In typical attempts to control spatio-temporal chaos, spatially extended systems were subjected to protocols that perturbed them as a whole, often overlooking the potential stabilizing interaction between adjacent regions. We have shown that through the application of a time-delayed feedback scheme to a specific localized region of a system periodic patterns can be generated that are distinct from those observed when controlling the whole system. In this thesis, we present the results of two interconnected studies: 1) Spatio-temporal patterns emerging from spatially localized time-delayed feedback perturbations within transient chaotic states of the Gray-Scott reaction-diffusion system 2) Spatio-temporal patterns emerging from spatially localized time-delayed feedback perturbations within chaotic states of the cubic complex Ginzburg-Landau equation We present an investigation of two model systems: the Gray-Scott reaction-diffusion equation and the complex Ginzburg-Landau equation. Specifically we numerically study two models characterized by exhibiting various chaotic regimes. We first consider a comprehensive study of the Gray-Scott model highlighting key details about different parameter space regimes and their relative proximity to the chaotic regime. Through a systematic investigation of the effects of the model control parameters, time-delayed feedback control strength parameters, perturbed region widths, and other quantities, we show that novel patterns can be formed through the appropriate choice of perturbation region and strength. For the second study we use spatially localized time-delayed feedback on the one-dimensional complex Ginzburg-Landau equation and demonstrate, through the numerical integration of the resulting real and imaginary equations, the stabilization of novel periodic patterns within three distinct chaotic regimes. In these studies we have shown that selectively applying a time-delayed feedback scheme to a specific spatially localized region of a chaotic system can bring forth periodic patterns that are distinct from those observed when applying a perturbation to the whole system. Depending on the protocol used, these new patterns can emerge either in the perturbed or the unperturbed region. The mechanism underlying the observed pattern generation is related to the interplay between diffusion across the interfaces separating the different regions and time-delayed feedback. Research was sponsored by the Army Research Office and was accomplished under Grant No. W911NF-17-1-0156. / Doctor of Philosophy / In typical attempts to control spatio-temporal chaos, spatially extended systems were subjected to protocols that perturbed them as a whole, often overlooking the potential stabilizing interaction between adjacent regions. We have shown that through the application of a time-delayed feedback scheme to a specific localized region of a system periodic patterns can be generated that are distinct from those observed when controlling the whole system. We present an investigation of two model systems: the Gray-Scott reaction-diffusion equation and the complex Ginzburg-Landau equation. We first consider a comprehensive study of the Gray-Scott model highlighting key details about different parameter space regimes and their relative proximity to the chaotic regime. Through a systematic investigation of the effects of the model control parameters, time-delayed feedback control strength parameters, perturbed region widths, and other quantities, we show that novel patterns can be formed through the appropriate choice of perturbation region and strength. For the second study we use spatially localized time-delayed feedback on the one-dimensional complex Ginzburg-Landau equation and demonstrate, through the numerical integration of the resulting real and imaginary equations, the stabilization of novel periodic patterns within chaotic regimes. In these studies we have shown that selectively applying a time-delayed feedback scheme to a specific region of a chaotic system can generate periodic patterns that are distinct from those observed when controlling the whole system. Depending on the protocol used, these new patterns can emerge either in the perturbed or the unperturbed region. The mechanism underlying the observed pattern generation is related to the interplay between diffusion across the interfaces separating the different regions and time-delayed feedback. Research was sponsored by the Army Research Office and was accomplished under Grant No. W911NF-17-1-0156.

