In a recent paper, in collaboration with Mathieu Lewin and Phan Thành Nam, we showed that nonlinear Gibbs measures based on Gross-Pitaevskii like functionals could be derived from many-body quantum mechanics, in a mean-field limit. This text summarizes these findings. It focuses on the simplest, but most physically relevant, case we could treat so far, namely that of the defocusing cubic NLS functional on a 1D interval. The measure obtained in the limit, which lives over , has been previously shown...
Je résume dans ce texte des travaux récents, en collaboration avec Mathieu Lewin, sur la modélisation des (multi-)polarons. Il s’agit de décrire le système physique formé par l’interaction entre une ou plusieurs particules chargées et un cristal constitué d’un nombre infini de noyaux classiques et d’électrons quantiques. Nous définissons un nouveau modèle en couplant l’équation de Schrödinger pour les particules chargées avec un modèle de type Hartree-Fock réduit décrivant la réaction des électrons...
We consider a multi-polaron model obtained by coupling the many-body Schrödinger equation for interacting electrons with the energy functional of a mean-field crystal with a localized defect, obtaining a highly non linear many-body problem. The physical picture is that the electrons constitute a charge defect in an otherwise perfect periodic crystal. A remarkable feature of such a system is the possibility to form a bound state of electrons via their interaction with the polarizable background....
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