Statistical Mechanics of the Uniform Electron Gas

Abstract

In this paper we define and study the classical Uniform Electron Gas (UEG), a system of infinitely many electrons whose density is constant everywhere in space. The UEG is defined differently from Jellium, which has a positive constant background but no constraint on the density. We prove that the UEG arises in Density Functional Theory in the limit of a slowly varying density, minimizing the indirect Coulomb energy. We also construct the quantum UEG and compare it to the classical UEG at low density.

arXiv commentFinal version to appear in J. Ec. polytech. Math

References in corpus (16)

• Geometric methods for nonlinear many-body quantum systems
• Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals
• Next Order Asymptotics and Renormalized Energy for Riesz Interactions
• Density functional theory for strongly-interacting electrons: Perspectives for Physics and Chemistry
• The Ground States of Large Quantum Dots in Magnetic Fields
• How tight is the Lieb-Oxford bound?
• Improved Lieb-Oxford exchange-correlation inequality with gradient correction
• Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions
• Strictly correlated uniform electron droplets
• Current Densities in Density Functional Theory
• Challenging the Lieb-Oxford Bound in a systematic way
• The strictly-correlated electron functional for spherically symmetric systems revisited
• Existence of the thermodynamic limit for disordered quantum Coulomb systems
• Floating Wigner molecules and possible phase transitions in quantum dots
• A smooth, complex generalization of the Hobby-Rice theorem
• The semi-classical limit of large fermionic systems

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• Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Coulomb and Riesz potentials
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• Toward a new theory of the fractional quantum Hall effect
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• Expansion into the vacuum of stochastic gases with long-range interactions
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