Download or read book Canonical Gibbs Measures written by H. O. Georgii and published by . This book was released on 2014-01-15 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Canonical Gibbs Measures written by H. O. Georgii and published by Springer. This book was released on 2006-11-15 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Canonical Gibbs Measures written by Hans-Otto Georgii and published by . This book was released on 1979 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Equilibrium and Non equilibrium Aspects of Gibbs Measures written by Younghak Kwon and published by . This book was released on 2021 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a one-dimensional lattice system of unbounded, real-valued spins with arbitrarystrong, quadratic, finite-range interaction. The first area of interest concerns the equivalence of the grand canonical ensemble and the canonical ensemble: on the level of thermodynamic functions, on the level of observables, and on the level of correlations. More precisely, in the thermodynamic limit (size N of the system goes to infinity), we show that the free energy, expectation of intensive observable, and correlation of two intensive functions are the same for the grand canonical ensemble and canonical ensemble. The second area of interest concerns the decay of correlations and uniqueness of infinite-volume Gibbs measure of the canonical ensemble. It is shown that the correlations of the canonical ensemble decay exponentially plus a volume correction term. As a consequence, we verify a conjecture that the infinite-volume Gibbs measure of the canonical ensemble is unique on the one-dimensional lattice, extending results that are known for the case of weak interaction. The third area of interest concerns the logarithmic Sobolev inequality (LSI). It is shown that the canonical ensemble satisfies a uniform LSI. The LSI constant is uniform in the boundary data, the external field and scales optimally in the system size. We deduce the LSI by combining two different methods, the two-scale approach and the Zegarlinski method. The last area of interest concerns the hydrodynamic limit. We deduce the hydrodynamic limit of Kawasaki dynamics. The main ingredients are uniform LSI and decay of correlations for the canonical ensemble. The proof is based on a method invented by Grunewald, Otto, Villani and Westdickenberg.
Download or read book Gibbs Measures and Phase Transitions written by Hans-Otto Georgii and published by Walter de Gruyter. This book was released on 2011-05-31 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Fredos Papangelou, Zentralblatt MATH The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.
Download or read book E Government ICT Professionalism and Competences Service Science written by Antonino Mazzeo and published by Springer. This book was released on 2008-07-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of Industry Oriented Conferences held at IFIP 20th World Computer Congress in September 2008. The IFIP series publishes state-of-the-art results in the sciences and technologies of information and communication. The scope of the series includes: foundations of computer science; software theory and practice; education; computer applications in technology; communication systems; systems modeling and optimization; information systems; computers and society; computer systems technology; security and protection in information processing systems; artificial intelligence; and human-computer interaction. Proceedings and post-proceedings of refereed international conferences in computer science and interdisciplinary fields are featured. These results often precede journal publication and represent the most current research. The principal aim of the IFIP series is to encourage education and the dissemination and exchange of information about all aspects of computing.
Download or read book Gibbs Measures On Cayley Trees written by Utkir A Rozikov and published by World Scientific. This book was released on 2013-07-11 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to present systematically all known mathematical results on Gibbs measures on Cayley trees (Bethe lattices).The Gibbs measure is a probability measure, which has been an important object in many problems of probability theory and statistical mechanics. It is the measure associated with the Hamiltonian of a physical system (a model) and generalizes the notion of a canonical ensemble. More importantly, when the Hamiltonian can be written as a sum of parts, the Gibbs measure has the Markov property (a certain kind of statistical independence), thus leading to its widespread appearance in many problems outside of physics such as biology, Hopfield networks, Markov networks, and Markov logic networks. Moreover, the Gibbs measure is the unique measure that maximizes the entropy for a given expected energy.The method used for the description of Gibbs measures on Cayley trees is the method of Markov random field theory and recurrent equations of this theory, but the modern theory of Gibbs measures on trees uses new tools such as group theory, information flows on trees, node-weighted random walks, contour methods on trees, and nonlinear analysis. This book discusses all the mentioned methods, which were developed recently.
