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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.

Continuer la lecture Partager

Sujets

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

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