Nesta dissertação, estuda-se a transição de esteira no escoamento ao redor de um aerofólio NACA 0012 com ângulos de ataque de zero dez e vinte graus. Dois casos são considerados: fólio isolado e fólio alinhado com um cilindro. Nas duas configurações, analisa-se a estabilidade linear em relação a perturbações tridimensionais. Tais perturbações foram estudadas usando a teoria de Floquet para um conjunto de números de Reynolds e ângulos de ataques. O escoamento base é calculado usando o método de elementos finitos espectrais para a discretização espacial. Dos resultados de estabilidade no caso do aerofólio isolado, pode-se observar dois picos de instabilidade com diferentes comprimentos de onda na envergadura. A simetria dos modos instáveis é também apresentada. Um dos modos instáveis presente na esteira do aerofólio isolado foi também observado no caso do cilindro alinhado com o fólio, enquanto o outro modo foi suprimido em tal geometria / Study of hydrodynamic stability of the flow around a cylinder aligned with on airfoil

Ce manuscrit décrit comment les champs de vitesses solutions de l'équation de Navier-Stokes se comportent à grande échelle pour un forçage à petite échelle. Il analyse aussi le comportement à grande échelle des champs magnétiques solutions de l'équation d'induction cinématique lorsque le champs de vitesse est de petite échelle. Les résultats présentés ont été obtenus à l'aide de simulations numériques directes utilisant des algorithmes pseudo-spectraux des équations non modifiées ou avec un développement utilisant la méthode Floquet. Dans le cadre hydrodynamique, les simulations utilisant la méthode de Floquet permettent de retrouver les résultats de l'effet AKA à bas Reynolds et de les étendre pour des Reynolds d'ordre un. Elles permettent aussi d'étudier des écoulements AKA-stable et de mettre en évidence une autre instabilité pouvant être interprétée comme un effet de viscosité négative. Dans le cadre magnétique, l'effet alpha est observé sur une gamme de séparation d'échelle dépassant par plusieurs ordres de grandeur les autres résultats connus. Il est aussi montré que le taux de croissance de l'instabilité devient indépendant de la séparation d'échelle une fois que le champs magnétique est destabilisé dans ses petites échelles. Le spectre d'énergie et le temps du corrélation d'équilibre absolu solution de l'équation d'Euler tronquée sont présentés. Un nouveau régime où le temps de corrélation est régit par l’hélicité est mis en évidence. Ces résultats sont aussi comparés à ceux des modes de grande échelle de solutions de l'équation de Navier-Stokes forcée dans les petites échelles. Ils montrent que le temps de corrélation croit avec l'hélicité. / This manuscript describes how solutions of the Navier-Stokes equations behave in the large scales when forced in the small scales. It analyzes also the large scale behavior of magnetic fields solution of the kinetic induction equation when the velocity is in the small scales. The results were acquired with direct numeric simulation (DNS) using pseudo-spectral algorithms of the equations as well as their Floquet development. In the hydrodynamical case, the Floquet DNS were able to confirm the results of the AKA effect at low Reynolds number and extend them for Reynolds number of order one. The DNS were also used to study AKA-stable flows and identified a new instability that can be interpreted as a negative viscosity effect. In the magnetic case, the alpha effect is observe for a range of scale separation exceed know results by several orders of magnitude. It is also shown that the growth rate of the instability becomes independent of the scale separation once the magnetic field is destabilized in its small scales. The energy spectrum and the correlation time of absolute equilibrium solution of the truncated Euler equation are presented. A new regime where the correlation time is governed by helicity is exhibited. These results are also compared with those coming from large scale modes of solutions of the Navier-Stokes equation forced in the small scales. They show that the correlation time increases with the helicity of the flow.

