Pour tout renseignement complémentaire, veuillez contacter les
organisateurs, Hakim
Boumaza, Mathieu
Lewin
ou Stéphane
Nonnenmacher.
| 14h - 15h |
Idriss Mazari-Fouquer (Paris-Dauphine). |
The Faber-Krahn inequality for the Stokes operator Abstract: In this work in collaboration with A. Henrot and Y. Privat, we investigate the minimisation of the first eigenvalue of the Dirichlet-Stokes operator in Rd. To be more specific, we consider the question of existence of optimal shapes, a query made more difficult by the incompressibility constraint, as well as the minimality of the ball. This latter point turns out to be dependent on the dimension, and starkly different from the case of the (scalar) Dirichlet-Laplacian. |
| 15h15 - 16h15 | Gaoyue Guo (CentraleSupelec) |
On large quantum systems : well-posedness and propagation of chaos under the purification hypothesis
Abstract: We consider infinite-dimensional quantum systems of cross-interactions whose states are identified by the so-called density operator. Under indirect measurements, the density operator evolves according to some SPDE, named the Belavkin equation, that is governed by a one-dimensional Wiener process. Its well-posedness is derived. Under an additional purification hypothesis, namely the fact that the initial density operator is of rank one, it is shown that the quantum system converges to some limit that is identified by a mean-field SPDE. |