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The subject of the thesis focuses on new approximations studied in a formalism based on a perturbation theory allowing to describe the electronic properties of many-body systems in an approximate way. We excite a system with a small disturbance, by sending light on it or by applying a weak electric field to it, for example and the system "responds" to the disturbance, in the framework of linear response, which means that the response of the system is proportional to the disturbance. The goal is to determine what we call the neutral excitations or bound states of the system, and more particularly the single excitations. These correspond to the transitions from the ground state to an excited state. To do this, we describe in a simplified way the interactions of the particles of a many-body system using an effective interaction that we average over the whole system. The objective of such an approach is to be able to study a system without having to use the exact formalism which consists in diagonalizing the N-body Hamiltonian, which is not possible for systems with more than two particles.

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We present the multi-channel Dyson equation that combines two or more many-body Green's functions to describe the electronic structure of materials. In this thesis, we use it to model photoemission spectra by coupling the one-body Green's function with the three-body Green's function and to model neutral excitation by coupling the two-body Green's function with the four-body Green's function . We demonstrate that, unlike methods using only the one-body Green's function, our approach puts the description of quasiparticles and satellites on an equal footing. We propose a multi-channel self-energy that is static and only contains the bare Coulomb interaction, making frequency convolutions and self-consistency unnecessary. Despite its simplicity, we demonstrate with a diagrammatic analysis that the physics it describes is extremely rich. Finally, we present a framework based on an effective Hamiltonian that can be solved for any many-body system using standard numerical tools. We illustrate our approach by applying it to the Hubbard dimer and show that it is exact both at 1/4 and 1/2 filling.

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We present the second release of the real-time time-dependent density functional theory code “Quantum Dissipative Dynamics” (QDD). It augments the first version [1] by a parallelization on a GPU coded with CUDA fortran. The extension focuses on the dynamical part only because this is the most time consuming part when applying the QDD code. The performance of the new GPU implementation as compared to OpenMP parallelization has been tested and checked on a couple of small sodium clusters and small covalent molecules. OpenMP parallelization allows a speed-up by one order of magnitude in average, as compared to a sequential computation. The use of a GPU permits a gain of an additional order of magnitude. The performance gain outweighs even the larger energy consumption of a GPU. The impressive speed-up opens the door for more demanding applications, not affordable before

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We present the multi-channel Dyson equation that combines two or more many-body Green's functions to describe the electronic structure of materials. In this work we use it to model photoemission spectra by coupling the one-body Green's function with the three-body Green's function. We demonstrate that, unlike methods using only the one-body Green's function, our approach puts the description of quasiparticles and satellites on an equal footing. We propose a multi-channel self-energy that is static and only contains the bare Coulomb interaction, making frequency convolutions and self-consistency unnecessary. Despite its simplicity, we demonstrate with a diagrammatic analysis that the physics it describes is extremely rich. Finally, we present a framework based on an effective Hamiltonian that can be solved for any many-body system using standard numerical tools. We illustrate our approach by applying it to the Hubbard dimer and show that it is exact both at 1/4 and 1/2 filling.

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Sujets

Explosion coulombienne Ionization mechanisms Metal cluster Dynamique moléculaire Mean-field Molecules GW approximation Agrégats Hubbard model Energy spectrum Au-delà du champ moyen Electron correlation CAO Relaxation Instability Lasers intenses Modèle de Hubbard Semiclassic Electric field Irradiation moléculaire Fission Neutronic Chaos Dynamics Fonction de Green Density Functional Theory Electronic excitation Matel clusters Clusters Diffusion Density-functional theory Champ-moyen Dissipative effects 3620Kd Méthodes des fonctions de Green Oxyde de nickel Deposition Molecular irradiation Green's function Hierarchical model Méthode multiréférence Landau damping Metal clusters Neutronique Angle-resolved photoelectron spectroscopy FOS Physical sciences Nucléaire Collisional time-dependent Hartree-Fock Electronic properties of sodium and carbon clusters 3115ee Multirefence methods Electronic properties of metal clusters and organic molecules Numbers 3360+q Corrélations Théorie de la fonctionnelle de la densité Corrélations dynamiques Ar environment Electron-surface collision Nanoplasma Approximation GW Electronic emission Molecular dynamics Laser Coulomb explosion Extended time-dependent Hartree-Fock Instabilité Inverse bremsstrahlung collisions Méchanismes d'ionisation 3640Cg Photo-electron distributions High intensity lasers Optical response Time-dependent density-functional theory MBPT Matrice densité Activation neutronique Aggregates Hierarchical method Interactions de photons avec des systèmes libres Damping Electron emission Monte-Carlo Embedded metal cluster Neutron Induced Activation Effets dissipatifs Nuclear Coulomb presssure Nickel oxide Corrélation forte Photo-Electron Spectrum Atom laser Photon interactions with free systems Collision frequency Greens function methods TDDFT Agregats Correction d'auto-interaction Deposition dynamics Environment Dissipation

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