Statistical Mechanics of the Uniform Electron Gas

  title={Statistical Mechanics of the Uniform Electron Gas},
  author={Mathieu Lewin and Elliott H. Lieb and Robert Seiringer},
  journal={arXiv: Mathematical Physics},
Dans cet article nous definissons et etudions le gaz uniforme d’electrons, un systeme comprenant une infinite de particules arrangees de sorte que la densite moyenne soit constante dans tout l’espace. Ceci est en principe different du Jellium, qui comprend une charge uniforme positive sans aucune contrainte sur la densite des electrons. Nous demontrons que le gaz uniforme d’electrons s’obtient en theorie de la fonctionnelle de la densite, dans la limite ou la densite du systeme varie lentement… 

Figures from this paper

Homogeneous electron gas in arbitrary dimensions

The homogeneous electron gas is one of the most studied model systems in condensed matter physics. It is also at the basis of the large majority of approximations to the functionals of density

Homogeneous electron gas in arbitrary dimensions beyond the random phase approximation

The ground state of the homogeneous electron gas is a cornerstone in quantum physics and chemistry. It is an archetypal system in the regime of slowly varying densities in which the

Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Coulomb and Riesz potentials

We consider two sharp next-order asymptotics problems, namely the asymptotics for the minimum energy for optimal point configurations and the asymptotics for the many-marginals Optimal Transport, in

Floating Wigner crystal with no boundary charge fluctuations

We modify the "floating crystal" trial state for the classical Homogeneous Electron Gas (also known as Jellium), in order to suppress the boundary charge fluctuations that are known to lead to a

Floating Wigner crystal and periodic jellium configurations

Extending on ideas of Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)], we present a modified “floating crystal” trial state for jellium (also known as the classical homogeneous electron

Macroscopic and edge behavior of a planar jellium

We consider a planar Coulomb gas in which the external potential is generated by a smeared uniform background of opposite-sign charge on a disc. This model can be seen as a two-dimensional Wigner

At the edge of a one-dimensional jellium

We consider a one-dimensional classical Wigner jellium, not necessarily charge neutral, for which the electrons are allowed to exist beyond the support of the background charge. The model can be seen

The classical Jellium and the Laughlin phase

I discuss results bearing on a variational problem of a new type, inspired by fractional quantum Hall physics. In the latter context, the main result reviewed herein can be spelled as “the phase of

Universal Functionals in Density Functional Theory

In this chapter we first review the Levy-Lieb functional, which gives the lowest kinetic and interaction energy that can be reached with all possible quantum states having a given density. We discuss

Mathematical study of some systems of particles in a disordered medium

This thesis is devoted to the mathematical study of some systems of classical and quantum particles, in a disordered medium. It comprises four published or submitted works. In the first one we



2D Coulomb Gases and the Renormalized Energy

We study the statistical mechanics of classical two-dimensional “Coulomb gases” with general potential and arbitrary β, the inverse of the temperature. Such ensembles also correspond to random matrix

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

We report diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range rs=100–150. We have tested different types of orbital for use in the approximate wave

The semi-classical limit of large fermionic systems

We study a system of N fermions in the regime where the intensity of the interaction scales as 1 / N and with an effective semi-classical parameter $$\hbar =N^{-1/d}$$ħ=N-1/d where d is the space

The charge fluctuations in classical Coulomb systems

We study the asymptotic behavior of the charge fluctuations 〈(QΛ − 〈(QΛ〉)2〉 in infinite classical systems of charged particles, and show, under certain clustering assumptions, that if the charge

Higher‐Dimensional Coulomb Gases and Renormalized Energy Functionals

We consider a classical system of n charged particles in an external confining potential in any dimension d ≥ 2. The particles interact via pairwise repulsive Coulomb forces and the coupling

The strictly-correlated electron functional for spherically symmetric systems revisited

The strong-interaction limit of the Hohenberg-Kohn functional defines a multimarginal optimal transport problem with Coulomb cost. From physical arguments, the solution of this limit is expected to

Density Functional Theory and Optimal Transportation with Coulomb Cost

We present here novel insight into exchange‐correlation functionals in density functional theory, based on the viewpoint of optimal transport. We show that in the case of two electrons and in the

Strictly correlated electrons in density-functional theory

Electrons at a fixed density approach a strictly correlated limit as their Coulomb interaction is scaled to infinity. We find the exact energy for strictly correlated electrons in spherical

Coulomb Systems at Low Density: A Review

Results on the correlations of low-density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical