MDFT SIGNED
Mathematics of Density Functional Theory
Total Cost €
0EC-Contrib. €
0Partnership
0Views
0MDFT project word cloud
Explore the words cloud of the MDFT project. It provides you a very rough idea of what is the project "MDFT" about.
Project "MDFT" data sheet
The following table provides information about the project.
| Coordinator |
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Organization address contact info |
| Coordinator Country | France [FR] |
| Total cost | 1˙534˙159 € |
| EC max contribution | 1˙534˙159 € (100%) |
| Programme |
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC)) |
| Code Call | ERC-2016-COG |
| Funding Scheme | ERC-COG |
| Starting year | 2017 |
| Duration (year-month-day) | from 2017-09-01 to 2022-08-31 |
Partnership
Take a look of project's partnership.
| # | ||||
|---|---|---|---|---|
| 1 | CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS | FR (PARIS) | coordinator | 1˙534˙159.00 |
Map
Project objective
Density Functional Theory (DFT) is one of the most famous methods used in quantum physics and chemistry to describe matter at the microscopic scale. The purpose of the proposal is to investigate the mathematical foundations of this theory. The questions which have to be solved involve advanced tools from nonlinear analysis, partial differential equations, spectral theory, optimal transport, and numerical analysis. Several have stayed unsolved for many years. The project is prone to have an impact in many areas of mathematics, as well as in physics and chemistry.
The proposal is divided into three main tasks. The first is focused on some important questions on the foundations of DFT, including excited states, its time-dependent formulation, and the local density approximation based on the uniform electron gas model. DFT can be formulated as an inverse problem, the main question being to find the external potential knowing only the density of particles in the system. We will investigate the invertibility of the potential-to-density map, both in the stationary and time-dependent cases.
The second task deals with the derivation of simple DFT models from the true Schrödinger equation, a problem which has been largely discussed in the literature. We will work on the most challenging open questions, including for instance the relativistic Scott correction, or the proof of Bose-Einstein condensation for an infinite Bose gas in the mean-field limit.
Finally, in the last task we study some particular DFT models, which are particularly challenging from the mathematical point of view. This includes for example a highly nonlinear model for neutrons and protons, infinite crystals with deterministic and random perturbations, and a time-dependent electromagnetic field solving Maxwell's equations coupled to the quantized Dirac quantum vacuum.
Publications
| year | authors and title | journal | last update |
|---|---|---|---|
| 2019 |
Mathieu Lewin, Elliott H. Lieb, Robert Seiringer Floating Wigner crystal with no boundary charge fluctuations published pages: , ISSN: 2469-9950, DOI: 10.1103/PhysRevB.100.035127 |
Physical Review B 100/3 | 2020-04-01 |
| 2018 |
Mathieu Lewin, Elliott H. Lieb, Robert Seiringer Statistical mechanics of the uniform electron gas published pages: 79-116, ISSN: 2270-518X, DOI: 10.5802/jep.64 |
Journal de l’École polytechnique — Mathématiques 5 | 2020-04-01 |
| 2018 |
Arnaud Triay Derivation of the Dipolar Gross--Pitaevskii Energy published pages: 33-63, ISSN: 0036-1410, DOI: 10.1137/17m112378x |
SIAM Journal on Mathematical Analysis 50/1 | 2020-04-01 |
| 2019 |
Raphael Ducatez A forward-backward random process for the spectrum of 1D Anderson operators published pages: , ISSN: 1083-589X, DOI: 10.1214/19-ECP232 |
Electronic Communications in Probability 24/0 | 2020-04-01 |
| 2019 |
Mathieu Lewin, Phan Thà nh Nam, Nicolas Rougerie Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases published pages: 61901, ISSN: 0022-2488, DOI: 10.1063/1.5094331 |
Journal of Mathematical Physics 60/6 | 2020-04-01 |
| 2020 |
Mathieu Lewin, Elliott H. Lieb, Robert Seiringer The local density approximation in density functional theory published pages: 35-73, ISSN: 2578-5885, DOI: 10.2140/paa.2020.2.35 |
Pure and Applied Analysis 2/1 | 2020-04-01 |
| 2019 |
Mathieu Lewin, Peter S. Madsen, Arnaud Triay Semi-classical limit of large fermionic systems at positive temperature published pages: 91901, ISSN: 0022-2488, DOI: 10.1063/1.5094397 |
Journal of Mathematical Physics 60/9 | 2020-04-01 |
| 2019 |
Louis Garrigue Hohenberg–Kohn Theorems for Interactions, Spin and Temperature published pages: 415-437, ISSN: 0022-4715, DOI: 10.1007/s10955-019-02365-6 |
Journal of Statistical Physics 177/3 | 2020-04-01 |
| 2019 |
David Gontier, Mathieu Lewin Spin Symmetry Breaking in the Translation-Invariant Hartree--Fock Electron Gas published pages: 3388-3423, ISSN: 0036-1410, DOI: 10.1137/19m1243142 |
SIAM Journal on Mathematical Analysis 51/4 | 2020-04-01 |
| 2020 |
Ioannis Anapolitanos, Mathieu Lewin Compactness of Molecular Reaction Paths in Quantum Mechanics published pages: 505-576, ISSN: 0003-9527, DOI: 10.1007/s00205-019-01475-5 |
Archive for Rational Mechanics and Analysis 236/2 | 2020-04-01 |
| 2018 |
Louis Garrigue Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem published pages: , ISSN: 1385-0172, DOI: 10.1007/s11040-018-9287-z |
Mathematical Physics, Analysis and Geometry 21/3 | 2019-06-06 |
| 2018 |
Mathieu Lewin Existence of Hartree–Fock excited states for atoms and molecules published pages: , ISSN: 0377-9017, DOI: 10.1007/s11005-017-1019-y |
Letters in Mathematical Physics | 2019-06-06 |
| 2018 |
Mathieu Lewin Semi-classical limit of the Levy–Lieb functional in Density Functional Theory published pages: 449-455, ISSN: 1631-073X, DOI: 10.1016/j.crma.2018.03.002 |
Comptes Rendus Mathematique 356/4 | 2019-06-06 |
| 2019 |
David Gontier, Christian Hainzl, Mathieu Lewin Lower bound on the Hartree-Fock energy of the electron gas published pages: , ISSN: 2469-9926, DOI: 10.1103/physreva.99.052501 |
Physical Review A 99/5 | 2019-06-06 |
| 2019 |
Maria Esteban, Mathieu Lewin, Éric Séré Domains for Dirac–Coulomb min-max levels published pages: , ISSN: 0213-2230, DOI: 10.4171/rmi/1074 |
Revista Matemática Iberoamericana | 2019-06-06 |
| 2018 |
Lewin , Mathieu; Nam , Phan Thà nh; Rougerie , Nicolas The interacting 2D Bose gas and nonlinear Gibbs measures published pages: , ISSN: , DOI: |
Oberwolfach Reports | 2019-06-06 |
Are you the coordinator (or a participant) of this project? Plaese send me more information about the "MDFT" project.
For instance: the website url (it has not provided by EU-opendata yet), the logo, a more detailed description of the project (in plain text as a rtf file or a word file), some pictures (as picture files, not embedded into any word file), twitter account, linkedin page, etc.
Send me an email (fabio@fabiodisconzi.com) and I put them in your project's page as son as possible.
Thanks. And then put a link of this page into your project's website.
The information about "MDFT" are provided by the European Opendata Portal: CORDIS opendata.