Les effets conjoints du désordre (i.e. des impuretés) et des interactions constituent une des questions les plus fondamentales de la Physique de la Matière Condensée qui a reçu énormément d'attention dans les dernières décennies. La transition de phase quantique du Superfluide vers le verre de Bose déclenchée par le désordre s'est révélée énigmatique tant pour les théoriciens que pour les expérimentateurs et des questions restent ouvertes malgré tous leurs efforts. Les travaux présentés dans ce manuscrit abordent certaines de ces questions pour deux modèles de bosons de coeur dur désordonnés à deux dimensions : valeurs des exposants critiques qui gouvernent la transition ; propriétés inhomogènes des phases en compétition ; scénario physique au point critique ; propriétés de localisation des excitations bosoniques. On utilise trois approches différentes pour la transition afin d'explorer ce problème. En premier lieu, on montre comment les fractions superfluide et du condensat de Bose-Einstein sont affectées par le désordre dans une approximation de Champ Moyen qui, bien qu'incapable de capturer la transition, donne accès à des caractéristiques qualitatives intéressantes. En se basant sur cette solution Champ Moyen, on introduit les fluctuations quantiques à travers une théorie d'ondes de spin linéaires dans l'espace réel qui capture la transition et dévoile un comportement non trivial du spectre d'excitations. Finalement, on explore minutieusement la région critique quantique par des simulations de Monte Carlo Quantique à l'état de l'art, menant à une évaluation précise des exposants critiques et à une surprenante absence d'auto-moyennation dans le régime du verre de Bose / The interplay of disorder (i.e. impurities) and interactions is one of the most fundamental questions in Condensed Matter Physics that has received a lot attention in the past couple of decades. The quantum phase transition from Superfluid to Bose glass driven by disorder has puzzled theoreticians and experimentalists alike, leaving unresolved questions despite their best efforts. The work presented in this thesis addresses some of these questions for two models of disordered hard-core bosons in two dimensions. In particular, the values of the critical exponents governing the transition, the inhomogeneous properties of the competing phases, the physical scenario at criticality and the bosonic excitations' localization properties are investigated. Three different approaches to the transition are used to explore this problem. We first show how Bose-condensate and superfluid fractions are affected by disorder in a Mean-Field approximation, which is unable to capture a transition, but reveals interesting qualitative features. Building on such a Mean-Field solution, quantum fluctuations are then introduced using a linear spin-wave theory in real space which does capture the transition and furthermore unveils a non-trivial behavior for the excitation spectrum. Finally, the quantum criticality is explored in great detail using state-of-the-art Quantum Monte Carlo simulations, leading to a precise evaluation of the critical exponents and a surprising absence of self-averaging in the Bose glass regime

Dans cette thèse, je présente ma contribution à la recherche du boson de Higgs du Modèle Standard dans son canal de désintégration en deux leptons taus dans le sous-canal τlepτhad. J’ai contribué aux différentes étapes de cette analyse. Premièrement, j’ai travaillé sur le développement du framework utilisé pour produire les fichiers d’analyse qui contiennent les informations nécessaires à cette étude. J’ai également participé au développement du framework utilisé pour introduire les prédictions des bruits de fond pour ce canal, tester l’accord entre ces prédictions et les données d’ATLAS, et à la production des fichiers utilisés dans l’étude statistique finale. J’ai également travaillé sur le modèle statistique, qui prend en compte les erreurs statistiques et systématiques, pour en extraire une mesure de la force du signal pour ce canal du couplage du Higgs aux leptons. Ma contribution à l’amélioration de la reconstruction d’un tau hadronique, à l’aide des algorithmes qui identifient les traces de conversion des photons provenant de la désintégration des pions neutres, est également détaillée. / In this thesis, I show my contribution to the search for the Standard Model Higgs Boson decaying into two tau leptons in the tlepthad sub-channel. I contributed to the different stages of this analysis. First, I worked on the development of the framework used to produce analysis files that contain the information necessary for this study. I also participated in the development of the framework used to introduce the predictions of the background for that channel, test the agreement between the predictionsand the ATLAS data, and on the production of files used in the final statistical analysis. I also worked on the statistical model, which takes into account the statistical and systematic errors to extract a measure of the signal strength for the Higgs coupling channel to leptons. My contribution to the improvement of reconstruction of a hadronic tau, using algorithms that identify photon conversion traces from the decay of neutral pions, is also detailed.

