Related papers: Thomas-Fermi approximation to electronic density
The rate of normal approximation for the integral norm of kernel density estimators is investigated in the case of densities with power-type singularities. The quantities from the formulations of published results by the author are…
We consider interacting Fermi systems close to the unitary regime and compute the corrections to the energy density that are due to a large scattering length and a small effective range. Our approach exploits the universality of the density…
We study small conducting particles and thin films in an oscillating longitudinal electric field. We find the charge, current, and field distribution in the particle, the polarizability and the electric dipole absorption. We account for…
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…
The equations of state for symmetric nuclear matter and pure neutron matter are investigated with the tensor-optimized Fermi Sphere method (TOFS) up to the density $\rho=0.5$~fm$^{-3}$. This method is based on a linked-cluster expansion…
We give the first mathematically rigorous justification of the Local Density Approximation in Density Functional Theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density…
Semiclassical expansions derived in the framework of the Extended Thomas-Fermi approach for the kinetic energy density tau(r) and the spin-orbit density J(r) as functions of the local density rho(r) are used to determine the central nuclear…
We propose a simple approach for studying systems of compressed matter based on the Thomas-Fermi statistical model of single atom. The central point of our work is the development of the concept of ``statistical ionization'' by compression;…
A stochastic minimization method for a real-space wavefunction, $\Psi({\bf r}_{1},{\bf r}_{2}\ldots{\bf r}_{n})$, constrained to a chosen density, $\rho({\bf r})$, is developed. It enables the explicit calculation of the Levy constrained…
Final representation of all those measures $\mu$ for which algebraic polynomials are dense in $L_p(R, d\mu)$ is found. The weighted analogue of the Weierstrass polynomial approximation theorem and a new version of the M. Krein's theorem…
The Thomas-Fermi approximation for an atomic wavefunction is used to calculate the interaction of a neutron spin with the atomic electric field, either through motional magnetic (v x E) or possibly electric (due to the possible existence of…
The saturation density of nuclear matter $\rho_0$ is a fundamental nuclear physics property that is difficult to predict from fundamental principles. The saturation density is closely related to the interior density of a heavy nucleus, such…
We consider a pseudorelativistic model of atoms and molecules, where the kinetic energy of the electrons is given by $\sqrt{p^2+m^2}-m$. In this model the eigenfunctions are generally not even bounded, however, we prove that the…
Based on the Thomas-Fermi approach, we describe and distinguish the electron distributions around extended nuclear cores: (i) in the case that cores are neutral for electrons bound by protons inside cores and proton and electron numbers are…
Imposing the Born rule as a fundamental principle of quantum mechanics would require the existence of normalizable wave functions also for relativistic particles. Indeed, the Fourier transforms of normalized k-space amplitudes yield…
We measured the temperature and fluence dependence of the time-resolved photoinduced optical reflectivity in a decagonal Al_{71.9}Ni_{11.1}Co_{17.0} quasicrystal. We find no evidence for the relaxation of a hot thermalized electron gas as…
This article concerns the description of the electron sea of an atomic ion with the Thomas-Fermi model. The normalized ion radius $X$, ionization potential $b$ and electronic binding energy $B$ of the Thomas-Fermi ion are functions of 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…
The nuclear binding energies for 28 nuclei including several isotopic chains with masses ranging from A=64 to A=226 were evaluated using the Skyrme effective nucleon-nucleon interaction and the Extended Thomas-Fermi approximation. The…
A new method to calculate level densities for non-interacting Fermions within the constant-spacing model with a finite number of states is developed. We show that asymptotically (for large numbers of particles or holes) the densities have…