Download or read book Lectures on Mathematical Statistical Mechanics written by Stefan Adams and published by . This book was released on 2006 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Gibbs Measures and Phase Transitions written by Hans-Otto Georgii and published by Walter de Gruyter. This book was released on 2011 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a review of the first edition: "This book [...] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. [...] It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert." (F. Papangelou
Download or read book E Government ICT Professionalism and Competences Service Science written by Antonino Mazzeo and published by Springer. This book was released on 2008-07-08 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of Industry Oriented Conferences held at IFIP 20th World Computer Congress in September 2008. The IFIP series publishes state-of-the-art results in the sciences and technologies of information and communication. The scope of the series includes: foundations of computer science; software theory and practice; education; computer applications in technology; communication systems; systems modeling and optimization; information systems; computers and society; computer systems technology; security and protection in information processing systems; artificial intelligence; and human-computer interaction. Proceedings and post-proceedings of refereed international conferences in computer science and interdisciplinary fields are featured. These results often precede journal publication and represent the most current research. The principal aim of the IFIP series is to encourage education and the dissemination and exchange of information about all aspects of computing.
Download or read book Gibbs Measures In Biology And Physics The Potts Model written by Utkir A Rozikov and published by World Scientific. This book was released on 2022-07-28 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.
Download or read book Statistical Mechanics of Lattice Systems written by Sacha Friedli and published by Cambridge University Press. This book was released on 2017-11-23 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Download or read book Infinite System of Brownian Balls Equilibrium Measures are Canonical Gibbs written by Sylvie Roelly and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Processes on a Lattice and Gibbs Measures written by Bernard Prum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many domains one encounters "systems" of interacting elements, elements that interact more forcefully the closer they may be. The historical example upon which the theory offered in this book is based is that of magnetization as it is described by the Ising model. At the vertices of a regular lattice of sites, atoms "choos e" an orientation under the influence of the orientations of the neighboring atoms. But other examples are known, in physics (the theories of gasses, fluids, .. J, in biology (cells are increasingly likely to become malignant when their neighboring cells are malignant), or in medecine (the spread of contagious deseases, geogenetics, .. .), even in the social sciences (spread of behavioral traits within a population). Beyond the spacial aspect that is related to the idea of "neighboring" sites, the models for all these phenomena exhibit three common features: - The unavoidable ignorance about the totality of the phenomenon that is being studied and the presence of a great number of often unsuspected factors that are always unquantified lead inevitably to stochastic models. The concept of accident is very often inherent to the very nature of the phenomena considered, so, to justify this procedure, one has recourse to the physicist's principle of indeterminacy, or, for example, to the factor of chance in the Mendelian genetics of phenotypes.
Download or read book Feynman Kac Type Formulae and Gibbs Measures written by József Lörinczi and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-01-20 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second updated and extended edition of the successful book on Feynman-Kac theory. It offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. The first volume concentrates on Feynman-Kac-type formulae and Gibbs measures
Download or read book Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics written by Marco Pettini and published by Springer Science & Business Media. This book was released on 2007-06-14 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The book contains numerous illustrations throughout and it will interest both mathematicians and physicists.
Download or read book Mathematical Results in Quantum Mechanics written by Michael Demuth and published by Springer Science & Business Media. This book was released on 1994 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the International Conference on Mathematical Results in Quantum Mechanics held in Blossin, Germany, May 17-21, 1993. Its purpose is to draw attention to the recent developments in quantum mechanics and related mathematical problems. The book is addressed to the wide audience of mathematicians and physicists interested in contemporary quantum physics and associated mathematical problems. The reader will find sections not only on traditional subjects such as Schrödinger and Dirac operators and generalized Schrödinger generators, but also on stochastic spectral analysis, many-body problems and statistical physics, chaos, and operator theory and its applications. Contributors: Schrödinger and Dirac operators: M.Sh. Birman, V. Grecchi, R. Hempel, M. Hoffmann-Ostenhof, Y. Saito, G. Stolz, M. Znojil • Generalized Schrödinger operators: J.-P. Antoine, J.F. Brasche, P. Duclos, R. Hempel, M. Klein, P. Stovicek • Stochastic spectral analysis: M. Demuth, V.A. Liskevich, E.M. Ouhabaz, P. Stollmann • Many-body problems and statistical physics: M. Fannes, R. Gielerak, M. Hübner, A.M. Khorunzhy, H. Lange, N. Macris, Yu.A. Petrina, K.B. Sinha, A. Verbeure • Chaos: J. Dittrich, P. Seba, K. Zyczkowski • Operator theory and its application: F. Bentosela, V. Buslaev, A.N. Kochubei, A.Yu. Konstantinov, V. Koshmanenko, H. Neidhardt, G. Nenciu, D. Robert