In this thesis, we study a broad range of physical phenomena from the perspectives of theory-driven, and machine learning models. We begin by introducing a generalization of the Momentum Average method for finding numerically exact Green's functions of arbitrary polaron systems at zero and finite temperature. This method utilizes the physical ansatz that phonons are produced largely in clouds, and systematically constructs a closure of auxiliary Green's functions to ultimately solve for the spectrum. We seamlessly apply this method to a variety of problems, including the Holstein, Peierls, and mixed-boson mode models. Next, we leverage fundamental quantum mechanics to develop a microscopic model of exciton and trion scattering in monolayer transition metal dichalcogenides. We conclude that elastic scattering mechanisms are largely the dominant contributor, and confirm that our calculated doping-dependent linewidths qualitatively agree with experiment. In addition, we use Monte Carlo dynamics to examine entropically activated dynamics in continuous phase space models, and show that global and local dynamics both exhibit entropy driven activation. The second type of work discussed in this thesis pertains to data-driven machine learning models. These approaches offer the utility of instantaneous inference, which has tremendous potential application in applied science in areas such as surrogate modeling and creating digital twins of expensive experiments. First, we demonstrate that x-ray absorption spectra can be used to classify absorbing sites' local atomic information, specifically its coordination number. Next, we show that graph-based neural networks can to quantitative accuracy, predict the x-ray absorption spectrum of small molecules in the QM9 database. We highlight the various ways in which these types of methodologies can be applied to e.g. closing the design loop and surrogate modeling in general.

Hadronic collisions at the LHC at CERN probe particle interactions at the highest energy scale of any experiment to date. We present a research program measuring Rjet = &sigmaWBR(W&rarr&mu&nu) / (&sigmaZBR(Z&rarr&mu&mu)) as a function of a number of hadronic variables. The measurements are performed with the ATLAS detector at the LHC, using the 2011 data set, consisting of 4.64 fb-1 of pp collisions at a center of mass energy of 7 TeV. This measurement is a robust way to test the Standard Model and the modeling of perturbative QCD, and is sensitive to a wide variety of possible new physics in events with high jet ET, including some variations of Supersymmetry. By taking the ratio of W/Z production, a large number of systematic uncertainties cancel, including those associated with luminosity, jet energy scale and resolution, and many theoretical uncertainties. The measurement of Rjet is performed as a function of the pT and rapidity of the 1st-4th leading jet, ST, HT, and a number of dijet variables, including invariant mass and angular separations. The measurements are compared with NLO theoretical predictions from Blackhat+Sherpa, as well as using leading order simulations from Alpgen and Sherpa. Over most of the kinematic phase-space, there is good agreement between the data and theoretical predictions. There is a significant deviation for exactly one selected jet above 30 GeV, where Blackhat+Sherpa over-estimates the ratio Rjet by 12%.

The Liouville resolvent method is an unconventional technique used for finding a Green function for a Hamiltonian. Implementation of the method entails the calculation of commutators of a second-quantized Hamiltonian operator with particular generalized stepping operators that are elements of a Hilbert space and that represent transitions between many-particle states. These commutators produce linear combinations of stepping operators, so the results can be arrayed as matrix elements of the Liouville operator L̂ in the Hilbert space of stepping operators. The resulting L̂ matrix is usually of infinite order, and in principle its eigenvalues and eigenvectors can be used to construct the Green function from the L̂ resolvent matrix. Approximations are usually necessary, at least in the form of truncation of the L̂ matrix, and if one produces a sequence of such matrices of increasing order and calculates the eigenvalues and eigenvectors of these matrices, a sequence of approximations for the L̂ resolvent matrix can be produced. This sequence is mathematically guaranteed to converge to the exact result for the L̂ resolvent matrix (except at its singularities). The accuracy of an approximation depends on the order of the matrix at which the sequence is truncated. Application of the method to a Hamiltonian representing interactions between fermions and bosons involves complications arising from the large number of terms generated by the commutation properties of boson operators. This dissertation describes the method and its use in the study of fermion-boson couplings. Approximations to second order in stepping operators are calculated for simplified Froehlich and Lee models. Limited thermodynamic results are obtained from the Lee model. Exact energy eigenvalues are obtained by operator algebra for simplified Froehlich, Lee and Dirac models. These exact solutions comprise the main contribution of this research and will prove to be valuable starting points for further research. Suggestions are made for further research. / Ph. D. / incomplete_metadata

