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THE REDUCED HARTREE-FOCK MODEL FOR SHORT-RANGE QUANTUM CRYSTALS WITH DEFECTS
- Mathematics
- 2013
In this article, we consider quantum crystals with defects in the reduced Hartree-Fock framework. The nuclei are supposed to be classical particles arranged around a reference periodic configuration.…
The Reduced Hartree–Fock Model for Short-Range Quantum Crystals with Nonlocal Defects
- Mathematics
- 2014
In this article, we consider quantum crystals with defects in the reduced Hartree–Fock framework. The nuclei are supposed to be classical particles arranged around a reference periodic configuration.…
Mathematical study of quantum and classical models for random materials in the atomic scale
- Mathematics
- 2013
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…
Removing a slab from the Fermi sea: the reduced Hartree-Fock model
- Physics
- 2018
Studying the electronic structure of defects in materials is an important subject in condensed matter physics. From a mathematical point of view, nonlinear mean-field models of localized defects in…
A reduced Hartree–Fock model of slice-like defects in the Fermi sea
- Physics
- 2018
Studying the electronic structure of defects in materials is an important subject in condensed matter physics. From a mathematical point of view, nonlinear mean-field models of localized defects in…
On stability of ground states for finite crystals in the Schrödinger-Poisson model
- Mathematics
- 2017
We consider the Schrödinger-Poisson-Newton equations for finite crystals under periodic boundary conditions with one ion per cell of a lattice. The electrons are described by one-particle Schrödinger…
A numerical study of the extended Kohn–Sham
ground states of atoms
- PhysicsCommunications in Applied Mathematics and Computational Science
- 2018
In this article, we consider the extended Kohn-Sham model for atoms subjected to cylindrically-symmetric external potentials. The variational approximation of the model and the construction of…
The reduced Hartree-Fock model with self-generated magnetic fields
- MathematicsJournal of Mathematical Physics
- 2019
We study the well-posedness of the reduced Hartree-Fock model for molecules and perfect crystals when taking into account a self-generated magnetic field. We exhibit a critical value $\alpha_c > 0$…
On orbital stability of ground states for finite crystals in fermionic Schr\"odinger--Poisson model
- Mathematics, Physics
- 2017
We consider the Schr\"odinger--Poisson--Newton equations for finite crystals under periodic boundary conditions with one ion per cell of a lattice. The electron field is described by the $N$-particle…
Mean--field stability for the junction of semi-infinite systems
- Physics
- 2019
Abstract Junction appears naturally when one studies the surface states or transport properties of quasi 1D materials such as carbon nanotubes, polymers and quantum wires. ese materials can be seen…
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