Non-perturbative Renormalization Group Approach to Some Out-of-Equilibrium Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Non-perturbative Renormalization Group Approach to Some Out-of-Equilibrium Systems write by Malo Tarpin. This book was released on 2020-03-19. Non-perturbative Renormalization Group Approach to Some Out-of-Equilibrium Systems available in PDF, EPUB and Kindle. This thesis presents the application of non-perturbative, or functional, renormalization group to study the physics of critical stationary states in systems out-of-equilibrium. Two different systems are thereby studied. The first system is the diffusive epidemic process, a stochastic process which models the propagation of an epidemic within a population. This model exhibits a phase transition peculiar to out-of-equilibrium, between a stationary state where the epidemic is extinct and one where it survives. The present study helps to clarify subtle issues about the underlying symmetries of this process and the possible universality classes of its phase transition. The second system is fully developed homogeneous isotropic and incompressible turbulence. The stationary state of this driven-dissipative system shows an energy cascade whose phenomenology is complex, with partial scale-invariance, intertwined with what is called intermittency. In this work, analytical expressions for the space-time dependence of multi-point correlation functions of the turbulent state in 2- and 3-D are derived. This result is noteworthy in that it does not rely on phenomenological input except from the Navier-Stokes equation and that it becomes exact in the physically relevant limit of large wave-numbers. The obtained correlation functions show how scale invariance is broken in a subtle way, related to intermittency corrections.
Non-perturbative Renormalisation Group Approach to Some Out of Equilibrium Systems
Non-perturbative Renormalisation Group Approach to Some Out of Equilibrium Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Non-perturbative Renormalisation Group Approach to Some Out of Equilibrium Systems write by Malo Tarpin. This book was released on 2018. Non-perturbative Renormalisation Group Approach to Some Out of Equilibrium Systems available in PDF, EPUB and Kindle. This thesis focus on the study of two critical systems out of equilibrium using the tools of the non-perturbative renormalization group (NPRG).The first system is the diffusive epidemic process. This stochastic process models the propagation of an epidemic within a population, where the infected individuals recover without immunization. This model exhibit a phase transition when the epidemic goes extinct. The study consisted in applied an approximate form of the NPRG named the modified local potential approximation to this transition. It led us to take a new look at the standard lore for this model, obtained through a perturbative renormalization group analysis. In particular, whether the phase transition belongs to the universality class of the directed percolation with a conserved quantity is called into question.The second system is fully developed homogeneous isotropic turbulence, as described by the Navier-Stokes equation. The stationary state of this driven-dissipative system shows a energy cascade whose phenomenology is typical of scale-invariant systems. A more in depth examination disclose that scale invariance is broken in a subtle way. This is the origin of intermittence phenomena in turbulence. We used a large wave-number expansion of the NPRG to study the temporal dependency of correlation functions in this system and whether the direct cascade in bidimensional turbulence could develop intermittency.
Non Perturbative Renormalization Group
Non Perturbative Renormalization Group - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Non Perturbative Renormalization Group write by Federico Benitez. This book was released on 2013. Non Perturbative Renormalization Group available in PDF, EPUB and Kindle. Many of the most important open problems in statistical mechanics are related with systems out of thermal equilibrium. In this work we use field theory methods to study some of these systems. To do so, we first introduce a field theory representation for the systems of interest, as well as the specific formalism to be used throughout, the so-called non perturbative renormalization group (NPRG). This formalism has emerged in the last years as a very efficient way to deal with strongly correlated systems, and has been applied with success to problems both in and out of equilibrium. Before treating the actual systems of interest, we develop some new tools and methods within the NPRG context, and test them in a simple scalar field theory, belonging to the Ising universality class. We are able to obtain results for the momentum-dependent scaling function of the d=3 Ising model, without having to fix any free parameter. Also, in order to tackle in an efficient way the physics of out of equilibrium systems, we study in detail some formal aspects of their passage to a field theory representation, as well as the equivalences between different possible ways to perform this passage. After these preliminaries, we concentrate in out of equilibrium active-to-absorbing phase transitions in reaction-diffusion systems, and in particular in the subclass known as branching and annihilating random walks (BARW). Among other results, we use the NPRG to find an exact solution to any vertex in a simple system, known as pure annihilation. With this, we analyze some properties of BARW at low branching rates, by means of an expansion in the branching rate around pure annihilation. This perturbative expansion, which is performed around a nontrivial model, allows us to find some striking exact results for some of the most important universality classes in these systems.
Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems
Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems write by Taiki Haga. This book was released on 2019-01-24. Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems available in PDF, EPUB and Kindle. This book investigates phase transitions and critical phenomena in disordered systems driven out of equilibrium. First, the author derives a dimensional reduction property that relates the long-distance physics of driven disordered systems to that of lower dimensional pure systems. By combining this property with a modern renormalization group technique, the critical behavior of random field spin models driven at a uniform velocity is subsequently investigated. The highlight of this book is that the driven random field XY model is shown to exhibit the Kosterlitz–Thouless transition in three dimensions. This is the first example of topological phase transitions in which the competition between quenched disorder and nonequilibrium driving plays a crucial role. The book also includes a pedagogical review of a renormalizaion group technique for disordered systems.
Introduction to a Renormalisation Group Method
Introduction to a Renormalisation Group Method - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to a Renormalisation Group Method write by Roland Bauerschmidt. This book was released on 2019-10-17. Introduction to a Renormalisation Group Method available in PDF, EPUB and Kindle. This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.
