The local density approximation in density functional theory
Copyright policy )The local density approximation in density functional theory
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.
Final version to appear in Pure and Applied Analysis
- College of New Jersey United States
- Centre national de la recherche scientifique France
- PSL Research University France
- University of Paris France
- Centre De Recherche en Mathématiques de la Décision France
FOS: Physical sciences, 510, 35Q40, astrophysique), Physics - Chemical Physics, Quantum equilibrium statistical mechanics (general), Schrödinger operators, Density Functional Theory, density functional theory, Mathematical Physics, Condensed Matter - Statistical Mechanics, PDEs in connection with quantum mechanics, Computational density functional analysis in statistical mechanics, Chemical Physics (physics.chem-ph), Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), 82B10, Mathematical Physics (math-ph), [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], 520, 81V55, Local Density Approximation, Sciences connexes (physique, statistical mechanics, uniform electron gas, Molecular physics, Quantum Physics (quant-ph)
FOS: Physical sciences, 510, 35Q40, astrophysique), Physics - Chemical Physics, Quantum equilibrium statistical mechanics (general), Schrödinger operators, Density Functional Theory, density functional theory, Mathematical Physics, Condensed Matter - Statistical Mechanics, PDEs in connection with quantum mechanics, Computational density functional analysis in statistical mechanics, Chemical Physics (physics.chem-ph), Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), 82B10, Mathematical Physics (math-ph), [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], 520, 81V55, Local Density Approximation, Sciences connexes (physique, statistical mechanics, uniform electron gas, Molecular physics, Quantum Physics (quant-ph)
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