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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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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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Subjets

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

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