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