Les nuages, le lait, le papier, les tissus biologiques appartiennent tous à une même classe de milieux que l'on nomme diffusants de part leur habilité à transformer une onde incidente collimatée en un faisceau diffus. L'imagerie, ou le transfert d'information à travers ces milieux est a priori plus difficile qu'en milieu homogène, et les méthodes actuelles nécessitent une caméra en transmission du milieu complexe considéré. La présence de cette caméra est souvent considérée comme une faille de ces méthodes car la transmission de ces milieux est souvent hors d'atteinte par l'opérateur. Dans cette thèse nous posons la question du lien qui existe entre la lumière réfléchie et la lumière transmise en milieux fortement diffusant. Nous traitons ce problème de manière statistique et nous intéressons à la dépendance statistique qui existe entre la lumière réfléchie et la lumière transmise. Nous verrons que ce lien statistique persiste même pour des milieux fortement diffusants. Ce lien statistique peut être a la base de nouvelles méthodes de contrôle du front d'onde en milieux diffusant n'utilisant que des informations réfléchies par le milieu, permettant l'imagerie, le dépôt d'énergie ou d'informations à travers des milieux fortement diffusants. / Clouds, milk, paper or biological tissues are called scattering media for light. Indeed when a plane wave encounters one a these media, the light is scattered and looses its preferential direction. Consequently, imaging through these media is more difficult than in homogeneous media. The existing methods rely on a CCD camera measuring the transmitted light. Nonetheless, the transmitted side of the sample is most of the time out of reach of the operator. In this thesis we interest ourselves to the link that exists between the reflected light and the transmitted light for thick scattering media. From a statistical point of view, this link is equivalent to the statistical dependency between the reflected light and the transmitted light. We show that the statistical dependency persists even for very thick media allowing us to propose new imaging modalities based on it. This statistical dependency between the reflected and the transmitted light is a very rich function of the parameters of the system, and may allow us to control the transmitted light using reflected information only.

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We report on calculations of smoothed spectral correlations in the twodimensional Anderson model for weak disorder. As pointed out in (M. Wilkinson, J. Phys. A: Math. Gen. 21, 1173 (1988)), an analysis of the smoothing dependence of the correlation functions provides a sensitive means of establishing consistency with random matrix theory. We use a semiclassical approach to describe these fluctuations and offer a detailed comparison between numerical and analytical calculations for an exhaustive set of two-point correlation functions. We consider parametric correlation functions with an external Aharonov-Bohm flux as a parameter and discuss two cases, namely broken time-reversal invariance and partial breaking of time-reversal invariance. Three types of correlation functions are considered: density-of-states, velocity and matrix element correlation functions. For the values of smoothing parameter close to the mean level spacing the semiclassical expressions and the numerical results agree quite well in the whole range of the magnetic flux.

Title: U in metastable systems: structure, magnetism, and superconductivity Author: Volodymyr Buturlim Department / Institute: Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University Supervisor of the doctoral thesis: Doc. RNDr. Ladislav Havela, CSc., Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, Prague, The Czech Republic Abstract: This thesis presents studies of U-Nb and U-Ti alloys and hydrides synthesized via different technological paths. Investigation of the microstructure of the alloys with different concentrations of Ti (Nb) allowed to find the optimum setting for stabilization of the metastable bcc U allotrope. Ultra-fast cooling accompanied by alloying leads to retention of materials with high degree of atomic disorder apparent from the studies of their transport properties. The alloys exhibit a weakly paramagnetic ground state and low-temperature superconductivity, the critical temperature of which has only moderate variations with Ti (Nb) concentrations and which has very high upper critical fields. Interaction with hydrogen allows to stabilize two distinctive forms of hydride: β-UH3 and UTi2Hx. β-UH3 alloyed by Ti (Nb) orders ferromagnetically with transition temperatures exceeding 170 K, weakly influenced...

The Standard Model of elementary particles (SM) predicts the existence of a neutral scalar Higgs boson. However, there are also extensions of the SM (such as the MSSM) in which a number of Higgs bosons is predicted. Especially the additional presence of pseudoscalar and charged Higgs bosons represents one of the crucial differences between the SM and its exten- sions. This work develops a method for determination of the spin and parity of the Higgs boson in several H → ττ decays, namely: H→ τ+ τ− → (h+ ντ )(h− ¯ντ ), H→ τ+ τ− → ( + ντ ¯ν )(π− ¯ντ ) and H→ τ+ τ− → ( + ντ ¯ν )( − ¯ντ ν ), where h denotes π or ρ meson. The method is based on the angular and energy correlations of charged final products from the decays mentioned above. Additionally, the work studies the possibility of signal (Higgs boson decay) and background (Z → ττ decay) discrimination, when one considers a decaying boson with spin 1. All calcula- tions are done in the leading order of perturbation theory. 1

Abstract This thesis project is divided in two parts. The first part examines the possibility that correlation matrix estimates based on an outlier sample would contain information about extreme events. According to my findings, such methods do not perform better than simple shrinkage methods where robust shrinkage targets are used. The method tested is especially outperformed when it comes to the extreme events, where a shrinkage of the correlation matrix towards the identity matrix seems to give the best result. The second part is about valuation of skewness in marginal distributions and the penalizing of heavy tails. I argue that it is reasonable to use a degrees of freedom parameter instead of kurtosis and a certain regression parameter, that I develop, instead of skewness due to robustness issues. When minimizing the one period draw-down is our target, the "value" of skewness seems to have a linear relationship with expected returns. Re-valuing of expected returns, in terms of skewness, in the standard Markowitz framework will tend to lower expected shortfall (ES), increase skewness and lower the realized portfolio variance. Penalizing of heavy tails will most times in the same way lower ES, lower kurtosis and realized portfolio variance. The results indicate that the parameters representing higher order moments in some way characterize the assets and also reflect their future behavior. These properties can be used in a simple optimization framework and seem to have a positive impact even on portfolio level

Critical and residual states are key soil conditions relevant to slope stability. Evaluating the available shear strength in relation to these conditions is crucial for reliable stability analyses. The best way to determine the strength parameters is through properly selected laboratory tests of soil mechanics. However, in specific cases, these parameters can be estimated based on other material properties of soils. The work clarifies the applicability of various correlation equations from the literature and proposes new relationships, created from laboratory- determined results of strength and index parameters of soils from the Bohemian Central Mountains. It shows how different equations or different material properties of soils can predict the required value of strength. The work also describes how the residual strength of soils and its estimation can be affected. This is mainly caused by the clay fraction proportion and by the shear rate used in its laboratory determination. The results are applied to a specific geotechnical problem - to estimate the critical state and the residual friction angle of soils from the selected study area of the D8 motorway, which is well known thanks to the stability problems. Last but not least, various errors and misunderstandings are discussed, which are often...

How can fluctuations in one-dimensional time series data be characterized and how can detected effects be decomposed into their dynamical origins or causes? In the context of these questions, a variety of problems are discussed and solutions are introduced. The first issue concerns the causes of anomalous diffusion. A previously proposed framework decomposes the Hurst exponent into the Joseph, Noah, and Moses effects. They represent violations of the three premises of the central limit theorem. Here the framework is applied to an intermittent deterministic system, which exhibits a rich combination of all three effects. Nevertheless, the results provide an intuitive interpretation of the dynamics. In addition, the framework is theoretically discussed and connected to a calculation that proves its validity for a large class of systems. Once the type of anomalous statistical behavior is classified, one might ask what the dynamical origin of the effects is. Especially the property of long range temporal correlations (the Joseph effect) is discussed in detail. In measurements, they might arise from different dynamical origins or can be explained as an emerging phenomenon. A collection of different routes to the observed behavior is established here. A popular tool for detecting long range correlations is detrended fluctuation analysis. Its advantages over traditional methods are stability and smoothness for timescales up to one fourth of the measurement time and the ability to neglect the slow dynamics and trends. Recently, a theory for an analytical understanding of this method was introduced. In this thesis, the method is further analyzed and developed. An approach is presented that enables scientists to use this method for short range correlated data, even if the dynamics is very complex. Fluctuations can be decomposed into a superposition of linear models that explain its features. Therefore, on the one hand, this thesis is about understanding the effects of anomalous diffusion. On the other hand, it is about widening the applicability of one of its detection methods such that it becomes useful for understanding normal or complex statistical behavior. A good example of a complex system, where the proposed stochastic methods are useful, is the atmosphere. Here it is shown how detrended fluctuation analysis can be used to uncover oscillatory modes and determine their periods. One of them is the El Ni\~no southern oscillation. A less well known and more challenging application is a 7--8 year mode in European temperature fluctuations. A power grid is a very different type of complex system. However, using the new method, it is possible to generate a data model that incorporates the important features of the grid frequency.

Lors du présent travail, des 4-nitrobenzochalcogénadiazoles ont été synthétisés et une étude cinétique approfondie de leur réactivité vis-à-vis diverses entités nucléophiles a été réalisée. Cette étude a permis la détermination des paramètres d’électrophile E de ces espèces et leur insertion dans l’échelle universelle d’électrophilie de Mayr. En outre, sur la base des diverses corrélations Structure-Réactivité étudiées, les mécanismes d’interaction entre les 4-nitrobenzochalcogénadiazoles et les nulcéophiles utilisés ont été élucidés et un mécanisme de transfert d’électrons (SET) a été suggéré pour la complexation du 4-nitrobenzofurazane par les anions de phénate en raison de l’obtention d’une valeur très élevée de βnuc (βnuc = 1,12). En vue d’activer les propriétés électrophiles de nos 4-nitrobenzochalcogénadiazoles, nous avons procédé à la quaternarisation de leurs motifs annélés. De nouveaux électrophiles positivement chargés ont été ainsi obtenus, et une étude cinétique approfondie de leur réactivité électophile vis-à-vis des anilines, des amines et des indoles, nous a permis de mettre l’accent sur la réactivité électrophile ambidente de ces espèces. D’une manière surprenante, l’interaction entre le 4-nitrobenfurazane et le 4-nitrobenzothiadiazole N-méthylés avec une série d’anilines para-Y-substituées a permis de définir des corrélations de Mayr, Hammett et Brönsted non linéaires. Cette déviation des divers graphes obtenus a été expliquée par le changement du mécanisme réactionnel. D’autre part, l’étude de la réactivité du 4-nitrobenzosélénadiazole N-méthylé vis-à-vis une série d’amines s’est révélée beaucoup plus originale que prévu en raison de la mise en évidence d’une corrélation linéaire de pente unité entre le log(kexp) et le log(kcal). / In the present work, 4-nitrobenzochalcogenadiazols have been synthesized and kinetics for σ-complexation of these compounds with various nucleophiles have been measured in aqueous solutions at 20 °C. According Mayr’s approach, E parameters of 4-nitrobenzochalcogenadiazols have been evaluated and using these values, a positioning of the reactivity of our electrophiles on the electrophilicity scale was possible. Based on Structure-Reactivity correlations, possible mechanistic pathways for each process were given and the abnormally high Brönsted coefficient βnuc of 1.12 reveals that the σ-complexation reaction of 4-nitrobenzofurazan with a series of 4-X-substituted phenoxide ions may proceed via single electron transfer process (SET).In order to increase the electrophilicity parameters of 4-nitrobenzochalcogenadiazols, we proceeded to the N-méthylation of their annelated rings.Thus, a new serie of positively charged electrophiles has been obtained. kinetic study of the coupling of N-methylated compounds with para-substituted anilines, indoles and amines showed that these salts can react as ambident electrophiles. Surprisingly, kinetics of coupling of N-méthylaed 4-nitrobenzofurazan and 4-nitrobenzothiadiazol with 4-Y-substituted anilines, resulted in a non linear Mayr type plot. Hammet and Brönsted plots were also non linear. These results have been interpreted as reflecting changes in the mechanistic process. Interestingly, when studying the reactivity of N-methylated benzoselenadiazol versus a series of amines, a satisfactory correlation between the log values of experimental and calculated rate constants with a slope very close to unity has been obtained and discussed.

