相关论文: Nonexistence in Thomas-Fermi-Dirac-von Weizs\"acke…

It has been previously proven that the Kohn-Sham kinetic energy functional scales homogeneusly under generalized coordinate scaling, in a way that is obeyed by the von Weiz\"acker functional, but seems to be in contradiction with the…

According to Dirac's ideas, the vacuum consists of infinitely many virtual electrons which completely fill up the negative part of the spectrum of the free Dirac operator $D^0$. In the presence of an external field, these virtual particles…

In this short note we argue that Thomas-Fermi Theory the simplest of all density functional theories, although failing to explain features such as binding or stability of negative ions, is surprisingly accurate in estimating sizes of atoms.…

We investigate the source of error in the Thomas-Fermi-von Weizs\"acker (TFW) density functional relative to Kohn-Sham density functional theory (DFT). In particular, through numerical studies on a range of materials, for a variety of…

We consider a large neutral atom of atomic number $Z$, modeled by a pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably rescaled one-particle ground state density on the Thomas--Fermi length scale $Z^{-1/3}$. Using an…

We study the Bogoliubov-Dirac-Fock model introduced by Chaix and Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989) which is a mean-field theory deduced from no-photon QED. The associated functional is bounded from below. In the presence of…

The purpose of this article is to extend the work by Anantharaman and Canc\`es [1], and prove the existence of minimizers for the spin-polarized Kohn-Sham model in the presence of a magnetic field within the local spin density…

A Thomas-Fermi-Weizsaecker type theory is constructed, by means of which we are able to give a relatively simple proof of the stability of relativistic matter. Our procedure has the advantage over previous ones in that the critical value of…

We consider the problem of existence of constrained minimizers for the focusing mass-subcritical Half-Wave equation with a defocusing mass-subcritical perturbation. We show the existence of a critical mass such that minimizers do exist for…

We assess the ability of the Thomas--Fermi--von Weizsacker (TFW) functional within orbital-free density functional theory (DFT) to describe itinerant magnetism. Magnetic stability is evaluated through the susceptibility obtained from the…

In 2001 Wolansky \cite{Wol} introduced a particle number-Casimir functional for the Einstein-Vlasov system. Two open questions are associated with this functional. First, a meaningful variational problem should be formulated and the…

We study minimum energy configurations of $N$ particles in $\R^3$ of charge -1 (`electrons') in the potential of $M$ particles of charges $Z_\alpha>0$ (`atomic nuclei'). In a suitable large-N limit, we determine the asymptotic electron…

This paper is concerned with a study of the classical isoperimetric problem modified by an addition of a non-local repulsive term. We characterize existence, non-existence and radial symmetry of the minimizers as a function of mass in the…

We study entire minimizers of the Allen-Cahn systems. The specific feature of our systems are potentials having a finite number of global minima, with sub-quadratic behaviour locally near their minima. The corresponding formal…

A new reference state for density functional theory, termed the independent atom ansatz, is introduced in this work. This ansatz allows for the exact representation of electron density in terms of non-interacting, atom-localized orbitals.…

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…

The magnetic extension of the Thomas-Fermi-Weizs\"acker kinetic energy is used within density-functional-theory to numerically obtain the ground state densities and energies of two-dimensional quantum dots. The results are thoroughly…

Motivated by the problem of optimal portfolio liquidation under transient price impact, we study the minimization of energy functionals with completely monotone displacement kernel under an integral constraint. The corresponding minimizers…

It is widely believed that classical electromagnetism is either unphysical or inconsistent, owing to pathological behavior when self-force and radiation reaction are non-negligible. We argue that there is no inconsistency as long as it is…

We study a multi--particle model including a kinetic energy and a non linear local self-interaction, both in the bosonic and fermionic cases. In both cases, we prove that the model is well-posed if the number of particles is large enough.…