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Séminaire Laurent Schwartz — EDP et applications

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Nicolas Rougerie
Sur la modélisation de l’interaction entre polarons et cristaux quantiques
Séminaire Laurent Schwartz — EDP et applications (2012-2013), Exp. No. 7, 24 p., doi: 10.5802/slsedp.36
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Résumé - Abstract

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 du cristal. Nous étudions l’existence d’états liés (minimiseurs de la fonctionnelle d’énergie) et démontrons que le modèle de Pekar pour le grand polaron peut se déduire du nôtre dans une limite macroscopique.

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