Centro Latino-Americano de Física / Os processos estocásticos com ruído branco multiplicativo são objeto de atenção constante em uma grande área da pesquisa científica. A variedade de prescrições possíveis para definir matematicamente estes processos oferece um obstáculo ao desenvolvimento de ferramentas gerais para seu tratamento. Na presente tese, estudamos propriedades de equilíbrio de processos markovianos com ruído branco multiplicativo. Para conseguirmos isto, definimos uma transformação de reversão temporal de tais processos levando em conta que a distribuição estacionária de probabilidade depende da prescrição. Deduzimos um formalismo funcional visando obter o funcional gerador das funções de correlação e resposta de um processo estocástico multiplicativo representado por uma equação de Langevin. Ao representar o processo estocástico neste formalismo (de Grassmann) funcional eludimos a necessidade de fixar uma prescrição particular. Neste contexto, analisamos as propriedades de equilíbrio e estudamos as simetrias ocultas do processo. Mostramos que, usando uma definição apropriada da distribuição de equilíbrio e considerando a transformação de reversão temporal adequada, as propriedades usuais de equilíbrio são satisfeitas para qualquer prescrição. Finalmente, apresentamos uma dedução detalhada da formulação supersimétrica covariante de um processo markoviano com ruído branco multiplicativo e estudamos algumas das relações impostas pelas funções de correlação através das identidades de Ward-Takahashi. / Multiplicativewhite-noise stochastic processes continuously attract the attention of a wide area of scientific research. The variety of prescriptions available to define it difficults the development of general tools for its characterization. In this thesis, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for this kind of processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. We deduce a functional formalism to derive a generating functional for correlation and response functions of a multiplicative stochastic process represented by a Langevin equation. Representing the stochastic process in this functional (Grassmann) formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicativeMarkovian white-noise process and study some of the constraints it imposes on correlation functions using Ward-Takahashi identities.

Este trabalho apresenta uma contribuição ao estudo das flutuações quânticas dos feixes sonda e de bombeio na condição de transparência induzida por laser. Com esse estudo conseguimos observar nas flutuações dos campos uma manifestação do caráter coerente da interação dos átomos com os feixes. Para alcançar nosso objetivo, derivamos a teoria do fenômeno da transparência induzida tratando ambos feixes dentro do formalismo quântico. Com tal formulação, encontramos que a condição de transparência induzida corresponde a um estado de equilíbrio dinâmico do sistema átomo - campo de bombeio - campo sonda onde, os átomos redistribuem os fótons entre os campos, correlacionando os mesmos e alterando, ao mesmo tempo, as propriedades estatísticas desses feixes. Utilizando dois critérios diferentes, mostrando que a correlação entre os feixes sonda e de bombeio é de natureza quântica, o que possibilita a aplicação desse sistema, por exemplo, na informação e computação quânticas. Os resultados experimentais obtidos confirmaram as previsões teóricas em relação às flutuações quânticas dos campos, e a existência de uma correlação entre eles. Trata-se da primeira investigação experimental de propriedades estatísticas dos campos em transparência induzida. A correlação de intensidade medida é o primeiro passo para a observação de emaranhamento entre feixes sonda e de bombeio na condiçào de transparência induzida. / In this work we presente a contribution to the study of quantum fluctuations of pump and probe filds in the Electromagnetically Induced Transparency (EIT) condition. We observed in the fields fluctuations evidence of the coherent character of the interaction between the atoms and the fields. To reach our purpose, the fields were treated quantum-mechanically in deriving the theory of the EIT phenomenon. Using this formulation, we concluded that the EIT condition corresponds to a state of dynamical equilibrium of the system atom pump field probe field, where the atoms redistribute the photons between both fields, correlating them and, at the same time, affecting their statistical properties. By means of two different criteria we showed that such a correlation is of quantum nature, making possible the application of this system in, for example, quantum information and quantum computation. The theoretical predictions were corroborated by our experimental results regarding the quantum fluctuations and the existence of a correlation between the pump and probe fields. This is the first experiment to investigate statistical properties of the fields in EIT. The intensity correlation measured is the first step towards the observation of entanglement between the fields.

