Neste trabalho estudamos um modelo estocástico com simetria Ising e dois estados absorventes em três dimensões com uma rede cúbica e em duas dimensões através de uma rede triangular. O estudo levou em conta cálculos de aproximação de campo médio e simulações de Monte Carlo. Os resultados mostraram que o modelo tem transição de segunda ordem de uma fase paramagnética para uma fase ferromagnética, uma transição da fase ferromagnética para uma fase absorvente, também de segunda ordem, e ainda uma transição de primeira ordem da fase paramagnética para a fase absorvente. No espaço de parâmetros as três linhas de transição se encontram no diagrama de fases em um ponto onde o modelo se comporta como o modelo do votante. / In this work we studied a stochastic model with ising symmetry and two simmetric absorbing configurations in a three-dimensional cubic lattice and in two dimensions using a triangular lattice. The study took into account simple mean-field approximations and Monte Carlo simulations. The results showed that the model has a second-order transition from a paramagnetic phase to a ferromagnetic phase and second-order transition from ferromagnetic phase to the absorbing one. A first-order phase transition from the paramagnetic phase to the absorbing phase is observed too. In the phase diagram the two second-order transition lines aproaches to the point where the model behaves like the voter model.

Um dos problemas mais importantes que precisa ser resolvido, tanto pela física de partículas como pela cosmologia, é a existência de assimetria bariônica. Entre os cenários mais atrativos para a geração dinâmica da assimetria bariônica (Bariogênese) encontra- se a denominada Leptogênese. Nesse cenário, cria-se uma assimetria leptônica que será convertida em assimetria bariônica por processos não perturbativos mediados por sphalerons. Na realização mais simples da Leptogênese, que será estudada nesta dissertação, neutrinos pesados de mão direita, produzidos termicamente, decaem violando CP, gerando um assimetria leptônica nesses decaimentos. O principal atrativo deste cenário é que conecta duas escalas aparentemente diferentes: a escala da geração de assimetria leptônica e a escala das massas e oscilações dos neutrinos ativos mediante o mecanismo de See-Saw. O estudo usual da Leptogênese utiliza equações de Boltzmann para determinar a evolução temporal da assimetria. Porém, a equação de Boltzmann é uma equação semiclássica, dado que envolve, por um lado, uma função clássica no espaço de fases, a função de distribuição, mas, por outro, os termos de colisão envolvem quantidades obtidas na teoria quântica de campos à temperatura nula. Em particular, a formulação de Boltzmann não permite descrever fenômenos quânticos como oscilações coerentes e efeitos de decoêrencia e interferência. Uma descrição quântica completa da evolução da assimetria leptônica na leptogênese deve, de fato, ser obtida no contexto da teoria quântica de campos fora do equilíbrio térmico. O formalismo de Schwinger-Keldysh permite realizar isso. Nesta dissertação descreveremos a leptogênese no formalismo de Schwinger-Keldysh para o caso em que são adicionados ao espectro de partículas do Modelo Padrão três neutrinos de mão direita, sem fazer qualquer suposição sobre a hierarquia de massas. / One of the most important problems that is needed to solve by the Elementary Particle Physics as well as by the Cosmology is the existence of baryonic asymmetry. Among the most attractive scenarios of dynamic generation of baryonic asymmetry (Baryogenesis) is the so-called Leptogenesis. In that scenario, a leptonic asymmetry is treated in such a way that it will be converted in baryonic asymmetry by non-perturbative processes mediated by sphalerons. In the simplest realization of Leptogenesis, that will be studied in this disertation, heavy right-handed neutrinos, produzed thermally, decay violating CP generating a leptonic asymmetry in these decays. The principal attractive of this scenario is that it connects two apparently different scales, the scale of leptonic asymmetry generation and the scale of masses and oscillations of the active neutrinos through the See-Saw mechanism. The usual study of the leptogenesis uses Boltzmann equations in order to determine the temporal evolution of the asymmetry. However, the Boltzmann equation is a semiclassical equations, since, on one side, it is formulated for a classical function in phases space, the distribution function, but, on the other hand, the collision term involves quantities obtained in the Quantum Field Theory at zero temperature. In particular, Boltzmann formulation does not allow to describe quantum phenomena such coherent oscillations and effects of decoherence and interference. Indeed, a proper quantum description of the evolution of the leptonic asymmetry must be obtained in the context of the Non-Equilibrium Quantum Field Theory. The Schwinger-Keldysh formalism allows to perform this. In this dissertation, leptogenesis is described using the Schwinger-Keldysh formalism for the case in which there are three right-handed neutrinos without a definite mass hierarchy.

Les atomes ultrafroids constituent depuis une vingtaine d’années un domaine fructueux pour l’étude de la physique à N corps. Cependant l’inhomogénéité des nuages atomiques, induite par les méthodes de piégeage utilisées habituellement, constitue une limite pour les études portant sur de grandes échelles de longueur. Nous reportons ici la mise en place d’un nouveau dispositif expérimental, combinant un potentiel modulable à bords raides et fond plat dans le plan atomique, avec un confinement versatile dans la troisième direction. Nous nous intéressons à différentes excitations du système, premièrement des degrés de liberté internes des atomes via leur interaction avec la lumière, puis deuxièmement de leur mouvement collectif avec la propagation de phonons. La répartition des atomes dans un plan est particulièrement adaptée aux études de diffusion de la lumière. Elle permet en effet de sonder de fortes densités atomiques, entraînant de fortes interactions dipôle-dipôle induites, tout en gardant un signal transmis suffisant pour effectuer des mesures. Nous avons mesuré la déviation au comportement d’un atome isolé pour de la lumière proche de résonance lorsque la densité atomique est modifiée. Nous avons également étudié la diffusion de photons dans un disque d’atomes en injectant de la lumière seulement au centre du disque. Nous nous sommes ensuite intéressés aux excitations collectives du gaz. Nous avons mesuré la vitesse du son dans le milieu, qui est liée à la fraction superfluide du système, et comparé nos résultats aux prédictions d’un modèle hydrodynamique à deux fluides. En utilisant une géométrie adaptée, nous avons en outre étudié la dynamique de retour à l’équilibre d’un système isolé, en imageant la phase du condensat de Bose-Einstein résultant de la fusion de jusqu’à douze condensats. / Ultracold atoms have proven to be a powerful platform for studying many-body physics. However the inhomegeneity of atomic clouds induced by potentials commonly used to trap the atoms constitutes a limitation for studies probing large length scales. Here we present the implementation of a new versatile setup to study two-dimensional Bose gases, combining a tunable in-plane box potential with a strong and efficient confinement along the third direction. We study different excitations of the system, either of internal degrees of freedom of the atoms with light scattering, or of their collective motion with phonon propagation. The slab geometry is particularly well suited for light scattering studies. It allows one to probe high atomic densities, leading to strong induced dipole-dipole interactions, while keeping a good enough light transmission for measurements. We monitor the deviation from the single atom behavior for near resonant light by varying the atomic density. We additionally monitor the spreading of photons inside the slab by injecting light only at the center of a disk of atoms. We also investigate collective excitations of the atomic gas. We measure the speed of sound which is linked to the superfluid density of the cloud and compare our results to a two-fluid hydrodynamic model predictions. Using a relevant geometry, we additionally study how an isolated system goes back to equilibrium. This is done by imaging the phase of the resulting Bose-Einstein condensate (BEC) after merging up to twelve BECs.

La première partie de ma thèse est consacrée à l’étude de l’auto-organisation de souches génétiquement modifiées de bactéries Escherichia coli. Ce projet, réalisé en collaboration avec des biologistes synthétiques de l’Université de Hong Kong, a pour objectif l’exploration et le décryptage d’un nouveau mécanisme d’auto-organisation dans des colonies bactériennes multi-espèces. Cela a été inspiré par la question fascinante de comment les écosystèmes bactériens comprenant plusieurs espèces de bactéries peuvent s’auto-organiser dans l’espace. En considérant des systèmes dans lesquels deux souches de bactéries régulent mutuellement leurs motilités, j’ai pu montrer que le contrôle de densité réciproque est une voie générique de formation de motifs: si deux souches tendent à faire augmenter mutuellement leur motilité (la souche A se déplace plus vite quand la souche B est présent, et vice versa), ils subissent un processus de formation de motifs conduisant à la démixtion entre les deux souches. Inversement, l’inhibition mutuelle de la motilité conduit à la formation de motifs avec colocalisation. Ces résultats ont étévalidés expérimentalement par nos collaborateurs biologistes. Par la suite, j’ai étendu mon étude à des systèmes composés de plus de deux espèces en interaction, trouvant des règles simples permettant de prédire l’auto-organisation spatiale d’un nombre arbitraire d’espèces dont la motilité est sous contrôle mutuel. Cette partie de ma thèse ouvre une nouvelle voie pour comprendre l’auto-organisation des colonies bactériennes avec des souches concurrentes, ce qui est une question importante pour comprendre la dynamique des biofilms ou des écosystèmes bactériens dans les sols. Le deuxième problème traité dans ma thèse est inspiré par le comportement collectif des moteurs moléculaires se déplaçant le long des microtubules dans le cytoplasme des cellules eucaryotes. Un modèle pertinent pour le mouvement des moteurs moléculaires est donné par un système paradigmatique de non-équilibre appelé Processus Asymmetrique d’Exclusion Simple, en anglais Asymmetric Simple Exclusion Process (ASEP). Dans ce modèle sur réseau unidimensionnel, les particules se déplacent dans les sites voisins vides à des taux constants, avec un biais gauche-droite qui déséquilibre le système.Lorsqu’il est connecté à ses extrémités à des réservoirs de particules, l’ASEP est un exemple prototypique de transitions de phase unidimensionnelles guidées par les conditions aux limites. Les exemples réalistes, cependant, impliquent rarement une seule voie:les microtubules sont constitués de plusieurs pistes de tubuline auxquelles les moteurs peuvent s’attacher. Dans ma thèse, j’explique comment on peut théoriquement prédire le comportement de phase de systèmes à plusieurs voies complexes, dans lesquels les particules peuvent également sauter entre des voies parallèles. En particulier, je montre que la transition de phase unidimensionnelle vue dans l’ASEP survit cette complexité supplémentaire mais implique de nouvelles caractéristiques telles que des courants transversaux stables non-nulles et une localisation de cisaillement. / The first part of my thesis is devoted to studying the self-organization of engineered strains of run-and-tumble bacteria Escherichia coli. This project, carried out in collaboration with synthetic biologists at Hong Kong University, has as its objective the exploration and decipherment of a novel self-organization mechanism in multi-species bacterial colonies. This was inspired by the fascinating question of how bacterial ecosystems comprising several species of bacteria can self-organize in space. By considering systems in which two strains of bacteria mutually regulate their motilities, I was able to show that reciprocal density control is a generic pattern-formation pathway: if two strains tend tomutually enhance their motility (strain A moves faster when strain B is present, and conversely),they undergo a pattern formation process leading to demixing between the two strains. Conversely, mutual inhibition of motility leads to pattern formation with colocalization. These results were validated experimentally by our biologist collaborators. Subsequently, I extended my study to systems composed of more than two interacting species, finding simple rules that can predict the spatial self-organization of an arbitrary number of species whose motility is under mutual control. This part of my thesis opens up a new route to understand the self-organization of bacterial colonies with competing strains, which is an important question to understand the dynamics of biofilms or bacterial ecosystems in soils.The second problem treated in my thesis is inspired by the collective behaviour ofmolecular motorsmoving along microtubules in the cytoplasm of eukaryotic cells. A relevant model for the molecularmotors’ motion is given by a paradigmatic non-equilibrium system called Asymmetric Simple Exclusion Process (ASEP). In this one-dimensional lattice- based model, particles hop on empty neighboring sites at constant rates, with a leftright bias that drives the systemout of equilibrium. When connected at its ends to particle reservoirs, the ASEP is a prototypical example of one-dimensional boundary driven phase transitions. Realistic examples, however, seldom involve only one lane: microtubules are made of several tubulin tracks to which the motors can attach. In my thesis, I explained how one can theoretically predict the phase behaviour of complex multilane systems, in which particles can also hop between parallel lanes. In particular, I showed that the onedimensional phase transition seen in the ASEP survives this additional complexity but involves new features such as non-zero steady transverse currents and shear localization.

Uno de los aspectos más fascinantes del mundo que nos rodea es la gran variedad de escalas a las que tienen lugar los diversos fenómenos. En muchos casos esta diversidad pone de manifiesto la estructura fractal de la Naturaleza y podemos hablar entonces de fenómenos complejos, en los que eventos de diferentes magnitudes no pueden analizarse de manera independiente. Dicha complejidad emerge como un fenómeno cooperativo a escalas microscópicas, que produce un complejo comportamiento macroscópico caracterizado por correlaciones de largo alcance e invarianza de escala. Aparecen así conceptos como leyes de escalado, universalidad y renormalización, pilares fundamentales dentro de la Física Estadística.El abanico de fenómenos complejos es muy amplio, y abarca sistemas de muy diversas disciplinas que van desde la Físicamás ortodoxa hasta la Biología, Sociología, Geología e, incluso, Economía. Esta Tesis se centra en fenómenos complejos extendidos en el espacio. En concreto hemos focalizado nuestra labor en tres grandes temas que constituyen importantes focos de interés dentro de la Mecánica Estadística: Crecimiento de Interfases, Sociofísica y Redes Complejas. / The ubiquity of complexity in Nature provides examples of a huge variety of systems to be analyzed by means of Statistical Mechanics and leads to the interconnection among various scientific disciplines. This Thesis focuses on three highlight topics of spatially extended complex systems: Interface Growth,Sociophysics, and Complex Networks. The document has been partitioned in three separated parts according to those topics.The first part deals with far-from-equilibrium growing interfaces. This subject represents one of the main fields in which fractal geometry has been widely applied, and is nowadays of great interest in Condensed Matter Physics. The Chapter 2 provides a brief and basic introduction to interface growth. We introduce some fractal and scaling concepts, as well as the main universality classes in presence of annealed disorder (EW and KPZ) in terms of both growth equations and discrete models. In Chapter 3 we focus on the elastic interface dynamics in disordered media, i.e., in presence of quenched randomness. This Chapter contains original research based on cellular automata simulations. We carry out a novel study of the dynamics by focusing on the discrete activity patterns that the interface sites describe during therelaxation toward the steady state. We analyze the spatio-temporal correlations of such patterns as the temperature is varied. We observe that, for some range of low temperatures, the out-of-equilibrium relaxation can be understood in the context of creep dynamics.The second part of the Thesis focus on Sociophysics. This discipline attends to the social interactions among individuals -most often mapped onto networks to provide them a topological structure- and has recently attracted much interest in the physics community. Social interactions give rise to adaptive systems that exhibit complex features as self-organization and cooperation. Therefore, Statistical Mechanics provides the necessary tools to analyze the behavior of such groups of agentsin a first level of simplification. The topics that Sociophysics deals with are quite a number, and we particularly focus on processes of opinion formation. The Chapter 4 presents a basic classification of the different opinion formation models present in the literature. In Chapter 5 we provide some analytical and numerical own results to describe the effect that the social temperature- understood as a simplified description of the interplay between an agent, its surroundings, and a collective climate parameter- may exert on such opinion formation processes. The thermal effect can be implemented in different ways. In the first part of the Chapter we work on a simple opinion formation model that, according to some procedural rules, reproduces the Sznajd dynamics. We include the thermal effect by means of some probability that the agents adopt the opposite opinion that the one indicated by such rules. In the second part of the Chapterwe consider a system with three different interacting groups of individuals, where the thermal effect is implemented as certain probability of spontaneous changes of the agents opinion. We exploit the van Kampen's expansion approach to analyze the macroscopic behavior of the different supporter group densities as well as the fluctuations around such macroscopic behavior.The third and last part of the document concerns Complex Networks, which have recently prompted the scientific community to investigate the mechanisms that determine their topology and dynamical properties.The rapid development of networks like the Internet and the World-Wide-Web, which represent today the basic substrate for all sort of communications at planetary level, has given rise to a number of interdisciplinary studies with highly technological applications. We first provide an introduction to complex networks in Chapter 6, where we introduce some basic concepts as scale-free graphs, mixing patterns, clustering coefficient, and small-world effect. In Chapter 7 we deal with traffic processes on networks, and specifically we focus on optimization of the routing protocols that define the connecting paths among all the pair of nodes. Such optimization pursues to avoid the traffic jams that emerge for huge quantities of matter or information flowing inthe graph. We propose an optimization algorithm that, in order to avert jamming, minimizes the number of paths that go through the most visited node (maximal betweenness) while keeping the path length as short as possible, i.e., in the proximities of the length distribution of the initial shortest-path protocol.

