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Introduction de la relaxation dans la théorie de la fonctionnelle de la densité dépendant du temps

Abstract : This thesis presents works in 5 areas where we aim at improving or extending toward dissipative cases the TDLDA (Time Dependent Local Density Approximation) method. - The propagation in a natural basis allows first to formalize technics which are a prerequisite to the operation of methods accounting for collisions. - The SIC (Self Interaction Correction) method improves the efficiency of the full Self Interaction Correction. It allows to use efficiently this method in complex conditions such as mixed systems of metallic and covalent molecules. - The TDCDFT (Time Dependent Current and Density Functional Theory) allows to consider some time delay effects by introducing a functional of time and current. It was extended to a 3 dimensional case on little atoms and clusters. The results confirm the damping already evidenced in previous works, but TDCDFT does not predict correctly the non-linear dependence of the damping versus the excitation energy. - The TDHF((Stochastic Time-Dependent Hartree Fock) method introduces correlation by a method of stochastics jumps, in separate time-histories. This method has been modified (Average Stochastic TDHF) to use only one mean field, the jumps are then accounted for by transition probabilities, which allow to modify the occupation numbers. In this form it can work only in a closed box. We show here its extension to an open calculation space. - The RTA (Relaxation Time Approximation) was developed in a 2 dimension model. We show here the extension of this method to 3 dimensions. The amplitude of the numerical method leads to the introduction of new optimization methods. But the results do confirm the tendencies observed in the 2 dimensional case. This method also allows calculation on new molecules.
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Marc Vincendon. Introduction de la relaxation dans la théorie de la fonctionnelle de la densité dépendant du temps. Mécanique des matériaux [physics.class-ph]. Université Paul Sabatier - Toulouse III, 2018. Français. ⟨NNT : 2018TOU30253⟩. ⟨tel-02329353⟩

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