A mean-field model for disordered crystals Date(s) : 02/06/2015 iCal10 h 00 min - 11 h 00 min In this talk, we consider disordered quantum crystals in the reduced Hartree-Fock (rHF) framework. The nuclei are supposed to be classical particles arrangedaround a reference periodic configuration. We first study crystals with extended defects, such as dislocations or doping in semi-conductors, with nuclear density$\mu = \mu_{per} + \nu$where $\mu_{per}$ is a periodic nuclear distribution corresponding to the backgroundperfect crystal and $\nu$ represents the defect. We next consider a family of nucleardistributions $\mu(\omega, \cdot)$, where $\omega$ spans a probability space $\Omega$. Under some assumptionson the nuclear distribution $\mu$, we prove the existence of an electronicground state $\gamma$, solution of the rHF equations with short-range Yukawa interaction for both types of systems. We obtain partial results for Coulombinteracting systems. We also consider the case of crystals with a low concentrationof random defects. [https://www.rocq.inria.fr/matherials/spip.php?rubrique170] Catégories Séminaire Analyse Appliquée (AA)