Understanding the behavior of complex, large-scale, interconnected systems in a rigorous and structured manner is one of the most pressing scientific and technological challenges of current times. These systems include, among many others, transportation and communications systems, smart grids and power grids, financial markets etc. Failures of these systems have potentially enormous social, environmental and financial costs. In this work, we investigate the failure mechanisms of load-sharing complex systems. The systems are composed of multiple nodes or components whose failures are determined based on the interaction of their respective strengths and loads (or capacity and demand respectively) as well as the ability of a component to share its load with its neighbors when needed. Each component possesses a specific strength (capacity) and can be in one of three states: failed, damaged or functioning normally. The states are determined based on the load (demand) on the component. We focus on two distinct mechanisms to model the interaction between components strengths and loads. The first, a Loss of Strength (LOS) model and the second, a Customer Service (CS) model. We implement both models on lattice and scale-free graph network topologies. The failure mechanisms of these two models demonstrate temporal scaling phenomena, phase transitions and multiple distinct failure modes excited by extremal dynamics. We find that the resiliency of these models is sensitive to the underlying network topology. For critical ranges of parameters the models demonstrate power law and exponential failure patterns. We find that the failure mechanisms of these models have parallels to failure mechanisms of critical infrastructure systems such as congestion in transportation networks, cascading failure in electrical power grids, creep-rupture in composite structures, and draw-downs in financial markets. Based on the different variants of failure, strategies for mitigating and postponing failure in these critical infrastructure systems can be formulated.

Neste trabalho estudamos um modelo estocástico com simetria Ising e dois estados absorventes em três dimensões com uma rede cúbica e em duas dimensões através de uma rede triangular. O estudo levou em conta cálculos de aproximação de campo médio e simulações de Monte Carlo. Os resultados mostraram que o modelo tem transição de segunda ordem de uma fase paramagnética para uma fase ferromagnética, uma transição da fase ferromagnética para uma fase absorvente, também de segunda ordem, e ainda uma transição de primeira ordem da fase paramagnética para a fase absorvente. No espaço de parâmetros as três linhas de transição se encontram no diagrama de fases em um ponto onde o modelo se comporta como o modelo do votante. / In this work we studied a stochastic model with ising symmetry and two simmetric absorbing configurations in a three-dimensional cubic lattice and in two dimensions using a triangular lattice. The study took into account simple mean-field approximations and Monte Carlo simulations. The results showed that the model has a second-order transition from a paramagnetic phase to a ferromagnetic phase and second-order transition from ferromagnetic phase to the absorbing one. A first-order phase transition from the paramagnetic phase to the absorbing phase is observed too. In the phase diagram the two second-order transition lines aproaches to the point where the model behaves like the voter model.

La plupart des processus dans notre vie quotidienne sont des processus hors équilibre. Un exemple de système hors équilibre est la cellule biologique et le transport qui a lieu dedans. Dans cette thèse ce transport intracellulaire est modélisé par des processus stochastiques. Pour cela deux approches différentes ont été utilisées : d’une part une modélisation explicite de particules actives avec des degrés de liberté internes obtenus expérimentalement, d’autre part une description phénoménologique des effets collectifs, qui est réalisée au moyen de processus d’exclusion.Un des résultats principaux pour le modèle explicite est qu’il est crucial de prendre en compte les fluctuations des forces pour reproduire les caractéristiques principales du mou- vement. Un autre élément important est la prise en considération de l’environnement cellu- laire, qui peut produire des effets non-triviaux, comme par exemple une inversion du sens de déplacement moyen. Pour étudier les effets collectifs il est possible de représenter le mou- vement des particules d’une manière simplifiée, en utilisant un processus d’exclusion avec des particules ayant des états internes. Le désordre sur les taux de saut qui en résulte peut provoquer une condensation dépendant de la densité.Un autre modèle étudié est un processus d’exclusion sur un réseau à deux voies. On suppose que deux types de particules se déplacent dans une géométrie tubulaire, inspirée par les champignons filamenteux. Ces hypothèses définissent un modèle minimal qui présente une transition de phase d’une phase de basse densité vers une phase pulsante caractérisée par des oscillations de densité. / Most processes in our daily life are far from equilibrium. The prime example is a cell and the transport occurring within. In this thesis intracellular transport is modeled by means of stochastic processes. For this, two different approaches are applied: the explicit mod- eling of active particles with internal degrees of freedom with characteristics as they were determined experimentally. And secondly, the collective effects occurring in many particle systems are studied in a phenomenological way by means of exclusion processes.In the explicit model one important result is given by the fact that force fluctuations are essential to capture the relevant motion characteristics. Further, the influence of the cellular environment creates counter-intuitive effects, like a possible inversion of the bias. The motion characteristics can be represented in a coarse-grained manner as an exclusion process for particles with internal states. Due to the resulting disorder in the hopping rates a density-dependent condensation occurs.In a second part, a two-lane exclusion model is studied. Two species in a tubular geometry inspired by filamentous fungi are considered.This can be seen as a minimal model exhibiting a phase transition from a low density phase to an intriguing phase with periodically changing particle densities.