Many chaotic and complicated systems cannot be analysed by traditional methods. In 1987 P.Bak, C.Tang, and K.A.Wiesenfeld developed a new concept called Self-Organised Criticality (SOC) to explain the behaviour of composite systems containing a large number of elements that interact over a short range. In general this theory applies to complex systems that naturally evolve to a critical state in which a minor event starts a chain reaction that can affect any number of elements in the system. It was later shown that many complex phenomena such as flux pinning in superconductors, dynamics of granular systems, earthquakes, droplet formation and biological evolution show signs of SOC. The dynamics of complex systems in nature often occurs in terms of punctuation, or avalanches rather than following a smooth, gradual path. Extremal dynamics is used to model the temporal evolution of many different complex systems. Specifically the Bak-Sneppen evolution model, the Sneppen interface depinning model, the Zaitsev flux creep model, invasion percolation, and several other depinning models. This thesis considers extremal dynamics at constant flux where M>1 smallest barriers are simultaneously updated as opposed to models in the limit of zero flux where only the smallest barrier is updated. For concreteness, we study the Bak-Sneppen (BS) evolution model [Phys. Rev. Lett. 71, 4083 (1993)]. M=1 corresponds to the original BS model. The aim of the present work is to understand analytically through mean field theory the random neighbour version of the generalised BS model and verify the results against the computer simulations. This is done in order to scrutinise the trustworthiness of our numerical simulations. The computer simulations are found to be identical with results obtained from the analytical approach. Due to this agreement, we know that our simulations will produce reliable results for the nearest neighbour version of the generalised BS model. Since the nearest neighbour version of the generalised BS model cannot be solved analytically, we have to rely on simulations. We investigate the critical behaviour of both versions of the model using the scaling theory. We look at various distributions and their scaling properties, and also measure the critical exponents accurately verifying whether the scaling relations holds. The effect of increasing from M=1 to M>1 is surprising with dramatic decrease in size of the scaling regime.

Non-equilibrium systems have no set method of analysis, and a wide array of dynamics can be present in such systems. In this work we present three very different non-equilibrium models, inspired by biological systems and phenomena, that we analyze through computational means to showcase both the range of dynamics encompassed by these systems, as well as various techniques used to analyze them. The first system we model is a surface plasmon resonance (SPR) cell, a device used to determine the binding rates between various species of chemicals. We simulate the SPR cell and compare these computational results with a mean-field approximation, and find that such a simplification fails for a wide range of reaction rates that have been observed between different species of chemicals. Specifically, the mean-field approximation places limits on the possible resolution of the measured rates, and such an analysis fails to capture very fast dynamics between chemicals. The second system we analyzed is an avalanching neural network that models cascading neural activity seen in monkeys, rats, and humans. We used a model devised by Lombardi, Herrmann, de Arcangelis et al. to simulate this system and characterized its behavior as the fraction of inhibitory neurons was changed. At low fractions of inhibitory neurons we observed epileptic-like behavior in the system, as well as extended tails in the avalanche strength and duration distributions, which dominate the system in this regime. We also observed how the connectivity of these networks evolved under the effects of different inhibitory fractions, and found the high fractions of inhibitory neurons cause networks to evolve more sparsely, while networks with low fractions maintain their initial connectivity. We demonstrated two strategies to control the extreme avalanches present at low inhibitory fractions through either the random or targeted disabling of neurons. The final system we present is a sparsely encoding convolutional neural network, a computational system inspired by the human visual cortex that has been engineered to reconstruct images inputted into the network using a series of "patterns" learned from previous images as basis elements. The network attempts to do so "sparsely," so that the fewest number of neurons are used. Such systems are often used for denoising tasks, where noisy or fragmented images are reconstructed. We observed a minimum in this denoising error as the fraction of active neurons was varied, and observed the depth and location of this minimum to obey finite-size scaling laws that suggest the system is undergoing a second-order phase transition. We can use these finite-size scaling relations to further optimize this system by tuning it to the critical point for any given system size. / Doctor of Philosophy / Non-equilibrium systems have no set method of analysis, and a wide array of dynamics can be present in such systems. In this work we present three very different non-equilibrium models, inspired by biological systems and phenomena, that we analyze through computational means to showcase both the range of dynamics encompassed by these systems, as well as various techniques used to analyze them. The first system we model is a surface plasmon resonance (SPR) cell, a device used to determine the binding rates between various species of chemicals. We simulate the SPR cell and compare these computational results with a mean-field approximation, and find that such a simplification fails for a wide range of reaction rates that have been observed between different species of chemicals. Specifically, the mean-field approximation places limits on the possible resolution of the measured rates, and such an analysis fails to capture very fast dynamics between chemicals. The second system we analyzed is an avalanching neural network that models cascading neural activity seen in monkeys, rats, and humans. We used a model devised by Lombardi, Herrmann, de Arcangelis et al. to simulate this system and characterized its behavior as the fraction of inhibitory neurons was changed. At low fractions of inhibitory neurons we observed epileptic-like behavior in the system, as well as extended tails in the avalanche strength and duration distributions, which dominate the system in this regime. We also observed how the connectivity of these networks evolved under the effects of different inhibitory fractions, and found the high fractions of inhibitory neurons cause networks to evolve more sparsely, while networks with low fractions maintain their initial connectivity. We demonstrated two strategies to control the extreme avalanches present at low inhibitory fractions through either the random or targeted disabling of neurons. The final system we present is a sparsely encoding convolutional neural network, a computational system inspired by the human visual cortex that has been engineered to reconstruct images inputted into the network using a series of “patterns” learned from previous images as basis elements. The network attempts to do so “sparsely,” so that the fewest number of neurons are used. Such systems are often used for denoising tasks, where noisy or fragmented images are reconstructed. We observed a minimum in this denoising error as the fraction of active neurons was varied, and observed the depth and location of this minimum to obey finite-size scaling laws that suggest the system is undergoing a second-order phase transition. We can use these finite-size scaling relations to further optimize this system by tuning it to the critical point for any given system size.

