Statistical Mechanics of the Uniform Electron Gas
@article{Lewin2017StatisticalMO, title={Statistical Mechanics of the Uniform Electron Gas}, author={Mathieu Lewin and Elliott H. Lieb and Robert Seiringer}, journal={arXiv: Mathematical Physics}, year={2017}, volume={5}, pages={79-116} }
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
32 Citations
Homogeneous electron gas in arbitrary dimensions
- Physics
- 2020
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
- Physics
- 2022
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
- Mathematics
- 2017
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
- PhysicsPhysical Review B
- 2019
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
- PhysicsJournal of Mathematical Physics
- 2021
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
- PhysicsJournal of Mathematical Physics
- 2020
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
- Physics
- 2020
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
- Physics
- 2022
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
- Mathematics
- 2019
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
- Mathematics
- 2018
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…
References
SHOWING 1-10 OF 89 REFERENCES
2D Coulomb Gases and the Renormalized Energy
- Mathematics
- 2012
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
- Physics
- 2004
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
- Mathematics, PhysicsCalculus of Variations and Partial Differential Equations
- 2018
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
- Physics
- 1980
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
- Physics
- 2013
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
- Mathematics
- 2017
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
- Mathematics
- 2011
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
- Physics
- 1999
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
- Physics
- 1999
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…