The electron transport through a molecular wire under the influence of an external laser field is studied using a reduced density matrix formalism. The full system is partitioned into the relevant part, i.e. the wire, electron reservoirs and a phonon bath. An earlier second-order perturbation theory approach of Meier and Tannor for bosonic environments which employs a numerical decomposition of the spectral density is used to describe the coupling to the phonon bath and is extended to deal with the electron transfer between the reservoirs and the molecular wire. Furthermore, from the resulting time-nonlocal (TNL) scheme a time-local (TL) approach can be determined. Both are employed to propagate the reduced density operator in time for an arbitrary time-dependent system Hamiltonian which incorporates the laser field non-perturbatively. Within the TL formulation, one can extract a current operator for the open quantum system. This enables a more general formulation of the problem which is necessary to employ an optimal control algorithm for open quantum systems in order to compute optimal control fields for time-distributed target states, e.g. current patterns. Thus, we take a fundamental step towards optimal control in molecular electronics. Numerical examples of the population dynamics, laser controlled current, TNL vs. TL and optimal control fields are presented to demonstrate the diverse applicability of the derived formalism.

In this thesis the path integral formalism is applied to the calculation of the dynamics of dissipative quantum systems. The time evolution of a system of bilinearly coupled bosonic modes is treated using the real-time path integral technique in coherent-state representation. This method is applied to a damped harmonic oscillator within the Caldeira-Leggett model. In order to get the stationary trajectories the corresponding Lagrangian function is diagonalized and then the path integrals are evaluated by means of the stationary-phase method. The time evolution of the reduced density matrix in the basis of coherent states is given in simple analytic form for weak system-bath coupling, i.e. the so-called rotating-wave terms can be evaluated exactly but the non-rotating-wave terms only in a perturbative manner. The validity range of the rotating-wave approximation is discussed from the viewpoint of spectral equations. In addition, it is shown that systems without initial system-bath correlations can exhibit initial jumps in the population dynamics even for rather weak dissipation. Only with initial correlations the classical trajectories for the system coordinate can be recovered. The path integral formalism in a combined phase-space and coherent-state representation is applied to the problem of curve-crossing dynamics. The system of interest is described by two coupled one-dimensional harmonic potential energy surfaces interacting with a heat bath. The mapping approach is used to rewrite the Lagrangian function of the electronic part of the system. Using the Feynman-Vernon influence-functional method the bath is eliminated whereas the non-Gaussian part of the path integral is treated using the perturbation theory in the small coordinate shift between potential energy surfaces. The vibrational and the population dynamics is considered in a lowest order of the perturbation. The dynamics of a Gaussian wave packet is analyzed along a one-dimensional reaction coordinate. Also the damping rate of coherence in the electronic part of the relevant system is evaluated within the ordinary and variational perturbation theory. The analytic expressions for the rate functions are obtained in the low and high temperature regimes.

In this thesis the path integral formalism is applied to the calculation of the dynamics of dissipative quantum systems. The time evolution of a system of bilinearly coupled bosonic modes is treated using the real-time path integral technique in coherent-state representation. This method is applied to a damped harmonic oscillator within the Caldeira-Leggett model. In order to get the stationary trajectories the corresponding Lagrangian function is diagonalized and then the path integrals are evaluated by means of the stationary-phase method. The time evolution of the reduced density matrix in the basis of coherent states is given in simple analytic form for weak system-bath coupling, i.e. the so-called rotating-wave terms can be evaluated exactly but the non-rotating-wave terms only in a perturbative manner. The validity range of the rotating-wave approximation is discussed from the viewpoint of spectral equations. In addition, it is shown that systems without initial system-bath correlations can exhibit initial jumps in the population dynamics even for rather weak dissipation. Only with initial correlations the classical trajectories for the system coordinate can be recovered. The path integral formalism in a combined phase-space and coherent-state representation is applied to the problem of curve-crossing dynamics. The system of interest is described by two coupled one-dimensional harmonic potential energy surfaces interacting with a heat bath. The mapping approach is used to rewrite the Lagrangian function of the electronic part of the system. Using the Feynman-Vernon influence-functional method the bath is eliminated whereas the non-Gaussian part of the path integral is treated using the perturbation theory in the small coordinate shift between potential energy surfaces. The vibrational and the population dynamics is considered in a lowest order of the perturbation. The dynamics of a Gaussian wave packet is analyzed along a one-dimensional reaction coordinate. Also the damping rate of coherence in the electronic part of the relevant system is evaluated within the ordinary and variational perturbation theory. The analytic expressions for the rate functions are obtained in the low and high temperature regimes.