In recent years a new interesting research avenue has emerged in non-equilibrium statistical physics, namely studies of collective responses in spatially inhomogeneous systems. Whereas substantial progress has been made in understanding the origins and the often universal nature of cooperative behavior in systems far from equilibrium, it is still unclear whether it is possible to control their global collective stochastic dynamics through local manipulations. Therefore, a comprehensive characterization of spatially inhomogeneous non-equilibrium systems is required. In the first system, we explore a variant of the Katz–Lebowitz–Spohn (KLS) driven lattice gas in two dimensions, where the lattice is split into two regions that are coupled to heat baths with distinct temperatures T > T_c and T_c respectively, where T_c indicates the critical temperature for phase ordering. The geometry was arranged such that the temperature boundaries are oriented perpendicular or parallel to the external particle drive and resulting net current. For perpendicular orientation of the temperature boundaries, in the hotter region, the system behaves like the (totally) asymmetric exclusion processes (TASEP), and experiences particle blockage in front of the interface to the critical region. This blockage is induced by extended particle clusters, growing logarithmically with system size, in the critical region. We observe the density profiles in both high- and low-temperature subsystems to be similar to the well-characterized coexistence and maximal-current phases in (T)ASEP models with open boundary conditions, which are respectively governed by hyperbolic and trigonometric tangent functions. Yet if the lower temperature is set to T_c, we detect marked fluctuation corrections to the mean-field density profiles, e.g., the corresponding critical KLS power-law density decay near the interfaces into the cooler region. For parallel orientation of the temperature boundaries, we have explored the changes in the dynamical behavior of the hybrid KLS model that are induced by our choice of the hopping rates across the temperature boundaries. If these hopping rates at the interfaces satisfy particle-hole symmetry, the current difference across them generates a vector flow diagram akin to an infinite flat vortex sheet. We have studied the finite-size scaling of the particle density fluctuations in both temperature regions, and observed that it is controlled by the respective temperature values. If the colder subsystem is maintained at the KLS critical temperature, while the hotter subsystem's temperature is set much higher, the interface current greatly suppresses particle exchange between the two regions. As a result of the ensuing effective subsystem decoupling, strong fluctuations persist in the critical region, whence the particle density fluctuations scale with the KLS critical exponents. However, if both temperatures are set well above the critical temperature, the particle density fluctuations scale according to the totally asymmetric exclusion process. We have also measured the entropy production rate in both subsystems; it displays intriguing algebraic decay in the critical region, while it saturates quickly at a small but non-zero level in the hotter region. The second system is a lattice gas that simulates the spread of COVID-19 epidemics using the paradigmatic stochastic Susceptible-Infectious-Recovered (SIR) model. In our effort to control the spread of the infection of a lattice, we robustly find that the intensity and spatial spread on the epidemic recurrence wave can be limited to a manageable extent provided release of these restrictions is delayed sufficiently (for a duration of at least thrice the time until the peak of the unmitigated outbreak). / Doctor of Philosophy / In recent years a new interesting research avenue has emerged in far-from-equilibrium statistical physics, namely studies of collective behavior in spatially non-uniform systems. Whereas substantial progress has been made in understanding the origins and the often universal nature of cooperative behavior in systems far from equilibrium, it is still unclear whether it is possible to control their global collective and randomly determined dynamics through local manipulations. Therefore, a comprehensive characterization of spatially non-uniform systems out of equilibrium is required. In the first system, we explore a variant of the two-dimensional lattice gas with completely biased diffusion in one direction and attractive particle interactions. By lattice gas we mean a lattice filled with particles that can hop on nearest-neighbor empty sites. The system we are considering is a lattice that is split into two regions, which in turn are maintained at distinct temperatures T > T_c and T_c, respectively, with T_c indicating the critical temperature for the second-order phase transition. The geometry of the