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Modélisation mathématique et analyse numérique des modèles de type Bloch pour les boîtes quantiques

Kole Keita 1 
1 EDP - Equations aux Dérivées Partielles
LJK - Laboratoire Jean Kuntzmann
Abstract : Quantum dots are nanostructures confined in the three space dimensions. Since many decades, numerous etudies have been devoted to these structures for their interesting electronic and optical properties. In this thesis, we model the electronic behaviour of quantum dots thanks to a Bloch type model derived in the Heisenberg formalism. The closure of equations leads to a nonlinear model steming from Coulomb and electron-phonon interactions. We study the qualitative properties of the obtained Bloch models (trace, hermicity and positiveness) and the Cauchy problem for the semi-classical model coupling Bloch and Maxwell equations to describe laser-quantum dot interaction. We derive also formally rate equations from the nonlinear Bloch equations. The discretizations of one-dimensional Maxwell-Bloch equations involve splitting methods for the Bloch equations, which enable the preservation of the qualitative properties of the continuous model. The validation of some simplification is performed thanks to self-induced transparency and coherence transfer test cases.
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Submitted on : Thursday, December 11, 2014 - 9:27:56 PM
Last modification on : Tuesday, October 19, 2021 - 11:13:14 PM
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  • HAL Id : tel-01094229, version 1

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Kole Keita. Modélisation mathématique et analyse numérique des modèles de type Bloch pour les boîtes quantiques. Mathématiques [math]. Université de Grenoble; Grenoble University, 2014. Français. ⟨NNT : ⟩. ⟨tel-01094229v1⟩

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