The work of this thesis focuses on the interaction of high Rydberg states of hydrogen molecules and atoms with various doped Si semiconductor surfaces with the results compared with those obtained with an atomically flat gold surface. The major part of the thesis was carried out using para-H₂ molecular Rydberg states with principal quantum number n = 17 - 21 and core rotational quantum number N⁺ = 2. Subsequently, this study was continued using H atomic Rydberg states with principal quantum number n = 29 - 34. The high Rydberg states have been produced using two-step laser excitation. For close Rydberg surface separation (< 6 n² a.u.), the Rydberg states may be ionized due to an attractive surface potential experienced by the Rydberg electron, and the remaining ion core may be detected by applying an external electric field. An efficient ion detectability method is introduced to compare the many surface ionization profiles quantitatively. The p-type doped Si surfaces enhance the detected ion-signal more than the n-type doped Si surfaces due to the presence of widely distributed positive dopant charge fields in the p-type doped Si surfaces. As the dopant density increases, the area sampled by the resultant ions becomes effectively more neutral, and the decay rate of the potential from the surface dopant charge with distance from the surface becomes more rapid. Therefore, the minimum ionization distance is also reduced with increasing dopant density. It is found that the detected ion-signal decreases with increasing dopant density of both p- and n- type doped Si surfaces. The higher-n Rydberg states have shown higher ion detectability than that of lower-n Rydberg states and this variation also becomes smaller when increasing the dopant density. Experiments involving H2 Rydberg molecules incident on various doped Si surfaces in the presence of a Stark field at the point of excitation are also presented here. The surface ionization profiles produced via both electron and ion detection schemes are measured by changing the Stark polarization. Positive surface dopant charges oppose production of backscattered electrons and negative surface dopant charges enhance the electron-signal. For the electron detection scheme, lightly doped n-type Si surfaces show higher detectability but in the case of p-type Si surfaces the more heavily doped Si surfaces give a higher detected signal. This different behaviour of the detected ion or electron signal implies a different production mechanism. Theoretical trajectory simulations were also carried out based on a new 2D surface potential model. The results qualitatively agree with the experimental results and explain the changes of the surface ionization profiles between the various dopant types and dopant densities of the Si surfaces.

No presente trabalho, investigamos os efeitos de correlações eletrostáticas no cálculo de propriedades termodinâmicas em suspensões coloidais carregadas. Esse estudo tem por objetivo estabelecer as causas dos desvios observados no cálculo das compressibilidades osmóticas quando obtidos pela teoria de flutuações e pela equação de estado do modelo de Jellium renormalizado. Os efeitos das correlações iônicas são analisados no contexto da teoria de funcionais de densidade e da teoria de equações integrais no modelo primitivo. Nossos resultados indicam que as discrepâncias podem estar associadas a efeitos de correlações iônicas ausentes na teoria de campo médio. / In the present work we investigate the effects of electrostatic correlations on the calculation of thermodynamic properties in charged colloidal suspensions. This study has the objective of establishing the causes of the observed deviations in the calculation of the osmotic compressibility obtained by the fluctuation theory and by the equation of state from the renormalized Jellium model. The effects of the ionic correlations are analyzed under the context of the density functional theory and of the integral equations theory in the primitive model. Our results indicate that the discrepancies may be associated to ionic correlation effects absent in the mean field level.

The properties of the macroscopic world around us, and of which we are a part, are largely determined by the low energy, collective behaviour of many interacting particles, including the nuclei and, especially, the electrons present. Although the fundamental laws governing the behaviour of these many-body systems are believed to be known in principle, the practical solution of the equations of quantum mechanics remains a challenging area of research. This thesis is concerned with the application of quantum Monte Carlo methods to two model systems: the spin-polarised homogeneous electron gas, and a hole-doped electron gas. Electronic structure theory is briefly reviewed before discussing in more detail the quantum Monte Carlo methods used in this thesis. A study of the three-dimensional spin-polarised homogeneous electron gas (HEG) is then reported, where the relatively new technique of twist averaging is investigated in detail and accurate energies and pair correlation functions are obtained over densities $r_s = 0.5 – 20$ a.u. and the full range of spin-polarisation, allowing comparison with the Perdew-Zunger interpolation scheme used in local spin density approximation exchange-correlation functionals. Following this, an impurity is added to the electron gas in the form of a positively charged hole, and the interaction is studied. Relaxation energies, pair correlation functions and momentum densities are reported. Trion formation is observed over a range of carrier densities and electron-hole mass ratios in agreement with experiment. Isolated trions are also studied, where the diffusion Monte Carlo method is exact. Methodological innovations developed while carrying out this work are discussed, including a variance reduction technique for twist-averaged calculations and a new trial wave function for impurity-in-HEG calculations.

