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The Local Density Approximation in Density Functional Theory

Mathematical Physics 2019-11-13 v2 Statistical Mechanics math.MP Chemical Physics Quantum Physics

Abstract

We give the first mathematically rigorous justification of the Local Density Approximation in Density Functional Theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the Uniform Electron Gas energy of this density. The error involves gradient terms and justifies the use of the Local Density Approximation in the situation where the density is very flat on sufficiently large regions in space.

Keywords

Cite

@article{arxiv.1903.04046,
  title  = {The Local Density Approximation in Density Functional Theory},
  author = {Mathieu Lewin and Elliott H. Lieb and Robert Seiringer},
  journal= {arXiv preprint arXiv:1903.04046},
  year   = {2019}
}

Comments

Final version to appear in Pure and Applied Analysis

R2 v1 2026-06-23T08:03:40.856Z