Download or read book Supermathematics and its Applications in Statistical Physics written by Franz Wegner and published by Springer. This book was released on 2016-03-25 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical systems, as well as related topics in statistical physics. Based on many courses and seminars held by the author, one of the pioneers in this field, the reader is given a systematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables is presented in part I. The mathematics of these variables is applied to a random matrix model, path integrals for fermions, dimer models and the Ising model in two dimensions. Supermathematics - the use of commuting and anticommuting variables on an equal footing - is the subject of part II. The properties of supervectors and supermatrices, which contain both commuting and Grassmann components, are treated in great detail, including the derivation of integral theorems. In part III, supersymmetric physical models are considered. While supersymmetry was first introduced in elementary particle physics as exact symmetry between bosons and fermions, the formal introduction of anticommuting spacetime components, can be extended to problems of statistical physics, and, since it connects states with equal energies, has also found its way into quantum mechanics. Several models are considered in the applications, after which the representation of the random matrix model by the nonlinear sigma-model, the determination of the density of states and the level correlation are derived. Eventually, the mobility edge behavior is discussed and a short account of the ten symmetry classes of disorder, two-dimensional disordered models, and superbosonization is given.
Download or read book Methods of Contemporary Mathematical Statistical Physics written by Marek Biskup and published by Springer Science & Business Media. This book was released on 2009-03-25 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools. An introductory chapter on lattice spin models is useful as a background for other lectures of the collection. The topics include new results on phase transitions for gradient lattice models (with introduction to the techniques of the reflection positivity), stochastic geometry reformulation of classical and quantum Ising models, the localization/delocalization transition for directed polymers. A general rigorous framework for theory of metastability is presented and particular applications in the context of Glauber and Kawasaki dynamics of lattice models are discussed. A pedagogical account of several recently discussed topics in nonequilibrium statistical mechanics with an emphasis on general principles is followed by a discussion of kinetically constrained spin models that are reflecting important peculiar features of glassy dynamics.
Download or read book Statistical Physics written by J. Honerkamp and published by Springer Science & Business Media. This book was released on 2002-06-10 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of statistical methods to physics is essential. This unique book on statistical physics offers an advanced approach with numerous applications to the modern problems students are confronted with. Therefore the text contains more concepts and methods in statistics than the student would need for statistical mechanics alone. Methods from mathematical statistics and stochastics for the analysis of data are discussed as well. The book is divided into two parts, focusing first on the modeling of statistical systems and then on the analysis of these systems. Problems with hints for solution help the students to deepen their knowledge. The second edition has been updated and enlarged with new material on estimators based on a probability distribution for the parameters, identification of stochastic models from observations, and statistical tests and classification methods (Chaps. 10-12). Moreover, a customized set of problems with solutions is accessible on the Web. The author teaches and conducts research on stochastic dynamical systems at the University of Freiburg, Germany.
Download or read book Statistical Physics written by Josef Honerkamp and published by Springer. This book was released on 2012-06-19 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of statistical methods to physics is essential. This unique book on statistical physics offers an advanced approach with numerous applications to the modern problems students are confronted with. Therefore the text contains more concepts and methods in statistics than the student would need for statistical mechanics alone. Methods from mathematical statistics and stochastics for the analysis of data are discussed as well. The book is divided into two parts, focusing first on the modeling of statistical systems and then on the analysis of these systems. Problems with hints for solution help the students to deepen their knowledge. The third edition has been updated and enlarged with new sections deepening the knowledge about data analysis. Moreover, a customized set of problems with solutions is accessible on the Web at extras.springer.com.
Download or read book Introduction to Mathematical Statistical Physics written by Robert Adolʹfovich Minlos and published by American Mathematical Soc.. This book was released on 2000 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a mathematically rigorous approach to the main ideas and phenomena of statistical physics. The introduction addresses the physical motivation, focusing on the basic concept of modern statistical physics, that is the notion of Gibbsian random fields. Properties of Gibbsian fields are analysed in two ranges of physical parameters: "regular" (corresponding to high-temperature and low-density regimes) where no phase transition is exhibited, and "singular" (low temperature regimes) where such transitions occur. Next, a detailed approach to the analysis of the phenomena of phase transitions of the first kind, the Pirogov-Sinai theory, is presented. The author discusses this theory in a general way and illustrates it with the example of a lattice gas with three types of particles. The conclusion gives a brief review of recent developments arising from this theory. The volume is written for the beginner, yet advanced students will benefit from it as well. The book will serve nicely as a supplementary textbook for course study. The prerequisites are an elementary knowledge of mechanics, probability theory and functional analysis.
