Statistical Mechanics of the Uniform Electron Gas

@article{Lewin2018StatisticalMO,
  title={Statistical Mechanics of the Uniform Electron Gas},
  author={Mathieu Lewin and Elliott H. Lieb and Robert Seiringer},
  journal={arXiv: Mathematical Physics},
  year={2018},
  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… 

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References

SHOWING 1-10 OF 89 REFERENCES

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

1D log gases and the renormalized energy: crystallization at vanishing temperature

We study the statistical mechanics of a one-dimensional log gas or $$\beta $$β-ensemble with general potential and arbitrary $$\beta $$β, the inverse of temperature, according to the method we

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
...