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The main topic of this thesis was to develop XUV sources for direct seeding and UV sources for high-gain harmonic generation (HGHG) at the second undulator beamline of the Free-Electron Laser in Hamburg (FLASH2). The thesis is divided into three topics: (i) UV- and (ii) XUV-seed sources and (iii) the seeding and diagnostic setups of FLASH2. In the UV section the opportunity to seed FLASH2 with HGHG is investigated. The seed radiation is generated with a purpose-built optical parametric chirped pulse amplifier (OPCPA) operating in a 10 Hz burst mode with an intra burst repetition rate of 100 kHz. The infra-red radiation is converted by third harmonic generation (THG) based on sum-frequency generation (SFG) in BBO-crystals to the UV region. In the XUV chapter, experiments with different XUV sources were carried out to investigate the option of direct XUV seeding at FLASH2. Two different concepts are considered in this thesis to enhance the conversion efficiency especially at short wavelengths. One approach is quasi-phase matching (QPM) using two different gases for the generation and the phase tuning of the XUV radiation, while the second approach is the generation of XUV radiation from ions. In addition the gas density distribution of the QPM dual gas foil target was measured with a Mach-Zehnder interferometer enabling a three dimensional analysis of the influence of adjacent jets on each other. The third section treats the development and implementation of the required equipment for seeding FLASH2. In particular the XUV spectrometer, which was used to analyse the first FEL radiation of FLASH2.

The study of chemical reactions in the finest detail, in cold collisions, offers far-reaching prospects in the fields of atomic and molecular physics, as well as the growing field of cold chemistry. The precise manipulation of the internal and external states of atoms and molecules allows unprecedented control over reaction processes. Also, influence over chemical pathways is crucial for potential applications to quantum information processing. This thesis focuses on the inelastic processes of charge transfer and radiative association in the [NaCa]^+ and [YbRb]^+ systems in the ultracold regime. These systems offer the possibility of microscopic manipulation of quantum coherences in a quantum gas, using the ion as a probe. However, ion loss from the inelastic processes can be significant, and the rate coefficient for ion loss has been measured experimentally for a Yb^+ ion immersed in Rb vapour. This thesis uses calculations from first principles to study different hybrid systems, and determines from them useful properties, including the potential energy curves, dipole moments, 'spectroscopic molecular constants, dispersion coefficients and scattering lengths for the lowest-lying energy states. The cross sections and rate coefficients for the total radiative decay processes are obtained using several different approaches, and the results are examined for a wide range of collision energies, with a particular focus on experimentally accessible energies. Consistency with experimental findings and former theoretical studies is examined, and the implication of discrepancies is discussed. This work thus provides the ongoing investigation of ultracold ion-atom hybrid systems and the broader field of ultracold chemistry with vital information needed for cooling processes like the sympathetic cooling of ions using a buffer gas of ultracold alkali atoms. In the field of quantum information processing, studies of this nature could prove especially useful in the cooling of qubits to maintain their quantum coherence

Rising interest in functionalising molecules and surface and building nano-devices, that is nanotechnology, has influenced demand for techniques that image molecules and surfaces with atomic precision. One such technique that has answered this call is Non-Contact Atomic Force Microscopy (NC-AFM), which has a very successful history of directly probing many atomic properties on a wide variety of systems. Interpretation of measurements, however, is highly dependent on knowledge of the atomic probe tip, which is generally elusive and is the most problematic issue surrounding the field. Another such issue is in understanding the atomic processes behind measurements, which to a large extent, also depends on knowledge of the atomic tip termination. Since its development, theorists have been attempting to fill in this knowledge gap, making signicant progress, but a substantial gap still remains. This thesis therefore addresses these two issues from a theoretical viewpoint. After describing the theoretical model used to simulate NC-AFM behaviour, it is used in conjunction with various theoretical techniques to study three important effects on NC-AFM measurements contributing to these issues: different tip terminations, chemical and structural; the relative stabilities of the surfaces and instabilities within the surface; surfaces defects. The systems studied were the p(2 1) and c(6 1) reconstructions of the oxidised copper (110) surface and the buckled dimer c(4 2) reconstruction of the silicon (001) surface. The stabilities of the two Cu(110):O surfaces were studied thermodynamically, where conventional theoretical methods were found to unexpectedly fail to accurately describe them, and corrections for this were studied. Using this knowledge, NC-AFM simulations were performed using two different chemical tip terminations, and were compared to experimental results, where tip identification was found to be possible on the c(6 1) surface and the p(2 1) surface if a common ad-atom defect is present. Instabilities in the third surface were studied using two different structural tip terminations, where dissipation signals were found to probe the tip-surface interactions in a specic way, due predominantly to soft modes in the surface. The role of defects in NC-AFM manipulations of this surface were then studied, which was found to be crucial to successful manipulation of the surface. As a result of these studies, a tip identification protocol whose successful implementation is novel as well as a novel atomic switching manipulation protocol have been demonstrated. This research demonstrates the important role of theory in addressing some of the most problematic issues limiting unambiguous interpretation of NC-AFM measurements. The studies have elucidated the atomic processes behind atomic NC-AFM dissipation signals when probing a surface with soft modes and have increased our ability to characterise different atomic tips.