Dans plusieurs domaines des statistiques, y compris le traitement du signal et des images, l'estimation en grande dimension est une tâche importante pour recouvrer un objet d'intérêt. Toutefois, dans la grande majorité de situations, ce problème est mal-posé. Cependant, bien que la dimension ambiante de l'objet à restaurer (signal, image, vidéo) est très grande, sa ``complexité'' intrinsèque est généralement petite. La prise en compte de cette information a priori peut se faire au travers de deux approches: (i) la pénalisation (très populaire) et (ii) l'agrégation à poids exponentiels (EWA). L'approche penalisée vise à chercher un estimateur qui minimise une attache aux données pénalisée par un terme promouvant des objets de faible complexité (simples). L'EWA combine une famille des pré-estimateurs, chacun associé à un poids favorisant exponentiellement des pré-estimateurs, lesquels privilègent les mêmes objets de faible complexité.Ce manuscrit se divise en deux grandes parties: une partie théorique et une partie algorithmique. Dans la partie théorique, on propose l'EWA avec une nouvelle famille d'a priori favorisant les signaux parcimonieux à l'analyse par group dont la performance est garantie par des inégalités oracle. Ensuite, on analysera l'estimateur pénalisé et EWA, avec des a prioris généraux favorisant des objets simples, dans un cardre unifié pour établir des garanties théoriques. Deux types de garanties seront montrés: (i) inégalités oracle en prédiction, et (ii) bornes en estimation. On les déclinera ensuite pour des cas particuliers dont certains ont été étudiés dans littérature. Quant à la partie algorithmique, on y proposera une implémentation de ces estimateurs en alliant simulation Monte-Carlo (processus de diffusion de Langevin) et algorithmes d'éclatement proximaux, et montrera leurs garanties de convergence. Plusieurs expériences numériques seront décrites pour illustrer nos garanties théoriques et nos algorithmes. / In many areas of statistics, including signal and image processing, high-dimensional estimation is an important task to recover an object of interest. However, in the overwhelming majority of cases, the recovery problem is ill-posed. Fortunately, even if the ambient dimension of the object to be restored (signal, image, video) is very large, its intrinsic ``complexity'' is generally small. The introduction of this prior information can be done through two approaches: (i) penalization (very popular) and (ii) aggregation by exponential weighting (EWA). The penalized approach aims at finding an estimator that minimizes a data loss function penalized by a term promoting objects of low (simple) complexity. The EWA combines a family of pre-estimators, each associated with a weight exponentially promoting the same objects of low complexity.This manuscript consists of two parts: a theoretical part and an algorithmic part. In the theoretical part, we first propose the EWA with a new family of priors promoting analysis-group sparse signals whose performance is guaranteed by oracle inequalities. Next, we will analysis the penalized estimator and EWA, with a general prior promoting simple objects, in a unified framework for establishing some theoretical guarantees. Two types of guarantees will be established: (i) prediction oracle inequalities, and (ii) estimation bounds. We will exemplify them for particular cases some of which studied in the literature. In the algorithmic part, we will propose an implementation of these estimators by combining Monte-Carlo simulation (Langevin diffusion process) and proximal splitting algorithms, and show their guarantees of convergence. Several numerical experiments will be considered for illustrating our theoretical guarantees and our algorithms.

Many novel graph neural network models have reported an impressive performance on benchmark dataset, but the theory behind these networks is still being developed. In this thesis, we study the trajectory of Gradient descent (GD) and Stochastic gradient descent (SGD) in the loss landscape of Graph neural networks by replicating Xing et al. [1] study for feed-forward networks. Furthermore, we empirically examine if the training process could be accelerated by an optimization algorithm inspired from Stochastic gradient Langevin dynamics and what effect the topology of the graph has on the convergence of GD by perturbing its structure. We find that the loss landscape is relatively flat and that SGD does not encounter any significant obstacles during its propagation. The noise-induced gradient appears to aid SGD in finding a stationary point with desirable generalisation capabilities when the learning rate is poorly optimized. Additionally, we observe that the topological structure of the graph plays a part in the convergence of GD but further research is required to understand how. / Många nya grafneurala nätverk har visat imponerande resultat på existerande dataset, dock är teorin bakom dessa nätverk fortfarande under utveckling. I denna uppsats studerar vi banor av gradientmetoden (GD) och den stokastiska gradientmetoden (SGD) i lösningslandskapet till grafiska faltningsnätverk genom att replikera studien av feed-forward nätverk av Xing et al. [1]. Dessutom undersöker vi empiriskt om träningsprocessen kan accelereras genom en optimeringsalgoritm inspirerad av Stokastisk gradient Langevin dynamik, samt om grafens topologi har en inverkan på konvergensen av GD genom att ändra strukturen. Vi ser att lösningslandskapet är relativt plant och att bruset inducerat i gradienten verkar hjälpa SGD att finna stabila stationära punkter med önskvärda generaliseringsegenskaper när inlärningsparametern har blivit olämpligt optimerad. Dessutom observerar vi att den topologiska grafstrukturen påverkar konvergensen av GD, men det behövs mer forskning för att förstå hur.

