First Order Expansion in the Semiclassical Limit of the Levy–Lieb Functional
We prove the conjectured first order expansion of the Levy-Lieb functional in the semiclassical limit, arising from Density Functional Theory (DFT). In particular, we prove a general asymptotic first order lower bound in terms of the zero point oscillation functional and the corresponding asymptotic upper bound in the case of two electrons in one dimension. This is accomplished by interpreting the problem as the singular perturbation of an Optimal Transport problem via a Dirichlet penalization.
Authors
- Simone Di Marino (ORCID: https://orcid.org/0000-0002-4959-6111)
- Maria Colombo (ORCID: https://orcid.org/0000-0003-3294-472X)
- Federico Stra (ORCID: https://orcid.org/0000-0001-8151-1045)
Institutions
- Politecnico di Torino (IT)
- Istituto Nazionale di Fisica Nucleare, Sezione di Genova (IT)
- École Polytechnique Fédérale de Lausanne (CH)
- University of Genoa (IT)
Publication Details
- Journal
- Archive for Rational Mechanics and Analysis
- Published
- 2025-11-07
- DOI
- https://doi.org/10.1007/s00205-025-02143-7
- Primary Topic
- Spectral Theory in Mathematical Physics
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- École Polytechnique Fédérale de Lausanne
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Ministero dell'Università e della Ricerca
- Air Force Office of Scientific Research