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Die vorliegende Arbeit beschreibt die Suche nach der Produktion des Standardmodell Higgs-Bosons in Assoziation mit einem Top-Antitop-Quarkpaar ttH). Der verwendete Datensatz basiert auf einer integrierten Luminositat von 36.1 1/fb, aufgenommen mit dem ATLAS Detektor am Large Hadron Collider in den Jahren 2015 und 2016. Die selektierten Ereignisse enthalten entweder ein oder zwei Leptonen vom Zerfall des Top-Antitop-Quarkpaares. Die Sensitivität der Analyse wurde erhöht, indem die Ereignisse in unterschiedliche Regionen unterteilt wurden, basierend auf der Anzahl der Jets sowie der Wahrscheinlichkeit b-Jets zu enthalten. Methoden basierend auf multivariaten Analysetechniken wurden entwickelt, um ttH Signalereignisse vom Untergrund zu separieren, der von der Produktion von Top-Antitop-Quarkpaaren mit zusätzlichen b-Jets dominiert wird. Alle in der Analyse verwendeten Regionen wurden in einem Profile-Likelihood-Fit kombiniert, um die Vorhersagen des Untergrunds einzuschr{\"a}nken und die systematischen Unsicherheiten zu reduzieren. Ein Überschuss an Ereignissen über dem erwarteten Standardmodell-Untergrund wurde mit einer beobachteten (erwarteten) Signifikanz von 1.4 (1.6) Standardabweichungen gemessen. Die Daten schliessen ttH Signalstärken von mehr als 2.0 mit einem Konfidenzniveau von 95% aus. / This thesis presents the search for the Standard Model Higgs boson produced in association with a pair of top-quarks (ttH). The analysis uses a 36.1 1/fb dataset of proton-proton collisions collected with the ATLAS detector, at the Large Hadron Collider during 2015 and 2016. The selected events contain either one or two leptons from the decay of the top-quark pair. In order to improve the sensitivity of the search, events are split in regions according to the number of jets and how likely these events are to contain b-jets. Methods based on multivariate techniques were developed and applied in the signal-enriched regions to discriminate ttH events against background events being dominated by top pair production with additional b-jets. All analysis regions are combined in a statistical model using a profile likelihood fit to constrain the background predictions and reduce the systematic uncertainties. An excess of events over the expected Standard Model background is found with an observed (expected) significance of 1.4 (1.6) standard deviations. A ttH signal strength larger than 2.0 is excluded at the 95% confidence level.

Les particules élémentaires ainsi que leur interactions sont décrites par le Modèle Standard. Malgré son grand succès, il y a encore des questions à répondre. Dans cette thése, le processus du Modèle Standard ZZ, lorsque les deux bosons Z se désintègrent en paires de leptons, a été étudié. Les données utilisées ont été prises par le détecteur ATLAS durant l'année 2012, ce qui correspond à une luminosité intégrée de 20 fb-1. L'énergie dans le centre de masse était de 8 TeV. Tous les éléments de l'analyse sont présentés dans ce document: la sélection du signal et son efficacité, l'estimation du bruit de fond, les systématiques associées à la mesure, ainsi que la méthode statistique employée pour l'extraction de la section efficace. La section efficace du processus ZZ sur couche de masse a été mesurée à 6.98±0.41(stat.)±0.36(syst.)±0.20(lumi) pb. La section efficace pour chaque canal a été aussi mesurée dans une volume cinématique ``restreint'', proche du volume reconstruit. Toutes les mesures obtenues sont en accord avec les prédictions theoriques. L'auto-interaction des bosons neutres est interdite dans le Modèle Standard. Si des couplages à trois bosons sont observés, ceux-ci indiqueront donc la présence d'une nouvelle physique. Des observables sensibles à la présence des couplages anormaux ont été examinées. L'impulsion transverse du boson le plus énergétique s'est avérée une des plus sensibles, et elle a été donc utilisée pour l'extraction des limites à 95% CL sur les couplages anormaux. Toutes les limites obtenues sont compatibles avec le Modèle Standard. La connaissance du champ magnétique toroïdal dans le détecteur ATLAS est essentielle pour l'estimation précise de la masse des particules. Une étude sur les senseurs utilisés pour la construction de la carte de champ du détecteur ATLAS a montré que 97% des senseurs sont fiables. La carte de champ existante a été examinée, et malgré l'observation d'anomalies, celles-ci ne sont pas susceptibles d'affecter la détermination de l'impulsion des muons, ni donc de l'estimation de la masse du boson de Higgs. / Elementary particles and their interactions are described by the Standard Model. Even successful, there are still some unanswered questions which need to be addressed. In this work, the ZZ Standard Model process was studied in the leptonic decay channel. The data used were collected by the ATLAS detector during 2012 and correspond to an integrated luminosity of 20 fb-1. The center of mass energy was 8 TeV. All the analysis elements, such as the signal selection and efficiencies, the background estimation, the measurement uncertainties and the statistical method employed for the cross section extraction, are discussed in this document. The total ZZ on-shell cross section is measured to be 6.98±0.41(stat.)±0.36(syst.)±0.20(lumi) pb. A measurement of the on-shell ``fiducial'' cross section, defined in a volume close to the reconstructed one, was also performed for each decay channel. Both total and fiducial measurements are in agreement, within uncertainties, with the SM predictions. The neutral boson-self interactions are forbidden in the SM. Therefore, if triple gauge boson couplings are observed, they will indirectly point to the existence of new physics. Observables sensitive to the presence of anomalous triple gauge couplings, along with the optimal binning were investigated. The traverse momentum of the most energetic boson was among the most sensitive observables, and it was thus used in order to extract 95% CL limits on the anomalous coupling parameters. All observed limits are found to be compatible with the SM expectations. In the framework of this thesis a performance study was conducted. In order to increase particles mass measurement precision, the accurate knowledge of the toroidal magnetic field inside the detector is essential. The sensors used for the production of the ATLAS toroidal magnetic field map were studied, and it was found that more than 97% of these sensors are reliable. The existing magnetic field map was probed, and even though inaccuracies were observed, they are not expected to impact muon momentum estimation and thus not to bias the Higgs boson mass measurement.