Non Perturbative Renormalisation Group Approach To Some Out Of Equilibrium Systems
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Non Perturbative Renormalization Group Approach To Some Out Of Equilibrium Systems
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Author : Malo Tarpin
language : en
Publisher: Springer Nature
Release Date : 2020-03-19
Non Perturbative Renormalization Group Approach To Some Out Of Equilibrium Systems written by Malo Tarpin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-19 with Science categories.
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
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Author : Malo Tarpin
language : en
Publisher:
Release Date : 2018
Non Perturbative Renormalisation Group Approach To Some Out Of Equilibrium Systems written by Malo Tarpin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
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.
Renormalization Group Analysis Of Nonequilibrium Phase Transitions In Driven Disordered Systems
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Author : Taiki Haga
language : en
Publisher: Springer
Release Date : 2019-01-24
Renormalization Group Analysis Of Nonequilibrium Phase Transitions In Driven Disordered Systems written by Taiki Haga and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-24 with Science categories.
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.
Non Perturbative Renormalization
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Author : Vieri Mastropietro
language : en
Publisher: World Scientific
Release Date : 2008
Non Perturbative Renormalization written by Vieri Mastropietro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providing a mathematical construction of models at low dimensions and discussing the removal of the ultraviolet and infrared cut-off, the verification of the axioms and the validity of Ward Identities with the relative anomalies. The second part is devoted to lattice 2D Statistical Physics, analyzing in particular the theory of universality in perturbed Ising models and the computation of the non-universal critical indices in Vertex or Ashkin-Teller models. Finally the third part is devoted to the analysis of complex quantum fluids showing Luttinger of Fermi liquid behavior, like the 1D or 2D Hubbard model.
Introduction To The Functional Renormalization Group
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Author : Peter Kopietz
language : en
Publisher: Springer
Release Date : 2010-04-22
Introduction To The Functional Renormalization Group written by Peter Kopietz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-22 with Science categories.
The renormalization group (RG) has nowadays achieved the status of a meta-theory, which is a theory about theories. The theory of the RG consists of a set of concepts and methods which can be used to understand phenomena in many different ?elds of physics, ranging from quantum ?eld theory over classical statistical mechanics to nonequilibrium phenomena. RG methods are particularly useful to understand phenomena where ?uctuations involving many different length or time scales lead to the emergence of new collective behavior in complex many-body systems. In view of the diversity of ?elds where RG methods have been successfully applied, it is not surprising that a variety of apparently different implementations of the RG idea have been proposed. Unfortunately, this makes it somewhat dif?cult for beginners to learn this technique. For example, the ?eld-theoretical formulation of the RG idea looks at the ?rst sight rather different from the RG approach pioneered by Wilson, the latter being based on the concept of the effective action which is ite- tively calculated by successive elimination of the high-energy degrees of freedom. Moreover, the Wilsonian RG idea has been implemented in many different ways, depending on the particular problem at hand, and there seems to be no canonical way of setting up the RG procedure for a given problem.
Scaling And Renormalization In Statistical Physics
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Author : John Cardy
language : en
Publisher: Cambridge University Press
Release Date : 1996-04-26
Scaling And Renormalization In Statistical Physics written by John Cardy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-04-26 with Science categories.
This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. It begins with a brief review of phase transitions in simple systems, then goes on to introduce the core ideas of the renormalisation group.
Quantum Gases
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Author : Nick Proukakis
language : en
Publisher: World Scientific
Release Date : 2013
Quantum Gases written by Nick Proukakis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Science categories.
This volume provides a broad overview of the principal theoretical techniques applied to non-equilibrium and finite temperature quantum gases. Covering Bose-Einstein condensates, degenerate Fermi gases, and the more recently realised exciton-polariton condensates, it fills a gap by linking between different methods with origins in condensed matter physics, quantum field theory, quantum optics, atomic physics, and statistical mechanics.
Lectures On Phase Transitions And The Renormalization Group
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Author : Nigel Goldenfeld
language : en
Publisher: CRC Press
Release Date : 2018-03-08
Lectures On Phase Transitions And The Renormalization Group written by Nigel Goldenfeld and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-08 with Science categories.
Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.
Order Disorder And Criticality Advanced Problems Of Phase Transition Theory Volume 6
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Author : Yurij Holovatch
language : en
Publisher: World Scientific
Release Date : 2020-06-22
Order Disorder And Criticality Advanced Problems Of Phase Transition Theory Volume 6 written by Yurij Holovatch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-22 with Science categories.
This book is the sixth volume of reviews on advanced problems of phase transitions and critical phenomena, with the first five volumes appearing in 2004, 2007, 2012, 2015, and 2018. It aims to provide an overview of those aspects of criticality and related topics that have attracted much attention due to the recent contributions. The six chapters discuss criticality of complex systems, where the new, emergent properties appear via collective behaviour of simple elements. Since all complex systems involve cooperative behaviour between many interconnected components, the field of phase transitions and critical phenomena provides a very natural conceptual and methodological framework for their study.As for the previous volumes, this book is based on the review lectures that were given in Lviv (Ukraine) at the 'Ising lectures' — a traditional annual workshop on phase transitions and critical phenomena which aims to bring together scientists working in the field of phase transitions with university students and those who are interested in the topic.The level of presentation makes the book readable both for professionals and the students in the field. On a larger scale, the book may contribute to promoting and deepening studies of phase transitions and critical phenomena.
Condensed Matter Field Theory
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Author : Alexander Altland
language : en
Publisher: Cambridge University Press
Release Date : 2010-03-11
Condensed Matter Field Theory written by Alexander Altland and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-11 with Science categories.
This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.