{"publication_status":"published","page":"35-73","status":"public","date_updated":"2024-01-29T09:01:12Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","intvolume":"         2","_id":"14891","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1903.04046","open_access":"1"}],"doi":"10.2140/paa.2020.2.35","article_processing_charge":"No","date_published":"2020-01-01T00:00:00Z","title":" The local density approximation in density functional theory","quality_controlled":"1","volume":2,"type":"journal_article","article_type":"original","day":"01","year":"2020","language":[{"iso":"eng"}],"author":[{"full_name":"Lewin, Mathieu","last_name":"Lewin","first_name":"Mathieu"},{"first_name":"Elliott H.","last_name":"Lieb","full_name":"Lieb, Elliott H."},{"full_name":"Seiringer, Robert","last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"issue":"1","department":[{"_id":"RoSe"}],"month":"01","date_created":"2024-01-28T23:01:44Z","oa":1,"publisher":"Mathematical Sciences Publishers","external_id":{"arxiv":["1903.04046"]},"citation":{"ieee":"M. Lewin, E. H. Lieb, and R. Seiringer, “ The local density approximation in density functional theory,” <i>Pure and Applied Analysis</i>, vol. 2, no. 1. Mathematical Sciences Publishers, pp. 35–73, 2020.","mla":"Lewin, Mathieu, et al. “ The Local Density Approximation in Density Functional Theory.” <i>Pure and Applied Analysis</i>, vol. 2, no. 1, Mathematical Sciences Publishers, 2020, pp. 35–73, doi:<a href=\"https://doi.org/10.2140/paa.2020.2.35\">10.2140/paa.2020.2.35</a>.","ama":"Lewin M, Lieb EH, Seiringer R.  The local density approximation in density functional theory. <i>Pure and Applied Analysis</i>. 2020;2(1):35-73. doi:<a href=\"https://doi.org/10.2140/paa.2020.2.35\">10.2140/paa.2020.2.35</a>","ista":"Lewin M, Lieb EH, Seiringer R. 2020.  The local density approximation in density functional theory. Pure and Applied Analysis. 2(1), 35–73.","apa":"Lewin, M., Lieb, E. H., &#38; Seiringer, R. (2020).  The local density approximation in density functional theory. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2020.2.35\">https://doi.org/10.2140/paa.2020.2.35</a>","short":"M. Lewin, E.H. Lieb, R. Seiringer, Pure and Applied Analysis 2 (2020) 35–73.","chicago":"Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “ The Local Density Approximation in Density Functional Theory.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2020. <a href=\"https://doi.org/10.2140/paa.2020.2.35\">https://doi.org/10.2140/paa.2020.2.35</a>."},"publication":"Pure and Applied Analysis","oa_version":"Preprint","abstract":[{"text":"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.","lang":"eng"}],"publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]}}