The electron transport through a molecular wire under the influence of an external laser field is studied using a reduced density matrix formalism. The full system is partitioned into the relevant part, i.e. the wire, electron reservoirs and a phonon bath. An earlier second-order perturbation theory approach of Meier and Tannor for bosonic environments which employs a numerical decomposition of the spectral density is used to describe the coupling to the phonon bath and is extended to deal with the electron transfer between the reservoirs and the molecular wire. Furthermore, from the resulting time-nonlocal (TNL) scheme a time-local (TL) approach can be determined. Both are employed to propagate the reduced density operator in time for an arbitrary time-dependent system Hamiltonian which incorporates the laser field non-perturbatively. Within the TL formulation, one can extract a current operator for the open quantum system. This enables a more general formulation of the problem which is necessary to employ an optimal control algorithm for open quantum systems in order to compute optimal control fields for time-distributed target states, e.g. current patterns. Thus, we take a fundamental step towards optimal control in molecular electronics. Numerical examples of the population dynamics, laser controlled current, TNL vs. TL and optimal control fields are presented to demonstrate the diverse applicability of the derived formalism.

La diffraction des rayons X à haute résolution (XRD) et celle des neutrons polarisés (PND) sont couramment utilisées pour modéliser les densités de charge et de spin dans l'espace des positions. Par ailleurs, la diffusion Compton et diffusion Compton magnétiques sont utilisées pour observer les plus diffus des électrons appariés et non appariés, en fournissant les profils Compton directionnels de charge (DCPs) et les profils Compton magnétique directionnels (DMCPs). Il est possible d'utiliser plusieurs DCPs et DMCPs non équivalents pour reconstituer la densité d'impulsion à deux ou trois dimensions. Puisque toutes ces techniques décrivent les mêmes électrons dans différentes représentations, nous nous concentrons sur l'association de la densité d'impulsion, reconstituée par DCPs (DMCPs) avec la densité de charge et spin, telle que déterminée à parties données XRD (PND).La confrontation théorie-experience, ou --plus rarement-- entre différentes techniques expérimentales, requièrent généralement les representations des densités reconstruites dans les espaces des positions et des impulsions. Le défi que pose la comparaison des résultats obtenus par calculs ab-initio et par des approches expérimentales (dans le cas de Nit(SMe)Ph) montre la nécessité de combiner plusieurs expériences et celle d'améliorer les modèles sur lesquels reposent les approches théoriques. Nous montrons que, dans le cas d'une densité de probabilité de présence d'électrons résolue en spin, une approche simple de type Hartree-Fock ou DFT ne suffit pas. Dans le cas de YTiO3, une analyse conjointe des espaces position et impulsion (PND & MCS) met en évidence un possible couplage ferromagnétique selon Ti--O1-Ti. Pour cela, une densité magnétique de "super-position" est proposée et s'avère permettre une vérification aisée de la cohérence entre densité de charge (spin) et densité de 'impulsion déterminées expérimentalement, sans la nécessité d'une étape ab-initio. Pour aller plus loin, un modèle "de Ti isolé", basé sur des coefficients orbitaux affinés par PND, souligne l'importance du couplage cohérent métal-oxygène nécessaire à rendre compte des observations dans l'espace des impulsions.La matrice densité réduite à un électron (1-RDM) est proposée comme socle de base permettant de systématiquement combiner les espaces des positions et des impulsions. Pour reconstruire cette 1-RDM à partir d'un calcul ab-initio périodique, une approche "cluster" est proposée. Il devient alors possible d'obtenir la 1-RDM théorique résolue en spin sur des chemins de liaison chimique particuliers. Ceci nous permet notamment de clarifier la différence entre les couplages Ti--O1--Ti et Ti-O2--Ti. Il est montré que l'importance des contributions du terme d'interaction entre les atomes (de métal et d'oxygène) est différente selon que l'on considère une représentation des propriétés dans l'espace des positions