Mathematical Physics and Harmonic Analysis Seminar

Date: February 25, 2021

Time: 11:00AM - 12:00PM

Location: Zoom

Speaker: Salma Lahbabi, ENSEM, UHII/MSDA, UM6P

Title: A mean-field model for disordered crystals

Abstract: In this talk, we consider disordered quantum crystals in the reduced Hartree- Fock (rHF) framework. The nuclei are supposed to be classical particles ar- ranged around a reference periodic configuration. In particular, we consider a family of nuclear distributions μ(ω, ·), where ω spans a probability space Ω. Under some assumptions on the nuclear distribution μ, the average energy per unit volume admits a minimizer, which is a solution of the rHF equations with short-range Yukawa interaction [2, 1]. We obtain partial results for Coulomb interacting systems. We also study localization properties of the mean-field Hamiltonian numerically [3]. References [1] Éric Cancès, Salma Lahbabi, and Mathieu Lewin. Mean-field electronic structure models for disordered materials. In Proceeding of the International Congress on Mathematical Physics, Aalborg (Denmark), August 2012. [2] Éric Cancès, Salma Lahbabi, and Mathieu Lewin. Mean-field models for disordered crystals. J. math. pures appl., 100(2):241274, 2013. [3] Salma Lahbabi. Étude mathématique de modèles quantiques et classiques pour les matériaux aléatoires à l'échelle atomique. PhD thesis, Université de Cergy-Pontoise, 2013.