Download or read book Mathematical Foundations of Classical Statistical Mechanics written by D.Ya. Petrina and published by CRC Press. This book was released on 2002-04-11 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov equations for the sequences of correlation functions in the thermodynamic limit. This is the first detailed investigation of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in the cases of both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. A comprehensive survey of results is also included; it concerns the properties of correlation functions for infinite systems and the corresponding equations. For this new edition, the authors have made changes to reflect the development of theory in the last ten years. They have also simplified certain sections, presenting them more systematically, and greatly increased the number of references. The book is aimed at theoretical physicists and mathematicians and will also be of use to students and postgraduate students in the field.
Download or read book From Microphysics to Macrophysics written by Roger Balian and published by Springer Science & Business Media. This book was released on 2006-11-13 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This popular, often cited text returns in a softcover edition to provide a thorough introduction to statistical physics and thermodynamics, and to exhibit the universality of the chain of ideas leading from the laws of microphysics to the macroscopic behaviour of matter. A wide range of applications illustrates the concepts, and many exercises reinforce understanding. Volume I discusses the probabilistic description of quantum or classical systems, the Boltzmann-Gibbs distributions, the conservation laws, and the interpretation of entropy as missing information. Thermodynamics and electromagnetism in matter are dealt with, as well as applications to dilute and condensed gases, and to phase transitions.
Download or read book Statistical Physics written by Daijiro Yoshioka and published by Springer Science & Business Media. This book was released on 2006-11-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive presentation of the basics of statistical physics. The first part explains the essence of statistical physics and how it provides a bridge between microscopic and macroscopic phenomena, allowing one to derive quantities such as entropy. Here the author avoids going into details such as Liouville’s theorem or the ergodic theorem, which are difficult for beginners and unnecessary for the actual application of the statistical mechanics. In the second part, statistical mechanics is applied to various systems which, although they look different, share the same mathematical structure. In this way readers can deepen their understanding of statistical physics. The book also features applications to quantum dynamics, thermodynamics, the Ising model and the statistical dynamics of free spins.
Download or read book From Microphysics to Macrophysics written by Roger Balian and published by Springer Science & Business Media. This book was released on 2007-06-26 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This popular, often cited text returns in a softcover edition to provide a thorough introduction to statistical physics and thermodynamics, and to exhibit the universal chain of ideas leading from the laws of microphysics to the macroscopic behaviour of matter. A wide range of applications illustrates the concepts, and many exercises reinforce understanding. Volume II applies statistical methods to systems governed by quantum effects, in particular to solid state physics, explaining properties due to the crystal structure or to the lattice excitations or to the electrons. The last chapters are devoted to non-equilibrium processes and to kinetic equations, with many applications included.
Download or read book C Algebras and Mathematical Foundations of Quantum Statistical Mechanics written by Jean-Bernard Bru and published by Springer Nature. This book was released on 2023-06-16 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive introduction to the mathematical foundations of quantum statistical physics. It presents a conceptually profound yet technically accessible path to the C*-algebraic approach to quantum statistical mechanics, demonstrating how key aspects of thermodynamic equilibrium can be derived as simple corollaries of classical results in convex analysis. Using C*-algebras as examples of ordered vector spaces, this book makes various aspects of C*-algebras and their applications to the mathematical foundations of quantum theory much clearer from both mathematical and physical perspectives. It begins with the simple case of Gibbs states on matrix algebras and gradually progresses to a more general setting that considers the thermodynamic equilibrium of infinitely extended quantum systems. The book also illustrates how first-order phase transitions and spontaneous symmetry breaking can occur, in contrast to the finite-dimensional situation. One of the unique features of this book is its thorough and clear treatment of the theory of equilibrium states of quantum mean-field models. This work is self-contained and requires only a modest background in analysis, topology, and functional analysis from the reader. It is suitable for both mathematicians and physicists with a specific interest in quantum statistical physics.
Download or read book Dynamical Systems and Statistical Mechanics written by I͡Akov Grigorʹevich Sinaĭ and published by American Mathematical Soc.. This book was released on 1991 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems and statistical mechanics have been developing in close interaction during the past decade, and the papers in this book attest to the productiveness of this interaction. The first paper in the collection contains a new result in the theory of quantum chaos, a burgeoning line of inquiry which combines mathematics and physics and which is likely in time to produce many new connections and applications. Another paper, related to the renormalization group method for the study of maps of the circle with singularities due to a jump in the derivative, demonstrates that the fixed point of the renormgroup can in this case be sufficiently described. In certain situations, the renormgroup methods work better than the traditional KAM method. Other topics covered include: thermodynamic formalism for certain infinite-dimensional dynamical systems, numerical simulation of dynamical systems with hyperbolic behaviour, periodic points of holomorphic maps, the theory of random media, statistical properties of the leading eigenvalue in matrix ensembles of large dimension, spectral properties of the one-dimensional Schrodinger operator. This volume will appeal to many readers, as it covers a broad range of topics and presents a view of some of the frontier research in the Soviet Union today.
Download or read book Contemporary Problems in Statistical Physics written by George H. Weiss and published by SIAM. This book was released on 1994-01-01 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of independent articles describes some mathematical problems recently developed in statistical physics and theoretical chemistry. The book introduces and reviews current research on such topics as nonlinear systems and colored noise, stochastic resonance, percolation, the trapping problem in the theory of random walks, and diffusive models for chemical kinetics. Some of these topics have never before been presented in expository book form. Applied mathematicians will be introduced to some contemporary problems in statistical physics. In addition, a number of unsolved problems currently attracting intensive research efforts are described, and some of the techniques used in this research are outlined, along with principal results and outstanding questions. A wide spectrum of mathematical techniques is covered, but the main emphasis is on introducing the mathematician to different research areas with open and interesting problems. This is an ideal starting point for the mathematician with an elementary acquaintance with the methodology of statistical physics. The material is meant to be introductory and terms are carefully defined. Many topics that require further study are introduced, providing new research ideas for the applied mathematician or thesis problems for the graduate student.
Download or read book The Statistical Mechanics of Quantum Lattice Systems written by and published by European Mathematical Society. This book was released on 2009 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum statistical mechanics plays a major role in many fields such as thermodynamics, plasma physics, solid-state physics, and the study of stellar structure. While the theory of quantum harmonic oscillators is relatively simple, the case of anharmonic oscillators, a mathematical model of a localized quantum particle, is more complex and challenging. Moreover, infinite systems of interacting quantum anharmonic oscillators possess interesting ordering properties with respect to quantum stabilization. This book presents a rigorous approach to the statistical mechanics of such systems, in particular with respect to their actions on a crystal lattice. The text is addressed to both mathematicians and physicists, especially those who are concerned with the rigorous mathematical background of their results and the kind of problems that arise in quantum statistical mechanics. The reader will find here a concise collection of facts, concepts, and tools relevant for the application of path integrals and other methods based on measure and integration theory to problems of quantum physics, in particular the latest results in the mathematical theory of quantum anharmonic crystals. The methods developed in the book are also applicable to other problems involving infinitely many variables, for example, in biology and economics.
Download or read book Nonlinear Systems and Their Remarkable Mathematical Structures written by Norbert Euler and published by CRC Press. This book was released on 2021-09-07 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained
Download or read book Random Matrix Theory with an External Source written by Edouard Brézin and published by Springer. This book was released on 2017-01-11 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.
Download or read book 50 Years Of The Renormalization Group Dedicated To The Memory Of Michael E Fisher written by Amnon Aharony and published by World Scientific. This book was released on 2024-07-26 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in the book are devoted to the memory of Michael E Fisher, and hence include many personal memories from people whose work was influenced by him. Also, the book is a collection of articles from leaders in the field of phase transitions and critical phenomena, to celebrate 50 years of the renormalization group and the 1972 paper by Wilson and Fisher. Many of the articles review, in tutorial form, the progress in the fields of phase transitions and the renormalization group.
Download or read book Mathematical Foundations of Classical Statistical Mechanics written by D.Ya. Petrina and published by CRC Press. This book was released on 2002-04-11 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov