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Les systèmes complexes résultent de l’interaction d’un grand nombre de constituants élémentaires, et présentent une architecture non triviale et adaptative. La compréhension de ces sytèmes s’est accrue considérablement grâce au récent développement de la science des réseaux, qui s’appuie sur la théorie des graphes. Cette approche permet de mettre en lumière une relation fonction-structure complexe, et simplifie l’étude théorique de nombreux processus dynamiques dont ils peuvent être le siège. On s’intéresse depuis peu à la dynamique instantanée de ces réseaux. Dans le cas particulier des réseaux sociaux, ces dynamiques non-markoviennes, c'est-à-dire présentant des effets de mémoire. Cette thèse a pour but d’approfondir notre compréhension des réseaux sociaux dynamiques, et en particulier de déterminer l'impact d’une topologie à dynamique non-markovienne sur les processus collectifs, de diffusion ou de propagation susceptibles d’apparaître au sein de tels systèmes. Nous appuyant sur un modèle stochastique existant de dynamique sociale à base d'agents actifs, nous généralisons à l'étude d'une distribution quelconque du temps d'attente entre deux interacions d'un agent. Supposée exponentielle dans le modèle original, cette distribution, mesurable dans les réseaux sociaux réels, suit en réalité une loi de puissance, révélant le caractère non-markovien de la dynamique sociale chez les êtres humains. Incluant cette propriété dans notre modèle, nous donnons une étude théorique détaillée des propriétés topologiques du réseau agrégé, union de tous les liens apparus au moins une fois dans une fenêtre temporelle donnée. / A complex system is formed by a large number of interacting elementary components, and presenting a non-trivial and adaptive architecture. The understanding of these systems has inflated through the recent development of network science, which is rooted in graph theory. This approach allows to highlight a complex function-structure relation, and to simplify the theoretical study of many dynamic processes possibly taking place in a network. The temporal nature of these networks, i.e. the fact that the links representing elementary interactions appear and disappear in time, has recently drawn a lot of attention. In the particular case of social networks, the patterns of interactions exhibit non-Markovian dynamics, i.e. memory effects are at play. This thesis dives into these issues, expanding the understanding of networks and in particular evaluating the impact of a non-Markovian dynamics on dynamical processes running on top of such systems.We build an extension of an existing stochastic agent based model of social dynamics, generalizing to the study of arbitrary distributions of the waiting time between two interactions of an agent. Assumed to be exponential in the original model, this distribution, measurable in real social networks, is in fact power law, revealing the non-Markovian character of human social dynamics. Taking this property into account in our model, we provide a detailed investigation of the topological properties of the aggregated network, formed by the union of all the links that have appeared at least once in a given temporal window.

Nous avons d'abord étudié les amplitudes de transition entre deux réseaux de spin limite avec diagramme dipolaire, fournis par l'EPRL spinfoam Lorentz modèle avec 2 sommets non-simpliciaux. Une évaluation systématique de ces amplitudes de transition ont été abordées, en identifiant lesquels étaient pertinents pour processus physiques. Grande échelle de spin le comportement et les corrélations entre la limite initiale et finale ont été exquis analytiquement pour un modèle simplifié et numériquement pour le modèle complet, en trouvant que les contributions de différents graphiques peuvent être organisées selon à leur comportement de mise à l'échelle dans une hiérarchie qui est également conservée à de petites pirouettes et bien capturée déjà par un modèle simplifié introduit. Ensuite, la dynamique cosmologique efficace dans la gravité de la boucle réduite quantique a été abordée au moyen d'une nouvelle schéma de régularisation basé sur des états préparés dans une superposition de graphes. De nouveaux hamiltoniens efficaces ont été calculés en montrant d'abord que les schémas de régularisation précédents introduits en boucle de cosmologie quantique (LQC) peuvent être obtenus dans ce nouveau modèle puis étendre le domaine de validité de notre schéma au cas non isotropique (Bianchi I). Pour le cas isotrope, le nouvel hamiltonien effectif génère une dynamique différente de celui fourni par LQC: le scénario de rebond symétrique est remplacé par un évolution qui est quasi stationnaire dans la phase de pré-rebond, puis d'accord avec le LQC un, soutenant la conjecture pour l'émergence de l'univers rebondissant à être un caractéristique générale du secteur isotrope de QRLG. / We first studied the transition amplitudes in loop quantum gravity (LQG) between two dipole spin-networks, as provided by the EPRL spinfoam model with 2 non-simplicial vertices. A systematic evaluation of these transition amplitudes has been discussed, identifying which ones were relevant for physical processes. Large scale spin behavior and correlations between the initial and final states has been evaluated, analytically for a simplified model and numerically for the full one, finding that the contributions of different graphs can be organized according to their behavior of setting to the scale in a hierarchy that is also preserved at small pirouettes and well captured already by a simplified model introduced.Beside, the effective quantum cosmological dynamics has been addressed for both isotropic and non isotropic models within the framework of Quantum reduced loop gravity (QRLG), a gauge fixed version of LQG. Dynamics has been addressed by means of a new regularization scheme based on states prepared in a superposition of graphs. New Hamiltonians have been computed, showing the usual regularization schemes introduced in loop quantum cosmology (LQC) naturally fit in this new scheme. Then we extended the domain of validity of our model to the non-isotropic case (Bianchi I spacetime). Both for isotropic and non isotropic cases, the new Hamiltonians generate a dynamics which is different from the one provided by LQC: in the isotropic case, the symmetric big bounce scenario is replaced by an evolution which is quasi stationary in the pre bounce phase and then follows the usual expansion. For Bianchi I an intriguing accelerated phase replaces the stationary one.

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