Related papers: A new look at Thomas-Fermi Theory
We consider a Thomas-Fermi mean-field model for large neutral atoms. That is, Schr\"odinger operators $H_Z^{\text{TF}}=-\Delta-\Phi_Z^{\text{TF}}$ in three-dimensional space, where $Z$ is the nuclear charge of the atom and…
We present analytical studies of a boson-fermion mixture at zero temperature with spin-polarized fermions. Using the Thomas-Fermi approximation for bosons and the local-density approximation for fermions, we find a large variety of…
The density linear response function for an inhomogeneous system of electrons in equilibrium with an array of fixed ions is considered. Two routes to its evaluation for extreme conditions (e.g., warm dense matter) are considered. The first…
We derive the criteria for the Thomas-Fermi regime of a dipolar Bose-Einstein condensate in cigar, pancake and spherical geometries. This also naturally gives the criteria for the mean-field one- and two-dimensional regimes. Our…
Due to the large value of the scattering length in nuclear systems, standard density--functional theories based on effective interactions usually fail to reproduce the nuclear Fermi liquid behavior both at very low densities and close to…
Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails,…
In the present paper, the pasta phase is studied at finite temperatures within a Thomas-Fermi (TF) approach. Relativistic mean field models, both with constant and density-dependent couplings, are used to describe this frustrated system. We…
We consider two-dimensional (2D) "artificial atoms" confined by an axially symmetric potential $V(\rho)$. Such configurations arise in circular quantum dots and other systems effectively restricted to a 2D layer. Using the semiclassical…
We introduce a new computationally efficient and accurate classical density-functional theory for water and apply it to hydration of hard spheres and inert gas atoms. We find good agreement with molecular dynamics simulations for the…
The average-density approximation is used to construct a nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas. This functional is then used to formulate a Thomas-Fermi von Weizs\"acker-like theory for the…
Elastic scattering probes directly the interaction potential. For weakly interacting condensates this potential is given by the condensate density. We investigate how the differential and total cross sections reflect the density. In…
We study the minimizers of an energy functional with a self-consistent magnetic field, which describes a quantum gas of almost-bosonic anyons in the average-field approximation. For the homogeneous gas we prove the existence of the…
We present the simplest nuclear energy density functional (NEDF) to date, determined by only 4 significant phenomenological parameters, yet capable of fitting measured nuclear masses with better accuracy than the Bethe-Weizs\"acker mass…
Density functional theory (DFT) provides a theoretical framework for efficient and fairly accurate calculations of the electronic structure of molecules and crystals. The main features of density functional theory are described and DFT…
Quantum electrodynamics is the first successful and still the most successful quantum field theory. Simple atoms, being essentially QED systems, allow highly accurate theoretical predictions. Because of their simple spectra, such atoms have…
This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in…
A novel Thomas-Fermi (TF) approach to inhomogeneous superfluid Fermi-systems is presented and shown that it works well also in cases where the Local Density Approximation (LDA) breaks down. The novelty lies in the fact that the…
We propose a neural-network-based variational framework for nuclear Density Functional Theory based on the extended Thomas--Fermi (ETF) model, in which proton and neutron number densities are represented by multilayer perceptrons and…
Faithful representations of atomic environments and general models for regression can be harnessed to learn electron densities that are close to the ground state. One of the applications of data-derived electron densities is to orbital-free…
We suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and…