Section: New Results

Mathematical Physics

Participant : Francis Nier.

In [10] , A. Aftalion and F. Nier answer questions asked by J. Dalibard about the feasibility of artificial gauge potentials. This analysis provides the range of small parameters within which the linear adiabatic argument used by the physicists is certainly not destroyed by the non linear effects.

In [43] , D. Le Peutrec, F. Nier and C. Viterbo give an accurate Arrhenius law for Witten Laplacian acting on p-forms. In the case of functions the exponentially small eigenvalues are given by exponentiated differences of enegy levels between local minima and saddle points (Arrhenius law). In the case of p-forms the association of critical points with index p and critical points with index p+1 or p-1, is more subtle and is provided by Barannikov's presentation of Morse theory.

In [11] , Z. Ammari and F. Nier have proved the mean field dynamics of general bosonic systems in the presence of singular pair interaction potentials, including the important 3 dimensional Coulombic case. As compared with their previous works, they developed a slightly new strategy relying on measure transportation techniques and results presented by Ambrosio-Gigli-Savaré in their book "Gradient Flows: In Metric Spaces And In The Space Of Probability Measures" (2005).