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PhD Defense
Organizers: Mathieu Lewin


PhD Defense of Salma Lahbabi (Cergy): "Mathematical study of quantum and classical models for random materials in the atomic scale"
Wednesday 03 July 2013, 10:00 - 12:00
Amphi Darboux


Abstract: The contributions of this thesis concern two topics. The first part is dedicated to the study of mean-field models for the electronic structure of materials with defects. In Chapter 2, we introduce and study the reduced Hartree-Fock (rHF) model for disordered crystals. We prove the existence of a ground state and establish, for (short-range) Yukawa interactions, some properties of this ground state. In Chapter 3, we consider crystals with extended defects. Assuming Yukawa interactions, we prove the existence of an electronic ground state, solution of the self-consistent field equation. We also investigate the case of crystals with low concentration of random defects. In Chapter 4, we present some numerical results obtained from the simulation of one-dimensional random systems. In the second part, we consider multiscale-in-time kinetic Monte Carlo models. We prove, for the three models presented in Chapter 6, that in the limit of large time-scale separation, the slow variables converge to an effective dynamics. Our results are illustrated by numerical simulations.

Key words: random Schrödinger operators, disordered crystals, electronic structure, reduced Hartree-Fock theory, thermodynamic limit, kinetic Monte-carlo type models, effective dynamics, multiscale-in-time problems, Poisson process.

Jury: Xavier BLANC (Paris 7), Éric CANCÈS (École des Ponts ParisTech), Maria J. ESTEBAN (CNRS & Université Paris-Dauphine), François GERMINET (Université de Cergy-Pontoise), Frédéric KLOPP (Paris 6), Mathieu LEWIN (CNRS & Université de Cergy-Pontoise), Gianluca PANATI (Università di Roma "La Sapienza"), Jan Philip SOLOVEJ (University of Copenhagen)