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Author | : Geza Odor |
Publisher | : World Scientific |
Total Pages | : 297 |
Release | : 2008-05-08 |
Genre | : Science |
ISBN | : 9814471305 |
Download Universality In Nonequilibrium Lattice Systems: Theoretical Foundations Book in PDF, ePub and Kindle
Universal scaling behavior is an attractive feature in statistical physics because a wide range of models can be classified purely in terms of their collective behavior due to a diverging correlation length. This book provides a comprehensive overview of dynamical universality classes occurring in nonequilibrium systems defined on regular lattices. The factors determining these diverse universality classes have yet to be fully understood, but the book attempts to summarize our present knowledge, taking them into account systematically.The book helps the reader to navigate in the zoo of basic models and classes that were investigated in the past decades, using field theoretical formalism and topological diagrams of phase spaces. Based on a review in Rev. Mod. Phys. by the author, it incorporates surface growth classes, classes of spin models, percolation and multi-component system classes as well as damage spreading transitions. (The success of that review can be quantified by the more than one hundred independent citations of that paper since 2004.)The extensions in this book include new topics like local scale invariance, tricritical points, phase space topologies, nonperturbative renormalization group results and disordered systems that are discussed in more detail. This book also aims to be more pedagogical, providing more background and derivation of results. Topological phase space diagrams introduced by Kamenev (Physical Review E 2006) very recently are used as a guide for one-component, reaction-diffusion systems.
Author | : Gza ?dor |
Publisher | : World Scientific |
Total Pages | : 297 |
Release | : 2008 |
Genre | : Science |
ISBN | : 981281227X |
Download Universality in Nonequilibrium Lattice Systems Book in PDF, ePub and Kindle
"Universal scaling behavior is an attractive feature in statistical physics because a wide range of models can be classified purely in terms of their collective behavior due to a diverging correlation length. This book provides a comprehensive overview of dynamical universality classes occurring in nonequilibrium systems defined on regular lattices. The factors determining these diverse universality classes have yet to be fully understood, but the book attempts to summarize our present knowledge, taking them into account systematically." "The book helps the reader to navigate in the zoo of basic models and classes that were investigated in the past decades, using field theoretical formalism and topological diagrams of phase spaces. The extensions in this book include new topics like local scale invariance, tricritical points, phase space topologies, nonperturbative renormalization group results and disordered systems that are discussed in more detail. This book also aims to be more pedagogical, providing more background and derivation of results."--BOOK JACKET.
Author | : Man Young Lee |
Publisher | : |
Total Pages | : 0 |
Release | : 2011 |
Genre | : Nonequilibrium statistical mechanics |
ISBN | : |
Download Absorbing State Transitions in Clean and Disordered Lattice Models Book in PDF, ePub and Kindle
"Nonequilibrium systems can undergo continuous phase transitions between different steady states. These transitions are characterized by collective fluctuations over large distances and long times similar to the behavior of equilibrium critical points. They also can be divided into different universality classes according to their critical behavior. This dissertation considers two types of nonequilibrium transitions. First study concerns absorbing state transitions on a randomly diluted lattice. Second study deals with nonequilibrium models with several absorbing states. We investigate two specific nonequilibrium lattice models, i.e., the contact process and the generalized contact process by means of both theoretical and computational approaches. In section 1, we introduce the basic arguments and theories to support our investigations for both problems. In sections 2 and 3, we investigate nonequilibrium phase transitions of the contact process and the generalized contact process on a percolating lattice, focusing on the transition across the lattice percolation threshold. In this study, we show that the interplay between geometric criticality due to percolation and dynamical fluctuations of the nonequilibrium system leads to a new universality class. The critical point is characterized by ultra-slow activated dynamical scaling and accompanied by strong Griffiths singularities. We support our theory by extensive Monte-Carlo simulations. In sections 4 and 5, we investigate the generalized contact process on one and two-dimensional lattices. We treat the creation rate of active sites between inactive domains as an independent parameter. It turns out that this model has an unusual phase diagram with two different nonequilibrium phase transitions. The special point separating them shares some characteristics with a multicritical point. For one dimension, a small boundary rate takes the system from the directed percolation universality class to the parity-conserved class. For two dimensions, the critical behavior on the generic transition line is of mean-field type with logarithmic corrections suggesting that the two-dimensional generalized contact process is in the generalized voter universality class"--Abstract, leaf iv
Author | : Alex Kamenev |
Publisher | : Cambridge University Press |
Total Pages | : 514 |
Release | : 2023-01-05 |
Genre | : Science |
ISBN | : 1108846440 |
Download Field Theory of Non-Equilibrium Systems Book in PDF, ePub and Kindle
The physics of non-equilibrium many-body systems is a rapidly expanding area of theoretical physics. Traditionally employed in laser physics and superconducting kinetics, these techniques have more recently found applications in the dynamics of cold atomic gases, mesoscopic and nano-mechanical systems, and quantum computation. This book provides a detailed presentation of modern non-equilibrium field-theoretical methods, applied to examples ranging from biophysics to the kinetics of superfluids and superconductors. A highly pedagogical and self-contained approach is adopted within the text, making it ideal as a reference for graduate students and researchers in condensed matter physics. In this Second Edition, the text has been substantially updated to include recent developments in the field such as driven-dissipative quantum systems, kinetics of fermions with Berry curvature, and Floquet kinetics of periodically driven systems, among many other important new topics. Problems have been added throughout, structured as compact guided research projects that encourage independent exploration.
Author | : Malte Henkel |
Publisher | : Springer Science & Business Media |
Total Pages | : 385 |
Release | : 2008-11-27 |
Genre | : Science |
ISBN | : 1402087659 |
Download Non-Equilibrium Phase Transitions Book in PDF, ePub and Kindle
This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.
Author | : Horatiu-Zeno Simon |
Publisher | : |
Total Pages | : 77 |
Release | : 1996 |
Genre | : |
ISBN | : |
Download Universality in One-dimensional Nonequilibrium Systems with Boundaries Book in PDF, ePub and Kindle
Author | : Joaquin Marro |
Publisher | : Cambridge University Press |
Total Pages | : 344 |
Release | : 2005-09-08 |
Genre | : Science |
ISBN | : 9780521019460 |
Download Nonequilibrium Phase Transitions in Lattice Models Book in PDF, ePub and Kindle
This book provides an introduction to nonequilibrium statistical physics via lattice models. Beginning with an introduction to the basic driven lattice gas, the early chapters discuss the relevance of this lattice model to certain natural phenomena, examining simulation results in detail. Later chapters discuss absorbing-state transitions, and examine a variety of systems subject to dynamic disorder. The book discusses the effects of multiparticle rules, nonunique absorbing-states and conservation laws, as well as the use of methods such as mean-field theory, Monte Carlo simulation and the concept of universality. It also includes detailed references and examples using simple respresentations of nature to describe real systems.
Author | : Malo Tarpin |
Publisher | : Springer Nature |
Total Pages | : 217 |
Release | : 2020-03-19 |
Genre | : Science |
ISBN | : 3030398714 |
Download Non-perturbative Renormalization Group Approach to Some Out-of-Equilibrium Systems Book 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.
Author | : François P. Landes |
Publisher | : Springer |
Total Pages | : 217 |
Release | : 2015-07-09 |
Genre | : Science |
ISBN | : 3319200224 |
Download Viscoelastic Interfaces Driven in Disordered Media Book in PDF, ePub and Kindle
This book offers an in-depth study of two well-known models of “avalanche” dynamics, modified minimally by the inclusion of relaxation. Many complex systems respond to continuous inputs of energy by accumulation of stress over time, interrupted by sudden energy releases called avalanches. The first model studied is the viscoelastic interface driven over disorder, which is shown to display the fundamental features of friction. In the mean-field limit, the friction force derived semi-analytically is compatible with laboratory experiments (displaying both velocity weakening and contact aging). In two dimensions, large-scale numerical simulations are in good agreement with the basic features of real earthquakes (Gutenberg-Richter Law, aftershock migration). The second model is a non-Markovian variant of Directed Percolation, in which we observe that the universality class is only partly modified by relaxation, a promising finding with respect to our first model.
Author | : Shun Maegochi |
Publisher | : Springer Nature |
Total Pages | : 109 |
Release | : |
Genre | : |
ISBN | : 9819729874 |
Download Nonequilibrium Phase Transitions in Driven Vortex Matter Book in PDF, ePub and Kindle