<p>Heavy flavor hadrons serve as valuable probes of the transport properties of the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. In this dissertation, we introduce a comprehensive framework that describes the full-time evolution of heavy flavor in heavy-ion collisions, including its initial production, in-medium evolution inside the QGP matter, hadronization process from heavy quarks to their respective mesonic bound states and the subsequent interactions between heavy mesons and the hadron gas.</p><p>The in-medium energy loss of heavy quarks is studied within the framework of a Langevin equation coupled to hydrodynamic models that simulate the space-time evolution of the hot and dense QGP matter. We improve the classical Langevin approach such that, apart from quasi-elastic scatterings between heavy quarks and the medium background, radiative energy loss is incorporated as well by treating gluon radiation as a recoil force term. The subsequent hadronization of emitted heavy quarks is simulated via a hybrid fragmentation plus recombination model. The propagation of produced heavy mesons in the hadronic phase is described using the ultra-relativistic quantum molecular dynamics (UrQMD) model. Our calculation shows that while collisional energy loss dominates the heavy quark motion inside the QGP in the low transverse momentum (pT) regime, contributions from gluon radiation are found to be significant at high pT. The recombination mechanism is important for the heavy flavor meson production at intermediate energies. The hadronic final state interactions further enhance the suppression and the collective flow of heavy mesons we observe. Within our newly developed framework, we present numerical results for the nuclear modification and the elliptic flow of D mesons, which are consistent with measurements at both the CERN Large Hadron Collider (LHC) and the BNL Relativistic Heavy-Ion Collider (RHIC); predictions for B mesons are also provided.</p><p>In addition, various transport properties of heavy quarks are investigated within our numerical framework, such as the thermalization process of heavy quarks inside the QGP, and how the initial configuration of the QGP as well as its properties affect the final state spectra and the elliptic flow of heavy mesons and their decay electrons. The effects of initial state fluctuations in heavy-ion collisions are also studied and found to enhance the heavy quark energy loss in a (2+1)-dimensional boost invariant scenario. Furthermore, a new set of observables -- heavy-flavor-tagged angular correlation functions -- are explored and found to be potential candidates for distinguishing different energy loss mechanisms of heavy quarks inside the QGP.</p> / Dissertation

No description available.

Part I of this thesis is concerned with cavity optomechanical systems subject to periodic driving. We develop a Floquet approach to solve time-periodic quantum Langevin equations in the steady state, show that two-time correlation functions of system operators can be expanded in a Fourier series, and derive a generalized Wiener-Khinchin theorem that relates the Fourier transform of the autocorrelator to the noise spectrum. Weapply our framework to optomechanical systems driven with two tones. In a setting used to prepare mechanical resonators in quantum squeezed states, we nd and study the general solution in the rotating-wave approximation. In the following chapter, we show that our technique reveals an exact analytical solution of the explicitly time-periodic quantum Langevin equation describing the dual-tone backaction-evading measurement of a single mechanical oscillator quadrature due to Braginsky, Vorontsov, and Thorne [Science 209, 547 (1980)] beyond the commonly used rotating-wave approximation and show that our solution can be generalized to a wide class of systems, including to dissipatively or parametrically squeezed oscillators, as well as recent two-mode backaction-evading measurements. In Part II, we study nonreciprocal optomechanical systems with several optical and mechanical modes. We show that an optomechanical plaquette with two cavity modes coupled to two mechanical modes is a versatile system in which isolators, quantum-limited phase-preserving, and phase-sensitive directional ampliers for microwave signals can be realized. We discuss the noise added by such devices, and derive isolation bandwidth, gain bandwidth, and gain-bandwidth product, paving the way toward exible, integrated nonreciprocal microwave ampliers. Finally, we show that similar techniques can be exploited for current rectication in double quantum dots, thereby introducing fermionic reservoir engineering. We verify our prediction with a weak-coupling quantum master equation and the exact solution. Directionality is attained through the interference of coherent and dissipative coupling. The relative phase is tuned with an external magnetic eld, such that directionality can be reversed, as well as turned on and off dynamically.

Investigating the arrangement of the packed DNA inside the nucleus has revealed the essential role of genome organisation in controlling genome function. Furthermore, genome architecture is highly dynamic and significant chromatin re-organisation occurs in response to environmental changes. However, the mechanisms that drive the 3D organisation of the genome remain largely unknown. To understand the effect of biophysical properties of chromatin on the dynamics and structure of chromosomes, I developed a 3D computational model of the nucleus of the yeast S. cerevisiae during interphase. In the model, each chromosome was a hetero-polymer informed by our bioinformatics analysis for heterogeneous occupancy of chromatin-associated proteins across the genome. Two different conditions were modelled, normal growth (25°C) and heat shock (37°C), where a concerted redistribution of proteins was observed upon transition from one temperature to the other. Movement of chromatin segments was based on Langevin dynamics and each segment had a mobility according to their protein occupancy and the expression level of their corresponding genes. The model provides a significantly improved match with quantitative microscopy measurements of telomere positions, the distributions of 3D distances between pairs of different loci, and the mean squared displacement of a labelled locus. The quantified contacts between chromosomal segments were similar to the observed Hi-C data. At both 25°C and 37°C conditions, the segments that were highly occupied by proteins had high number of interactions with each other, and the highly transcribed genes had lower contacts with other segments. In addition, similar to the experimental observations, heat-shock genes were found to be located closer to the nuclear periphery upon activation in the simulations. It was also shown that the determined distribution of proteins along the genome is crucial to achieve the correct genome organisation. Hence, the heterogeneous binding of proteins, which results in differential mobility of chromatin segments, leads to 3D self-organisation.

Cette thèse présente une étude théorique de protéines de la famille de la Green Fluorescent Protein, GFP. Ces protéines permettent grâce à leur propriétés de fluorescence d'explorer un nombre croissant de processus biologiques in vivo. Les approches numériques, complémentaires aux études expérimentales, peuvent apporter une compréhension microscopique des processus mis en jeu et contribuer à l'interprétation des propriétés photophysiques de ces protéines. La première partie de ce manuscrit présente l'étude par simulation moléculaire de l'effet du changement de pH sur la structure de la Cerulean et sur son spectre d'absorption. Ces calculs nous ont permis d'établir que le décalage du spectre d'absorption, observé expérimentalement en fonction du pH, est dû à une isomérisation du chromophore liée au changement de l'orientation de la chaîne latérale d'un acide aminé proche. proteine La deuxième partie de ce manuscrit aborde l'étude d'un mécanisme de désactivation de la fluorescence dans la GFP. Nous avons proposé une approche, combinant des simulations de dynamique moléculaire biaisée et de dynamique brownienne, afin de déterminer la cinétique d'un mécanisme de désactivation de la fluorescence lié à une torsion du chromophore. Nous avons pu obtenir des distributions de temps de nème passage aux géométries critiques et en déduire des informations quantitatives sur le déclin de fluorescence. Les outils développés et leurs futurs développements permettront de progresser dans la compréhension de la relation entre l'isomérisation du chromophore, le pH et le déclin de la fluorescence qui sont étroitement liés dans les protéines fluorescentes.

Afin d'étudier l'influence des fluctuations sur différents phénomènes physiques liés aux collisions entre ions lourds, une équation de Langevin a été obtenue à partir d'un modèle microscopique. Les paramètres entrant dans cette équation sont entièrement déterminés à partir de grandeurs microscopiques caractérisant la matière nucléaire. Cette équation a été appliquée à des phénomènes physiques aux énergies intermédiaires. Une première partie concerne les mouvements collectifs de faible amplitude, à savoir les résonnances géantes. Les effets de mémoire dans le terme decollisions de l'équation de Boltzmann ont été étudiés. Une approche formelle à l'influencedes fluctuations sur plusieurs modes couplés est aussi proposée. Une deuxième partie concerne les mouvements collectifs de grande amplitude où une étude détaillée de la fission thermique est faite . Le taux de fission est calculé et confronté aux résultats expérimentaux. Enfin, un travail préliminaire sur la multifragmentation est proposé.