No presente trabalho, investigamos os efeitos de correlações eletrostáticas no cálculo de propriedades termodinâmicas em suspensões coloidais carregadas. Esse estudo tem por objetivo estabelecer as causas dos desvios observados no cálculo das compressibilidades osmóticas quando obtidos pela teoria de flutuações e pela equação de estado do modelo de Jellium renormalizado. Os efeitos das correlações iônicas são analisados no contexto da teoria de funcionais de densidade e da teoria de equações integrais no modelo primitivo. Nossos resultados indicam que as discrepâncias podem estar associadas a efeitos de correlações iônicas ausentes na teoria de campo médio. / In the present work we investigate the effects of electrostatic correlations on the calculation of thermodynamic properties in charged colloidal suspensions. This study has the objective of establishing the causes of the observed deviations in the calculation of the osmotic compressibility obtained by the fluctuation theory and by the equation of state from the renormalized Jellium model. The effects of the ionic correlations are analyzed under the context of the density functional theory and of the integral equations theory in the primitive model. Our results indicate that the discrepancies may be associated to ionic correlation effects absent in the mean field level.

No presente trabalho, investigamos os efeitos de correlações eletrostáticas no cálculo de propriedades termodinâmicas em suspensões coloidais carregadas. Esse estudo tem por objetivo estabelecer as causas dos desvios observados no cálculo das compressibilidades osmóticas quando obtidos pela teoria de flutuações e pela equação de estado do modelo de Jellium renormalizado. Os efeitos das correlações iônicas são analisados no contexto da teoria de funcionais de densidade e da teoria de equações integrais no modelo primitivo. Nossos resultados indicam que as discrepâncias podem estar associadas a efeitos de correlações iônicas ausentes na teoria de campo médio. / In the present work we investigate the effects of electrostatic correlations on the calculation of thermodynamic properties in charged colloidal suspensions. This study has the objective of establishing the causes of the observed deviations in the calculation of the osmotic compressibility obtained by the fluctuation theory and by the equation of state from the renormalized Jellium model. The effects of the ionic correlations are analyzed under the context of the density functional theory and of the integral equations theory in the primitive model. Our results indicate that the discrepancies may be associated to ionic correlation effects absent in the mean field level.

Cette thèse est consacrée à l’étude mathématique de divers systèmes de particules classiques et quantiques, en milieu désordonné. Elle comprend quatre travaux publiés ou soumis. Dans le premier nous fournissons une nouvelle formule permettant de prouver la localisation d’Anderson en une dimension d’espace et de caractériser la décroissance des fonctions propres à l’infini. Le second contient l’une des premières preuves de la localisation pour une infinité de particules en intéraction, dans l’approximation d’Hartree-Fock. Le troisième est dédié au modèle d’Anderson soumis à une perturbation périodique en temps. Sous certaines conditions sur la fréquence d’oscillation nous prouvons l’absence de diffusion. Dans le dernier travail nous montrons la décroissancedes corrélations pour le modèle du Jellium en une dimension dans un fond inhomogène, en utilisant la distance de Hilbert sur les cônes et le théorème de Birkhoff-Hopf. / This thesis is devoted to the mathematical study of some systems of classical and quantum particles, in a disordered medium. It comprises four published or submitted works. In the first one we provide a new formula allowing to prove Anderson localisation in one space dimension and to characterise the decay at infinity of the eigenfunctions. The second contains one of the first proofs of localisation for infinitely many particles in interaction, in the Hartree-Fock approximation. The third work is dedicated to the Anderson model in a time-periodic perturbation. Under certain conditions on the oscillation frequency we prove the absence of diffusion. In the last work we show the decay of correlations for the one-dimensional Jellium model in an inhomogeneous background, using the Hilbert distance on cones and the Birkhoff-Hopf theorem

Theoretical studies using the Kohn-Sham density functional formalism have been carried out to identify and investigate the stability of a variety of atomic clusters for their use in cluster assembled materials. The stable behavior found in a cluster system provides a way to classify inorganic clusters. The clusters in this study can be categorized in one of the following, jellium, all-metal aromatic, Zintl analogue or as a covalent metal-carbide. By understanding the electronic structure and ultimately the stable nature of a cluster first, it is proposed one can construct assemblies based on the stable cluster. The methodology presented is a viable way to design future nanomaterials with a variety of architectures and precise control over properties based on stable cluster motifs.

Abstract In this work an experimental study of size varied, neutral, and free metal clusters using synchrotron radiation excited photoelectron spectroscopy was performed. The combined core-level and valence photoelectron spectroscopic investigation indicates metallic properties for nanoscale Rb, K, Sn, and Bi clusters. In the case of Sn the experimental results suggest a metal-to-insulator transition occurring at the studied size range. In addition to the experimental results the technical implementation of the cluster production set-up is presented and jellium-model-based simulations are compared with the experimental results of the Rb and K clusters.