L'étude des dynamiques collectives, observables chez de nombreuses espèces animales, a motivé dans les dernières décennies un champ de recherche actif et transdisciplinaire. De tels comportements sont souvent modélisés par de la matière active, c'est-à-dire par des modèles dans lesquels chaque individu est caractérisé par une vitesse propre qui tend à s'aligner avec celle de ses voisins.Dans un modèle fondateur proposé par Vicsek et al., ainsi que dans de nombreux modèles de matière active liés à ce dernier, une transition de phase entre un comportement chaotique à forte température, et un comportement global et cohérent à faible température, a été observée. De nombreuses preuves numériques de telles transitions de phase ont été obtenues dans le cadre des dynamiques collectives. D'un point de vue mathématique, toutefois, ces systèmes actifs sont encore mal compris. Plusieurs résultats ont été obtenus récemment sous une approximation de champ moyen, mais il n'y a encore à ce jour que peu d'études mathématiques de modèles actifs faisant intervenir des interactions purement microscopiques.Dans ce manuscrit, nous décrivons un système de particules actives sur réseau interagissant localement pour aligner leurs vitesses. L'objet de cette thèse est l'obtention rigoureuse, à l'aide du formalisme des limites hydrodynamiques pour les gaz sur réseau, de la limite macroscopique de ce système hors-équilibre, qui pose de nombreuses difficultés techniques et théoriques. / Collective dynamics can be observed among many animal species, and have given rise in the last decades to an active and interdisciplinary field of study. Such behaviors are usually modeled by active matter, in which each individual is self-driven and tends to align its velocity with that of its neighbors.In a classical model introduced by Vicsek & al., as well as in numerous related active matter models, a phase transition between chaotic behavior at high temperature and global order at low temperature can be observed. Even though ample evidence of these phase transitions has been obtained for collective dynamics, from a mathematical standpoint, such active systems are not fully understood yet. Some progress has been achieved in the recent years under an assumption of mean-field interactions, however to this day, few rigorous results have been obtained for models involving purely local interactions.In this manuscript, we describe a lattice active particle system interacting locally to align their velocities. This thesis aims at rigorously obtaining, using the formalism developed for hydrodynamic limits of lattice gases, the scaling limit of this out-of-equilibrium system, for which numerous technical and theoretical difficulties arise.

This thesis describes an experimental study on fluctuations of a Brownian particle immersed in a fluid, confined by optical tweezers and subject to two different kinds of non-equilibrium conditions. We aim to gain a rather general understanding of the relation between spontaneous fluctuations, linear response and total entropy production for processes away from thermal equilibrium. The first part addresses the motion of a colloidal particle driven into a periodic non-equilibrium steady state by a nonconservative force and its response to an external perturbation. The dynamics of the system is analyzed in the context of several generalized fluctuation-dissipation relations derived from different theoretical approaches. We show that, when taking into account the role of currents due to the broken detailed balance, the theoretical relations are verified by the experimental data. The second part deals with fluctuations and response of a Brownian particle in two different aging baths relaxing towards thermal equilibrium: a Laponite colloidal glass and an aqueous gelatin solution. The experimental results show that heat fluxes from the particle to the bath during the relaxation process play the same role of steady state currents as a non-equilibrium correction of the fluctuation-dissipation theorem. Then, the present thesis provides evidence that the total entropy production constitutes a unifying concept which links the statistical properties of fluctuations and the linear response function for non-equilibrium systems either in stationary or non stationary states.