It is commonly expected, that the entanglement entropy for eigenstates of quantum chaotic systems can be described by random matrix theory. However, the random matrix predictions account for structureless random states, only. It is unclear, how the subsystem structure of actual bipartite systems influences the entanglement. We investigate the effect of such a structure on the bipartite entanglement for eigenstates of time-periodically kicked Floquet systems. To this end, the expression for the eigenstate entanglement is transferred into a dynamical quantity, which is particularly suited for an evaluation using analytical methods for time evolution. We present three approaches and apply each to an appropriate minimal model. Based on the supersymmetry method, we compute the entanglement of structureless random matrices and thereby establish exact results for the entropy of random matrix eigenstates. The Weingarten calculus is used for computing the entanglement of an inherent bipartite random matrix ensemble. Moreover, based on semiclassical path integrals, we devise a trace formula, which quantifies entanglement of chaotic Floquet systems in terms of classical orbits. We thereby show, that the entanglement of strongly coupled bipartite Floquet systems coincides in the semiclassical limit with the entanglement of structureless random matrices. Several possible generalizations of our methods to autonomous systems and other entropies are discussed.:1. Introduction 2. Fundamentals on bipartite systems and entanglement 2.1. Classical and quantum chaotic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1. Classical mechanical systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2. Quantum systems and random matrix theory . . . . . . . . . . . . . . . . . . . 8 2.2. Bipartite systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3. Entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4. Objective of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3. Random matrix methods for entanglement in bipartite chaotic systems 3.1. Entropy formulation in terms of Green’s functions . . . . . . . . . . . . . . . . . . . . . 23 3.2. Weingarten calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.1. Spectral form factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.2. Inverse participation ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2.3. Linear entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.3. Linear entropy by the supersymmetry method . . . . . . . . . . . . . . . . . . . . . . . 43 3.3.1. Gaussian integrals and the generating function . . . . . . . . . . . . . . . . . . 44 3.3.2. Supersymmetric integrals and generating function . . . . . . . . . . . . . . . . . 46 3.3.3. Entropy of the CUE case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4. Semiclassical method for entanglement in bipartite chaotic systems 4.1. Path integrals and trace formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.1.1. Path integral formulation of propagators . . . . . . . . . . . . . . . . . . . . . . 60 4.1.2. Trace formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2. Rescaled path integral formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2.1. Spectral form factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.2.2. Linear entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.2.3. Order \hbar correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5. Generalizations 5.1. Supersymmetry method for bipartite systems . . . . . . . . . . . . . . . . . . . . . . . 80 5.2. Resummation via Cayley-Hamilton inverse . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.3. Havrda-Charvát-Tsallis entropies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.4. Autonomous systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.5. Entanglement generated by a time evolution . . . . . . . . . . . . . . . . . . . . . . . . 93 6. Summary and outlook Appendix A. Weingarten calculus for the first steps of the IPR signal function . . . . . . . . . . .99 B. Color-Flavor transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 C. Detailed calculation of moments using SVD . . . . . . . . . . . . . . . . . . . . . . . . 102 D. Integral I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 E. Stationary phase approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 F. Ergodic average of the coupling term . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 List of Figures List of Tables / Es wird üblicherweise angenommen, dass die Verschränkungsentropie von Eigenzuständen quantenchaotischer Systeme durch die Theorie der Zufallsmatrizen beschrieben wird. Diese Zufallsmatrixvorhersage bezieht sich nur auf strukturlose Zufallszustände. Es ist nicht klar, wie sich die Subsystemstruktur realer, bipartiter Systeme auf die Verschränkung auswirkt. Wir untersuchen die Konsequenzen einer solchen Struktur auf die bipartite Verschränkung der Eigenzustände von zeit-periodisch gestoßenen Floquet-Systemen. Dazu wird der Ausdruck für die Eigenzustandsverschränkung in eine dynamische Größe überführt, welche besonders geeignet ist für die Anwendung analytischer Methoden zur Zeitentwicklung. Wir präsentieren drei Ansätze und wenden jeden auf ein zugehöriges minimales Modell an. Basierend auf der Supersymmetriemethode berechnen wir die Verschränkung in strukturlosen Zufallsmatrizen und erhalten exakte Resultate für die Entropie von Zufallsmatrixeigenzuständen. Der Weingarten-Formalismus wird genutzt, um die Verschränkung in einem inhärent bipartiten Zufallsmatrixmodell zu berechnen. Außerdem stellen wir, basierend auf semiklassischen Pfad-Integralen, eine Spurformel auf, welche die Verschränkung in chaotischen Floquet-Systemen mittels klassischer Orbits ausdrückt. Wir zeigen über diesen Weg, dass die Verschränkung in stark gekoppelten, bipartiten Floquet-Systemen im semiklassischen Limes mit der Verschränkung in strukturlosen Zufallsmatrizen übereinstimmt. Es werden mehrere Verallgemeinerungen unserer Methoden für autonome Systeme und andere Entropien diskutiert.:1. Introduction 2. Fundamentals on bipartite systems and entanglement 2.1. Classical and quantum chaotic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1. Classical mechanical systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2. Quantum systems and random matrix theory . . . . . . . . . . . . . . . . . . . 8 2.2. Bipartite systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3. Entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4. Objective of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3. Random matrix methods for entanglement in bipartite chaotic systems 3.1. Entropy formulation in terms of Green’s functions . . . . . . . . . . . . . . . . . . . . . 23 3.2. Weingarten calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.1. Spectral form factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.2. Inverse participation ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2.3. Linear entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.3. Linear entropy by the supersymmetry method . . . . . . . . . . . . . . . . . . . . . . . 43 3.3.1. Gaussian integrals and the generating function . . . . . . . . . . . . . . . . . . 44 3.3.2. Supersymmetric integrals and generating function . . . . . . . . . . . . . . . . . 46 3.3.3. Entropy of the CUE case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4. Semiclassical method for entanglement in bipartite chaotic systems 4.1. Path integrals and trace formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.1.1. Path integral formulation of propagators . . . . . . . . . . . . . . . . . . . . . . 60 4.1.2. Trace formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2. Rescaled path integral formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2.1. Spectral form factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.2.2. Linear entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.2.3. Order \hbar correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5. Generalizations 5.1. Supersymmetry method for bipartite systems . . . . . . . . . . . . . . . . . . . . . . . 80 5.2. Resummation via Cayley-Hamilton inverse . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.3. Havrda-Charvát-Tsallis entropies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.4. Autonomous systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.5. Entanglement generated by a time evolution . . . . . . . . . . . . . . . . . . . . . . . . 93 6. Summary and outlook Appendix A. Weingarten calculus for the first steps of the IPR signal function . . . . . . . . . . .99 B. Color-Flavor transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 C. Detailed calculation of moments using SVD . . . . . . . . . . . . . . . . . . . . . . . . 102 D. Integral I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 E. Stationary phase approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 F. Ergodic average of the coupling term . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 List of Figures List of Tables

Made available in DSpace on 2014-12-17T14:55:39Z (GMT). No. of bitstreams: 1 RobsonHCM.pdf: 3964230 bytes, checksum: b66d62a3ab0ff3d24888963581fbde31 (MD5) Previous issue date: 2009-08-12 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This work presents a theoretical and numerical analysis for the cascading of frequency selective surfaces, which uses rectangular patches and triangular Koch fractals as elements. Two cascading techniques are used to determine the transmission and reflection characteristics. Frequency selective surfaces includes a large area of Telecommunications and have been widely used due to its low cost, low weight and ability to integrate with others microwaves circuits. They re especially important in several applications, such as airplane, antennas systems, radomes, rockets, missiles, etc.. FSS applications in high frequency ranges have been investigated, as well as applications of cascading structures or multi-layer, and active FSS. Furthermore, the analyses uses the microwave circuit theory, with the Floquet harmonics, it allows to obtain the expressions of the scattering parameters of each structure and also of the composed structure of two or more FSS. In this work, numeric results are presented for the transmission characteristics. Comparisons are made with experimental results and simulated results using the commercial software Ansoft Designer? v3. Finally, some suggestions are presented for future works on this subject / Este trabalho apresenta uma an?lise te?rica e num?rica do cascateamento de superf?cies seletivas de frequ?ncia, que usa patches retangulares e fractais de Koch triangular como elementos. Para isto, s?o utilizadas duas t?cnicas de cascateamento, visando ? determina??o das caracter?sticas de transmiss?o e de reflex?o. Superf?cies seletivas de frequ?ncia abrangem uma grande ?rea das Telecomunica??es e t?m sido largamente utilizadas devido a seu baixo custo, peso reduzido e possibilidade de se integrar com outros circuitos de microondas. Elas s?o especialmente importantes em diversas aplica??es, como avi?es, sistemas de antenas, radomes, foguetes, m?sseis, etc. Aplica??es de FSS em faixas de freq??ncia elevadas t?m sido investigadas, assim como aplica??es destas estruturas em cascata ou multicamadas, e FSS ativas. Especificamente, as an?lises usam a teoria de circuitos de microondas, em conjunto com os harm?nicos de Floquet, permite a obten??o das express?es dos par?metros de espalhamento de cada estrutura e tamb?m da estrutura composta por duas ou mais FSS. Nesse trabalho, s?o apresentados resultados num?ricos para as caracter?sticas de transmiss?o. S?o feitas compara??es com resultados experimentais e tamb?m com resultados simulados utilizando o software comercial Ansoft Designer? v3. S?o apresentadas, ainda, sugest?es de continuidade do trabalho

This dissertation presents a self-contained study of periodically-driven quantum systems. Following a brief introduction to Floquet theory, we introduce the inverse-frequency expansion, variants of which include the Floquet-Magnus, van Vleck, and Brillouin-Wigner expansions. We reveal that the convergence properties of these expansions depend strongly on the rotating frame chosen, and relate the former to the existence of Floquet resonances in the quasienergy spectrum. The theoretical design and experimental realisation (`engineering') of novel Floquet Hamiltonians is discussed introducing three universal high-frequency limits for systems comprising single-particle and many-body linear and nonlinear models. The celebrated Schrieffer-Wolff transformation for strongly-correlated quantum systems is generalised to periodically-driven systems, and a systematic approach to calculate higher-order corrections to the Rotating Wave Approximation is presented. Next, we develop Floquet adiabatic perturbation theory from first principles, and discuss extensively the adiabatic state preparation and the corresponding leading-order non-adiabatic corrections. Special emphasis is thereby put on geometrical and topological objects, such as the Floquet Berry curvature and the Floquet Chern number obtained within linear response in the presence of the drive. Last, pre-thermalisation and thermalisation in closed, clean periodically-driven quantum systems are studied in detail, with the focus put on the crucial role of Floquet many-body resonances for energy absorption.

[pt] Excitação paramétrica se dá a partir de coeficientes variantes no tempo na dinâmica de um sistema. Este tipo de excitação tem sido um amplo tema de pesquisa desde os campos da mecânica e eletrônica até dinâmica de fluidos. Ela aparece em problemas envolvendo sistemas dinâmicos, por exemplo, como uma forma de controle de vibrações em sistemas auto excitados, tornando este assunto digno de mais investigações. Abordando estabilidade no sentido de Lyapunov, esta dissertação fornece uma base didática de estabilidade desde conceitos básicos, como pontos de equilíbrio e planos de fase, até conceitos mais avançados, como excitação paramétrica e teoria de Floquet. Os objetos de estudo aqui são sistemas lineares com parâmetros periódicos no tempo, o que permite usar a teoria de Floquet para fazer afirmações a respeito da estabilidade da solução trivial do sistema. Vários exemplos são discutidos fazendo uso de um procedimento numérico desenvolvido para construir mapas de estabilidade e planos de fase. Os exemplos apresentados abrangem sistemas mecânicos, eletromagnéticos e eletromecânicos. Fazendo uso de mapas de estabilidade, diversas características de análise de estabilidade são abordadas. Duas estratégias diferentes para avaliar a estabilidade da solução trivial são comparadas: multiplicadores de Floquet e valor máximo dos expoentes característicos de Lyapunov. / [en] Parametric excitation is a type of excitation that arises from timevarying coefficients in a system s dynamics. More specifically, this dissertation deals with time-periodic coefficients. This type of excitation has been an extended topic of research from the fields of mechanics and electronics to fluid dynamics. It appears in problems involving dynamical systems, for example, as a way of controlling vibrations in self-excited systems, making this subject worthy of more investigations. By approaching stability in the sense of Lyapunov, this dissertation provides a didactic stability background from basic concepts, such as equilibrium points and phase diagrams, to more advanced ones, like parametric excitation and Floquet theory. The objects of study here are linear systems with time-periodic parameters. Floquet theory is used to make stability statements about the system s trivial solution. Several examples are discussed by making use of a developed numerical procedure to construct stability maps and phase diagrams. The examples presented herein encompass mechanical, electromagnetic and electromechanical systems. By making use of stability maps, several features that can be discussed in stability analysis are approached. Two different strategies to evaluate the stability of the trivial solution are compared: Floquet multipliers and the maximum value of Lyapunov characteristic exponents.

For simulations of highly complex geometries, frequently encountered in many fields of science and engineering, the process of generating a high-quality, body-fitted grid is very complicated and time-intensive. Thus, one of the principal goals of contemporary CFD is the development of numerical algorithms, which are able to deliver computationally efficient, and highly accurate solutions for a wide range of applications involving multi-physics problems, e.g. Fluid Structure Interaction (FSI). Immersed interface/boundary methods provide considerable advantages over conventional approaches, especially for flow problems containing moving boundaries.In the present work, a novel, robust, highly-accurate, Immersed Interface Method (IIM) is developed, which is based on a local Taylor-series expansion at irregular grid points enforcing numerical stability through a local stability condition. Various immersed methods have been developed in the past; however, these methods only considered the order of the local truncation error. The numerical stability of these schemes was demonstrated (in a global sense) by considering a number of different test-problems. None of these schemes used a concrete local stability condition to derive the irregular stencil coefficients. This work will demonstrate that the local stability constraint is valid as long as the DFL-number does not reach a limiting value. The IIM integrated into a newly developed Incompressible Navier-Stokes (INS) solver is used herein to simulate fully coupled FSI problems. The extension of the novel IIM to a higher-order method, the compressible Navier-Stokes equations and the Maxwell's equations demonstrate the great potential of the novel IIM.In the second part of this dissertation, the newly developed INS solver is employed to study the flow of a stalled airfoil and steady/unsteady stenotic flows. In this context, a new biglobal stability analysis approach based on solving an Initial Value Problem (IVP), instead of the traditionally used EigenValue Problem (EVP), is presented. It is demonstrated that this approach based on an IVP is computationally less expensive compared to EVP approaches while still capturing the relevant physics.

This thesis is concerned with a variety of topics grouped together under the general theme of periodically driven atomic systems. Periodic driving is ubiquitous in most techniques used in atomic physics, be it laser cooling, ion trapping or AC magnetic fields. An in-depth understanding of the behaviour of such systems can be provided through Floquet theory which will develop as a central theme in the following chapters. The thesis is divided in two parts: neutral atoms, and ions and biomolecules. In the first part I discuss a new ⁴¹K-⁸⁷Rb mixture experiment, built during the first year of my DPhil. This species combination has some very broad and low-loss interspecies Feshbach resonances that are instrumental for carrying out the experiments discussed in the first chapter. Unfortunately, the mixture experiment had to be put aside and our attention was shifted to Time-Averaged Adiabatic Potentials (TAAPs) and how these can be extended using multiple Radio-Frequency (RF) fields. This technique opens up the way for precise interferometric measurements. Lastly, the peculiar behaviour of Modulation Transfer Spectroscopy (MTS) of ³⁹K is investigated and a linearising transformation for four-wave mixing processes is presented. In the second part we turn our attention to charged ions and biomolecules and the techniques of ion trapping. We propose a novel technique for co-trapping charged particles with vastly different mass-to-charge ratios and thoroughly explore its consequences. The behaviour of the trap and the stability of equations with periodic coefficients in general is studied using Floquet theory. The normal modes and symmetries of the system also need to be considered in relation to the effectiveness of the sympathetic cooling of the ions. Small systems were simulated using a Molecular Dynamics (MD) approach in order to capture the effect of micromotion and other heating processes.

Este trabalho descreve a análise e simulação do fenômeno de resonância solo em helicópteros com rotores de duas pás. Este problema pode ser resolvido por uma análise de autovalores, no sistema girante, considerando-se propriedades isotrópicas do suporte e, pela aplicação da teoria de Floquet, no sistema não-girante, considerando-se propriedades anisotrópicas do suporte. Os resultados obtidos, via simulação, incluem os diagramas para as variações da freqüência e do amortecimento modais, em função da freqüência angular de rotação do rotor, com ênfase na região de instabilidade, e sua comparação com os diagramas clássicos apresentados por Coleman e Feingold para assegurar a validade, do ponto de vista teórico, do modelamento adotado.

This thesis covers my work in the field of closed, repeatedly driven, Hamiltonian systems. These systems do not exchange particles with the surrounding environment and their time-evolution is described by Hamilton's equations of motion (in the classical framework) or the Schroedinger equation (in the quantum framework). Their interaction with the environment is encoded into the time-dependence of the system's Hamiltonian. Chapter 1 is an "Overview" in which the status of the field, my contributions and future prospective are outlined. Chapters 2 to 4 provide the theoretical background which is used in Chapters 5 to 7 to derive some original results. These results show that in Hamiltonian systems, after many driving events, universal properties emerge. In particular, using the framework of the linear Boltzmann equation, I have studied the dynamics of a mobile, light impurity in a gas of heavy particles. The impurity's kinetic energy increases and, in the long time limit, approaches a non-thermal asymptotic distribution. The significance of this work is to show explicitly the emergence of a non-thermal distribution in a closed, driven system. Moreover, using the work-fluctuation theorems, I have studied the character of the energy distribution of a generic isolated system driven according a generic protocol. Both thermal and non-thermal distributions can be realized for the same system by changing the characteristics of the driving protocol. These two different regimes are separated by a dynamical phase transition. Finally, I have used the Floquet Theory and the Magnus Expansion to analyze the behavior of a generic interacting system which is driven periodically in time. For fast driving the system is unable to absorb energy and remains localized in the low energy part of the Hilbert space while for slow driving the system absorbs energy and, in the long time limit, it is delocalized in the entire Hilbert space. These two qualitatively different behaviors are separated by a many-body localization transition which is related to the break down of the Magnus expansion at the critical value of the driving frequency.