lattice was arranged such that the temperature boundaries are oriented perpendicular or parallel to the external particle drive that is responsible for a completely biased diffusion. When the temperature boundaries are oriented perpendicular to the drive, in the hotter region with temperature T > T_c, the system evolves as if there are no attractive interactions between the particles, and experiences particle blockage in front of the temperature boundary from the hotter region held at T>T_c to the critical region held at T_c. This accumulation of particles at the temperature boundary is induced by elongated collections of particle, i.e., particle clusters in the critical region. We observe the particle density profiles (ρ(x) vs x plots) in both high-and low-temperature subsystems to be similar to the density profiles found for other well-characterized (T)ASEP models with open boundary conditions, which are in the coexistence and maximal-current phases, and which are respectively governed by hyperbolic and trigonometric tangent functions. Yet if the lower temperature is set to T_c, we detect marked corrections to the hyperbolic and trigonometric tangent-like density profiles due to fluctuations, e.g., we observe the algebraic power-law decay of the density near the interfaces into the cooler region with the critical KLS exponent. For a parallel orientation of the temperature boundaries, we have explored the changes in the particle dynamics of the two-temperature KLS model that are induced by our choice of the particle hopping rates across the temperature boundaries. If these particle hopping rates at the temperature interfaces satisfy particle-hole symmetry (i.e. remain unchanged when particles are replaced with holes and vice versa), the particle current difference across them generates a current vector flow diagram akin to an infinite flat vortex sheet. We have studied how the particle density fluctuations in both temperature regions scale with the system size, and observed that the scaling is controlled by the respective temperature values. If the colder subsystem is maintained at the KLS critical temperature T_cold = T_c, while the hotter subsystem's temperature is set much higher T_hot >> T_c, the particle currents at the interface greatly suppresses particle exchange between the two temperature regions. As a result of the ensuing effective subsystem separation from each other, strong fluctuations persist in the critical region, whence the particle density fluctuations scale with the KLS critical exponents. However, if both temperatures are set well above the critical temperature, the particle density fluctuations scale with different scaling exponents, that fall into the totally asymmetric exclusion process (TASEP) universality class. We have also measured the rate of the entropy production in both subsystems; it displays intriguing algebraic decay in the critical region, while it reaches quickly a small but non-zero value in the hotter region. The second system is a lattice filled with particles of different types that hop around the lattice and are subjected to different sorts of reactions. That process simulates the spread of the COVID-19 epidemic using the paradigmatic random-process-based Susceptible-Infectious-Recovered (SIR) model. In our effort to control the spread of the infection of a lattice, we robustly find that the intensity and spatial spread of the epidemic second wave can be limited to a manageable extent provided release of these restrictions is delayed sufficiently (for a duration of at least thrice the time until the peak of the unmitigated outbreak).

We present an investigation of two non-equilibrium systems: spatial many-species predator-prey games and systems of interacting magnetic skyrmions. We numerically study two predator-prey systems characterized by nested pattern formations. We first consider a six species game in which spiral patterns spontaneously form within coarsening domains. Through a systematic investigation of relevant correlation functions, the interface width, and other quantities, we show that the non-trivial in-domain dynamics affect the coarsening process and the interfacial properties. The exponents which govern domain growth, aging, and interface fluctuations differ from those expected from curvature driven coarsening. The response to perturbations of the reaction rates is also studied. Furthermore, we introduce a nine species model characterized by nested spiral pattern formations. Quantitative evidence of the existence of two length and time scales associated to the spiral levels is presented in the form of correlation lengths and a temporal Fourier analysis of the species densities. A generalized interaction scheme is proposed for dynamically generated hierarchies. Magnetic skyrmions are particle-like spin configurations found in certain chiral magnets. We study the effect of the Magnus force on the relaxation dynamics through Langevin molecular dynamics simulations. The Magnus force enhances the disorder of the system at high noise strengths while we observe a dynamic regime with slow decaying correlations at low noise strengths. The different regimes are characterized by changes in the aging exponent. In general, the Magnus force accelerates the approach to the steady state. In the presence of quenched disorder, we find that the relaxation dynamics are more robust in systems with a strong Magnus force. We also examine periodically driven skyrmion systems and show that a transition from reversible to irreversible flow exists in the presence of attractive defects. The Magnus force enhances the irreversible regime in this case. The work on predator-prey systems was supported by the U.S. National Science Foundation through Grant No. DMR-1606814 whereas the work on skyrmions was supported by the US Department of Energy, Office of Basic Energy Sciences (DOE-BES), under Grant No. DE-FG02-09ER46613. / Doctor of Philosophy / We present an investigation of two non-equilibrium systems: spatial many-species predator- prey games and systems of interacting magnetic skyrmions. We numerically study two predator-prey systems characterized by nested pattern formations. We first consider a six species game in which spiral patterns spontaneously form within coarsening domains. Through a systematic investigation of relevant correlation functions, the interface width, and other quantities, we show that the non-trivial in-domain dynamics affect the coarsening process and, to a greater extent, properties at the interface between competing groups of species. The exponents which govern domain growth, aging, and interface fluctuations are shown to differ from those expected in typical games of competition. We also study the change of the system due to a perturbation of the reaction rates, which could represent an abrupt change in the environment. Furthermore, we introduce a nine species model characterized by the emergence of nested spiral pattern formations. Quantitative evidence of the existence of two distinct spiral levels is presented. We also propose a generalized interaction scheme for dynamically generated spiral hierarchies. Magnetic skyrmions are particle-like spin configurations found in certain chiral magnets. We study the effect of the Magnus force on the dynamic properties of skyrmion systems through particle-based simulations. The Magnus force enhances the disorder of the system at high noise strengths while accelerating the formation of the triangular lattice at low noise strengths. We find that, in general, the Magnus force accelerates the approach to the steady state. In the presence of randomly placed attractive pinning sites, we find that a strong Magnus force can prevent caging effects and allow skyrmions to more easily move around pinning sites. We also examine periodically driven skyrmion systems and show that a transition from reversible to irreversible flow exists in the presence of attractive defects. The Magnus force is shown to enhance the irreversible regime in this case. The work on predator-prey systems was supported by the U.S. National Science Foundation through Grant No. DMR-1606814 whereas the work on skyrmions was supported by the US Department of Energy, Office of Basic Energy Sciences (DOE-BES), under Grant No. DE-FG02-09ER46613.

This thesis uses methods and models from non-equilibrium statistical physics to describe intracellular processes. Bidirectional microtubule-based transport within axons is modeled as a quasi-one-dimensional stochastic lattice gas with two particle species moving in opposite directions under mutual exclusion interaction. Generically occurring clusters of particles in current models for intracellular transport can be dissolved by additionally considering the dynamics of the transport lattice, i.e., the microtubule. An idealized model for the lattice dynamics is used to create a phase transition toward a homogenous state with efficient transport in both directions. In the thermodynamic limit, a steady state property of the dynamic lattice limits the maximal size of clusters. Lane formation mechanisms which are due to specific particle-particle interactions turn out to be very sensitive to the model assumptions. Furthermore, even if some particle-particle interaction is considered, taking the lattice dynamics into account almost always improves transport. Thus the lattice dynamics seems to be the key aspect in understanding how nature regulates intracellular traffic. The last part introduces a model for the dynamics of a microtubule which is limited in its growth by the cell boundary. The action of a rescue-enhancing protein which is added to the growing tip of a microtubule and then slowly dissociates leads to interesting aging effects which should be experimentally observable.

No description available.

Dans cette thèse, des méthodes de la physique statistique hors équilibre sont utilisées pour décrire deux processus intracellulaires. Le transport bidirectionnel sur les microtubules est décrit à l'aide d'un gaz sur réseau stochastique quasi-unidimensionnel. Deux espèces de particules sautent dans des directions opposées en interagissant par exclusion. La présence habituelle d'accumulations de particules peut être supprimée en rajoutant la dynamique du réseau, c'est-à-dire de la microtubule. Un modèle simplifié pour la dynamique du réseau produit une transition de phase vers un état homogène avec un transport très efficace dans les deux directions. Dans la limite thermodynamique, une propriété de l'état stationnaire limite la longueur maximale des accumulations. La formation de voies peut être causée par des interactions entre particules. Néanmoins, ces mécanismes s'avèrent peu robustes face à une variation des paramètres du modèle. Dans presque tous les cas, la dynamique du réseau a un effet positif et bien plus important sur le transport que la formation de voies. Par conséquent, la dynamique du réseau semble un point-clé pour comprendre la régulation du transport intracellulaire. La dernière partie introduit un modèle pour la dynamique d'une microtubule sous l'action d'une protéine qui favorise les sauvetages. Des phénomènes intéressants de vieillissement apparaissent alors, et devraient être observables dans des expériences. / This thesis uses methods and models from non-equilibrium statistical physics to describe intracellular processes. Bidirectional microtubule-based transport within axons is modeled as a quasi-one-dimensional stochastic lattice gas with two particle species moving in opposite directions under mutual exclusion interaction. Generically occurring clusters of particles in current models for intracellular transport can be dissolved by additionally considering the dynamics of the transport lattice, i.e., the microtubule. An idealized model for the lattice dynamics is used to create a phase transition toward a homogenous state with efficient transport in both directions. In the thermodynamic limit, a steady state property of the dynamic lattice limits the maximal size of clusters. Lane formation mechanisms which are due to specific particle-particle interactions turn out to be very sensitive to the model assumptions. Furthermore, even if some particle-particle interaction is considered, taking the lattice dynamics into account almost always improves transport. Thus the lattice dynamics seems to be the key aspect in understanding how nature regulates intracellular traffic. The last part introduces a model for the dynamics of a microtubule which is limited in its growth by the cell boundary. The action of a rescue-enhancing protein which is added to the growing tip of a microtubule and then slowly dissociates leads to interesting aging effects which should be experimentally observable.

Quand le mouvement de particules sous l'action d'un forçage extérieur est restreint par des mécanismes d'exclusion ou de blocage, des corrélations spatio-temporelles non triviales peuvent être observées, dans une dynamique caractérisé par des hétérogénéités spatiales et grandes fluctuations dans le temps.Dans cette thèse, nous étudions deux exemples d'un tel type de mouvement, en prenant en considération deux processus d'exclusion sur des réseaux discrètes en 2d et en 1d.Le premier modèle est inspiré par les mécanismes de relaxation lents observés dans le cisaillement ou le forçage de systèmes colloïdaux ou granulaires: pour des densités élevées, en augmentant le forçage la viscosité peut croitre énormément. Nous expliquons le mécanisme de blocage à grandes densités comme conséquence de l'existence simultanée de régions bloquées et mobiles dans le système, et nous déterminons la signature d'une telle dynamique par le moyen de la thermodynamique des histoires. Nous mesurons aussi l'extension spatiale des structures hétérogènes et fournissons un modèle phénoménologique reliant les propriétés microscopiques de la dynamique au comportement macroscopique de l'écoulement.Le deuxième modèle consiste en un processus d'exclusion en une dimension, incluant les effets dus à la présence structurelle d'un défaut dynamique localisé. Inspirés par la complexité et la richesse du processus de translation du ARN messager, nous proposons un nouveau modèle pour la dynamique de particules dont le mouvement est affecté par des modification stochastiques et structurelles de leur conditions de transport. Nous fournissons une description complète du modèle, avec la caractérisation de tous les régimes dynamiques possibles et une explication quantitative des profils macroscopiques du courant. / When the motion of particles driven by external forces is restricted by exclusion mechanisms or bottlenecks, non-trivial space-time correlations in their motion may be observed, giving rise to a dynamics which involves spatial heterogeneities and large fluctuations in time.Here we study two examples of such kind of motion, considering two exclusion processes on discrete lattices in 2d and 1d.The first model is inspired by the slow relaxation occurring when stirring or shearing colloidal or granular materials: at high densities (or packing fractions) increasing the external forcing may lead to a strong increase in the viscosity. We explain the blockage dynamics at high density as the coexistence of blocked and mobile regions and we determine the signature of such dynamics with the use of the thermodynamics of histories. We also quantify the spatial extension of such structures and provide a phenomenological model relating the microscopic properties of the dynamics to the macroscopic flow behavior.The second model consists in a one-dimensional exclusion process incorporating a structural, localized, dynamical defect. Inspired by the complexity and richness of mRNA translation, we propose a new model for the dynamics arising when the particles flow is regulated by structural or conformational changes in the transport medium. We provide a complete description of the model, characterizing all the possible dynamical regimes and addressing a quantitative explanation of the macroscopic current profiles.

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.