ou des impulsions. Ceci est clairement observé dans les liaisons chimiques métal-oxygène et peut être illustré par une analyse séparant les contributions par orbitales. Les grandeurs decrivant les électrons dans l'espace des phases comme la fonction de Moyal peuvent également être déterminées par cette construction en "cluster". Ceci peut revêtir un intérêt particulier si la technique de diffusion Compton aux positions de Bragg pouvait être généralisée. Les premiers résultats d'un affinement de modèle simple de 1-RDM résolu en spin sont exposés. Le modèle respecte la N-représentabilité et est adapté pour plusieurs données expérimentales (telles que XRD, PND, CS, MCS ou XMD). Le potentiel de ce modèle n'est pas limité à une analyse en spin mais son usage est ici circonscrit à la description des électrons non appariés, ses limites sont identifiées et des voies d'amélioration future sont proposées. / High resolution X-ray diffraction (XRD) and polarized neutron diffraction (PND) are commonly used to model charge and spin densities in position space. Additionally, Compton scattering (CS) and magnetic Compton scattering (MCS) are the main techniques to observe the most diffuse electrons and unpaired electrons by providing the “Directional Compton Profiles" (DCPs) and ”Directional magnetic Compton Profiles" (DMCPs), respectively. A set of such DCPs (DMCPs) can be used to reconstruct two-dimensional or three-dimensional electron momentum density. Since all these techniques describe the same electrons in different space representations, we concentrate on associating the electron momentum density reconstructed from DCPs (resp. DMCPs) with electron density refined using XRD (resp. PND) data.The confrontation between theory and experiment, or between different experiments, providing several sets of experimental data, is generally obtained from the reconstructed electron densities and compared with theoretical results in position and momentum spaces. The challenge of comparing the results obtained by ab-initio computations and experimental approaches (in the Nit(SMe)Ph case) shows the necessity of a multiple experiments joint refinement and also the improvement of theoretical computation models. It proves that, in the case of a spin resolved electron density, a mere Hartree-Fock or DFT approach is not sufficient. In the YTiO3 case, a joint analysis of position and momentum spaces (PND & MCS) highlights the possible ferromagnetic pathway along Ti--O1--Ti. Therefore, a “super-position" spin density is proposed and proves to allow cross-checking the coherence between experimental electron densities in posittion and momentum spaces, without having recourse to ab initio results. Furthermore, an ”isolated Ti model" based on PND refined orbital coefficients emphasizes the importance of metal-oxygen coherent coupling to properly account for observations in momentum space.A one-electron reduced density matrix (1-RDM) approach is proposed as a fundamental basis for systematically combining position and momentum spaces. To reconstruct 1-RDM from a periodic ab initio computation, an "iterative cluster" approach is proposed. On this basis, it becomes possible to obtain a theoretical spin resolved 1-RDM along specific chemical bonding paths. It allows a clarification of the difference between Ti--O1--Ti and Ti--O2--Ti spin couplings in YTiO3. It shows that interaction contributions between atoms (metal and oxygen atoms) are different depending on whether the property is represented in position or momentum spaces. This is clearly observed in metal-oxygen chemical bonds and can be illustrated by an orbital resolved contribution analysis. Quantities for electron descriptions in phase space, such as the Moyal function, can also be determinerd by this "cluster model", which might be of particular interest if Compton scattering in Bragg positions could be generalized. The preliminary results of a simple spin resolved 1-RDM refinement model are exposed. The model respects the N-representability and is adapted for various experimental data (e.g.: XRD, PND, CS, MCS, XMD etc.). The potential of this model is not limited to a spin analysis but its use is limited here to the unpaired electrons description. The limitations of this model are analysed and possible improvements in the future are also proposed.