the problem of Antenna Domain Formation (ADF) in cloud RAN systems, whereby multiple remote radio-heads (RRHs) are each to be assigned to a set of antenna domains (ADs), such that the total interference between the ADs is…
Using the Kohn-Sham (KS) inversion method of Hollins et al. [J. Phys.: Condens. Matter 29, 04LT01 (2017)], we invert densities from variational and diffusion quantum Monte Carlo (QMC) calculations to obtain benchmark QMC-KS potentials for a…
In this paper, we systematically investigate the general dark matter-electron interactions within the framework of effective field theories (EFT). We consider both the non-relativistic (NR) EFT and the relativistic EFT descriptions of the…
We show that Fermi repulsion can lead to cored density profiles in dwarf galaxies for sub-keV fermionic dark matter. We treat the dark matter as a quasi-degenerate self-gravitating Fermi gas and calculate its density profile assuming…
We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on $s$-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have…
The electronic density of states of graphene is equivalent to that of relativistic electrons. In the absence of disorder or external doping the Fermi energy lies at the Dirac point where the density of states vanishes. Although transport…
Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization…
We present an accurate local density-functional for electronic-structure calculations within the density functional theory (DFT). The functional is derived by analyzing the structure of the standard perturbative expansion of the correlation…
Kernel mean embedding is a useful tool to represent and compare probability measures. Despite its usefulness, kernel mean embedding considers infinite-dimensional features, which are challenging to handle in the context of differentially…
A density functional theory (DFT) of lattice fermion models is presented, which uses the single-particle density matrix gamma_{ij} as basic variable. A simple, explicit approximation to the interaction-energy functional W[gamma] of the…
The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis…
A variational Monte Carlo calculation of the one-body density matrix and momentum distribution of a system of Fermi hard rods (HR) is presented and compared with the same quantities for its bosonic counterpart. The calculation is exact…
We introduce the particle-hole map (PHM), a visualization tool to analyze electronic excitations in molecules in the time or frequency domain, to be used in conjunction with time-dependent density-functional theory (TDDFT) or other ab…
This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet…