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Hedin's equations provide an elegant route to compute the exact one-body Green's function (or propagator) via the self-consistent iteration of a set of non-linear equations. Its first-order approximation, known as $GW$, corresponds to a resummation of ring diagrams and has shown to be extremely successful in physics and chemistry. Systematic improvement is possible, although challenging, via the introduction of vertex corrections. Considering anomalous propagators and an external pairing potential, we derive a new self-consistent set of closed equations equivalent to the famous Hedin equations but having as a first-order approximation the particle-particle (pp) $T$-matrix approximation where one performs a resummation of the ladder diagrams. This pp version of Hedin's equations offers a way to go systematically beyond the $T$-matrix approximation by accounting for low-order pp vertex corrections.

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The Bethe–Salpeter equation (BSE) is the key equation in many-body perturbation theory based on Green's functions to access response properties. Within the GW approximation to the exchange-correlation kernel, the BSE has been successfully applied to several finite and infinite systems. However, it also shows some failures, such as underestimated triplet excitation energies, lack of double excitations, ground-state energy instabilities in the dissociation limit, etc. In this work, we study the performance of the BSE within the GW approximation as well as the T-matrix approximation for the excitation energies of the exactly solvable asymmetric Hubbard dimer. This model allows one to study various correlation regimes by varying the on-site Coulomb interaction U as well as the degree of the asymmetry of the system by varying the difference of potential Δv between the two sites. We show that, overall, the GW approximation gives more accurate excitation energies than GT over a wide range of U and Δv. However, the strongly correlated (i.e., large U) regime still remains a challenge.

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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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Sujets

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

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