Welcome to the webpage of the ANR DYRAQ ANR-17-CE40-0016-01

This project is funded by the French National Research Agency (Agence Nationale de la Recherche).

The aim of this project is the study of relativistic quantum systems in interaction within the framework of time-dependent partial differential equations (PDEs). We will derive and analyze effective equations in various asymptotic regimes, obtaining a simpler description of complex physical phenomena.

Relativistic systems are described using the Dirac operator, a matrix-valued first order differential operator. Contrary to its nonrelativistic analogue, the Laplacian, the Dirac operator is associated with an indefinite energy functional. In the systems we consider, the interactions are modeled by coupling the Dirac equation to other evolution equations or via a nonlinearity in the Dirac equation. Both the indefiniteness of the energy and the presence of interactions seriously complicate the analysis regarding issues of well-posedness, long time behavior of solutions and accurate estimates in the parameters of the problem.

On the mathematically rigorous basis of the analysis of nonlinear PDEs and spectral theory, we aim to develop original methods to increase the theoretical knowledge of relativistic quantum systems and their asymptotic analysis.

Scientific Team

Scientific coordinator

The scientific coordinator of this project, Simona Rota Nodari, is Maître de conférences (assistant professor) at the Institut de Mathématiques de Bourgogne, part of the Université de Bourgogne Franche-Comté, since September 2015. She works on nonlinear PDEs arising in Mathematical Physics. Using a large variety of tools ranging from variational methods to numerical analysis, she already obtained outstanding results on nonlinear effective models from relativistic quantum physics involving the Dirac operator. Recent works include results on orbital stability for infinite-dimensional Hamiltonian systems.

Scientific coordinator team

The team working on the project consists of the following members:


Simona Rota Nodari

Institut de Mathématiques de Bourgogne, Université de Bourgogne
UFR Sciences et Techniques
Faculté des Sciences Mirande, Aile A
9 avenue Alain Savary
21078 Dijon Cedex