Les photons apparaissent comme des vecteurs d'information fiables, car ils interagissent peu avec leur environnement. Malheureusement, ils interagissent si faiblement entre eux que la réalisation directe de portes logiques optiques à deux qubits est impossible. La propagation à travers des milieux atomiques non-linéaires permet néanmoins d'engendrer des interactions photon-photon effectives. L'utilisation du phénomène de transparence électromagnétiquement induite (EIT) permet d'induire une forte non-linearité résonante -- néanmoins pas encore détectable dans le domaine quantique, sur une transition d'un système à trois niveaux en “échelle”. Pour augmenter les effets non-linéaires et atteindre le régime quantique, il a récemment été proposé de combiner l'approche EIT au blocage d'excitation induit par les fortes interactions dipôle-dipôle entre atomes de Rydberg. En plaçant le milieu en cavité, on impose à la lumière des passages multiples et on accroît encore la non-linéarité optique. Ce type de dispositif a été étudié théoriquement et expérimentalement dans le régime dispersif et pour une non-linéarité faible, pour lequel un traitement classique du champ est adapté. Dans le présent mémoire, nous nous intéressons aux effets optiques non-linéaires induits par un milieu Rydberg dans le régime quantique.Dans le chapitre 1, nous présentons notre système d'étude, ses équations dynamiques et rappelons la définition et les principales propriétés de la fonction de corrélation d'intensité g^{2}que nous utilisons pour caractériser l'action de la non-linéarité sur le champ incident. Dans le chapitre 2, nous considérons le régime dispersif, i.e. lorsque l'état intermediaire est très désaccordé et peut être éliminé adiabatiquement. Nous utilisons l'approximation des bulles Rydberg selon laquelle le système peut être effectivement ramené à un ensemble de superatomes à deux niveaux couplés au mode de la cavité, décrit par le modèle de Tavis-Cummings forcé. Nous calculons analytiquement et numériquement la fonction g^{2}pour la lumière transmise, qui, selon les paramètres de la cavité, peut être “groupée” ou “dégroupée”. Dans le chapitre 3, nous présentons un traitement alternatif du système, qui nous permet d'étudier le régime résonant. Dans la limite d'un champ incident faible, nous dérivons analytiquement la fonction de corrélation g^{2} pour les lumières transmise et réfléchie, grâce à la factorisation des moyennes de produits d'opérateurs à l'ordre le plus bas de la théorie de perturbation. Nous proposons ensuite un modèle effectif non-linéaire à trois bosons pour le système couplé atomes-cavité. Enfin, nous étudions le régime résonant et observons de nouvelles caractéristiques de la fonction de corrélation g^{2}qui attestent la relation entre les conditions d'adaptation d'impédance de la cavité pour les différentes composantes du champ et les interactions dipôle-dipôle entre les atomes. Dans le chapitre 4, nous analysons le système dans le formalisme de Schwinger-Keldysh. En appliquant le théorème de Wick, nous développons perturbativement les fonctions de corrélation par rapport au Hamiltonien d'alimentation de la cavité et au Hamiltonien d'interaction dipôle-dipôle et effectuons une resommation complète par rapport à ce dernier. Nous retrouvons par cette méthode les résultats du Chapitre 3, sous une forme analytique. Nous allons aussi au-delà et derivons des expressions analytiques pour les composantes élastique et inélastique du spectre en transmission de la cavité. Nous identifions une structure de résonance polaritonique, jusque-là inconnue, que nous interprétons physiquement. Dans le chapitre 5, nous décrivons un protocole de porte photonique de phase de haute fidélité fondé sur le blocage Rydberg dans un ensemble atomique placé dans une cavité optique. Ce protocole peut être réalisé avec des cavités de finesse modérée et permet en principe un traitement efficace de l'information quantique codée dans des photons. / Photons appear as reliable information messengers since they interact very weakly with their environment. Unfortunately, they interact so weakly with each other that the direct implementation of optical two-qubit gates is impossible. The propagation through atomic nonlinear media however allows one to achieve effective photon-photon interactions. The technique of electromagnetically induced transparency (EIT) allows one to induce a strong resonant non-linearity -- not strong enough to be noticeable in the quantum domain though, on one of the transitions of a three-level ladder system. To enhance the nonlinear effects and reach the quantum regime, it was recently proposed to combine the EIT approach with the excitation blockade induced by the strong dipole-dipole interactions between Rydberg atoms. By putting the medium in a cavity, one imposes multiple passes to the light therefore increasing the optical nonlinearity. This kind of setup was studied both theoretically and experimentally in the dispersive regime and for a relatively weak nonlinearity, for which a classical treatment of the field is still valid. In this dissertation, we investigate the optical nonlinear effects induced by a Rydberg medium in the quantum regime.In chapter 1, we present our system, its dynamical equations and recall the definition and basic properties of the intensity correlation function g^{left(2right)}that we use to characterize the action of nonlinearity on the photonic field. In chapter 2, we consider the so-called dispersive regime, i.e. when the intermediate state is far detuned and can be adiabatically eliminated. We employ the Rydberg bubble approximation in which the system effectively consists in an ensemble of two-level superatoms coupled to the cavity mode, described by the driven Tavis-Cummings model. We compute analytically and numerically the g^{left(2right)}function of the transmitted light, which, depending on the cavity parameters, is shown to be either bunched or antibunched. In chapter 3, we present an alternative treatment of the system, which allows us to investigate the resonant regime. In the low-feeding limit, we analytically derive the correlation function g^{left(2right)}left(tauright)for the transmitted and reflected lights, based on the factorization of the lowest perturbative order of operator product averages. We then propose an effective non-linear three-boson model for the coupled atom-cavity system. Finally, we investigate the resonant regime and observe novel features of the correlation function g^{left(2right)}showing the interplay of impedance matching conditions and dipole-dipole interactions. In chapter 4, we analyze the system in the Schwinger-Keldysh formalism. Applying Wick's theorem, we perturbatively expand correlation functions with respect to both, feeding and dipole-dipole interactions Hamiltonians and perform a complete resummation with respect to the latter. By this method we recover the results of Chap. 3 in an analytic form. We also go beyond and derive analytic expressions for the elastic and inelastic components of the cavity transmission spectrum. We identify a polaritonic resonance structure in this spectrum, to our knowledge unreported so far, that we physically interpret. In chapter 5, we describe a novel scheme for high fidelity photonic controlled-phase gates using Rydberg blockade in an ensemble of atoms in an optical cavity. This protocol can be implemented with cavities of moderate finesse allowing for highly efficient processing of quantum information encoded in photons.