English
The local density approximation in density functional theory
Post-edited
Auteurs : Seiringer, Robert (Auteur de la Conférence)
CIRM (Editeur )
81V70 - Many-body theory; quantum Hall effect
82B03 - Foundations
49K21 - Problems involving relations other than differential equations
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2066/Slides/Seiringer2019.pdf
CIRM (Editeur )
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| Density functional theory Local density approximation Uniform electron gas Exchange-correlation energy Locality of the indirect energy Graf-Schenker inequality Tensor products |
Résumé :
We present a 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 situations where the density is very flat on sufficiently large regions in space. (Joint work with Mathieu Lewin and Elliott Lieb)
Keywords : density functional theory; uniform electron gas
Codes MSC : Keywords : density functional theory; uniform electron gas
81V70 - Many-body theory; quantum Hall effect
82B03 - Foundations
49K21 - Problems involving relations other than differential equations
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2066/Slides/Seiringer2019.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 26/11/2019 Date de captation : 21/10/2019 Sous collection : Research talks arXiv category : Mathematical Physics ; Condensed Matter ; Quantum Physics Domaine : Mathematical Physics Format : MP4 (.mp4) - HD Durée : 00:52:35 Audience : Researchers Download : https://videos.cirm-math.fr/2019-10-21_Seiringer.mp4 
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Informations sur la Rencontre
Nom de la rencontre : The Analysis of Complex Quantum Systems: Large Coulomb Systems and Related Matters / Analyse des systèmes complexes: grands systèmes coulombiens et systèmes apparentésOrganisateurs de la rencontre : Barbaroux, Jean-Marie ; Panati, Annalisa ; Siedentop, Heinz Dates : 21/10/2019 - 25/10/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2066.html
Données de citation
DOI : 10.24350/CIRM.V.19570803Citer cette vidéo: Seiringer, Robert (2019). The local density approximation in density functional theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19570803 URI : http://dx.doi.org/10.24350/CIRM.V.19570803 |
Voir aussi
- [Multi angle] Combined mean-field and semiclassical limits large fermionic system / Auteur de la Conférence Chen, Li.
- [Multi angle] Microscopic description of Coulomb gases / Auteur de la Conférence Serfaty, Sylvia.
- [Multi angle] From the many-body quantum dynamics to the Vlasov equation / Auteur de la Conférence Saffirio, Chiara.
- [Multi angle] A critical Poincaré-Sobolev inequality / Auteur de la Conférence van den Bosch, Hanne.
Bibliographie
- LEWIN, Mathieu, LIEB, Elliott H., et SEIRINGER, Robert. The Local Density Approximation in Density Functional Theory. arXiv preprint arXiv:1903.04046, 2019. - https://arxiv.org/abs/1903.04046
