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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences physical sciences electromagnetism and electronics electromagnetism
- natural sciences physical sciences quantum physics
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
- natural sciences mathematics applied mathematics numerical analysis
You need to log in or register to use this function
We are sorry... an unexpected error occurred during execution.
You need to be authenticated. Your session might have expired.
Thank you for your feedback. You will soon receive an email to confirm the submission. If you have selected to be notified about the reporting status, you will also be contacted when the reporting status will change.
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
-
H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
ERC-COG - Consolidator Grant
See all projects funded under this funding scheme
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2016-COG
See all projects funded under this callHost institution
Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
75794 PARIS
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.