This book covers the broad subject of equilibrium statistical mechanics along with many advanced and modern topics such as nucleation, spinodal decomposition, inherent structures of liquids and liquid crystals. Unlike other books on the market, this comprehensive text not only deals with the primary fundamental ideas of statistical mechanics but also covers contemporary topics in this broad and rapidly developing area of chemistry and materials science.

Der Grundkurs Theoretische Physik deckt in 7 Banden alle fur das Diplom und fur Bachelor/Master-Studiengange massgeblichen Gebiete ab. Jeder Band vermittelt das im jeweiligen Semester notwendige theoretisch-physikalische Rustzeug. UEbungsaufgaben mit ausfuhrlichen Loesungen dienen der Vertiefung des Stoffs. Der 6. Band zur Statistischen Physik wurde fur die Neuauflage grundlegend uberarbeitet und um aktuelle Entwicklungen erganzt. Durch die zweifarbige Gestaltung ist der Stoff jetzt noch ubersichtlicher gegliedert.

This invaluable book provides a broad introduction to a rapidly growing area of nonequilibrium statistical physics. The first part of the book complements the classical book on the Langevin and Fokker-Planck equations (H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications (Springer, 1996)). Some topics and methods of solutions are presented and discussed in details which are not described in Risken's book, such as the method of similarity solution, the method of characteristics, transformation of diffusion processes into the Wiener process in different prescriptions, harmonic noise and relativistic Brownian motion. Connection between the Langevin equation and Tsallis distribution is also discussed.Due to the growing interest in the research on the generalized Langevin equations, several of them are presented. They are described with some details.Recent research on the integro-differential Fokker-Planck equation derived from the continuous time random walk model shows that the topic has several aspects to be explored. This equation is worked analytically for the linear force and the generic waiting time probability distribution function. Moreover, generalized Klein-Kramers equations are also presented and discussed. They have the potential to be applied to natural systems, such as biological systems.

This book presents recent results of basic research in the field of Raman scattering by optic and acoustic phonons in semiconductors, quantum wells and superlattices. It also describes various new applications for analytical materials research which have emerged alongside with scientific progress. Trends in Raman techniques and instrumentation and their implications for future developments are illustrated.

This book is the fifth volume of papers on advanced problems of phase transitions and critical phenomena, the first four volumes appeared in 2004, 2007, 2012, and 2015. It aims to compile reviews in those aspects of criticality and related subjects that are of current interest. The seven 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 the first four 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 subject.

This text presents an introduction to the field of statistical physics of macromolecules, from the basic concepts to modern achievements. Applications in various fields of polymer physical chemistry and molecular biophysics are also covered, as are: the fundamentals of statistical theory of polymer solutions and melts; classical, sealing and renormalization group approaches; the main ideas of statistical theories of polymer liquid crystals, polymer networks and polyelectrolytes; dynamic viscoelastic behavior of polymer systems; models of house, Zimm and reptation concepts; and specific features of main biopolymers - DNA and proteins. This English edition also includes sections describing the most important recent advances such as: statistical theory of DNA gel-electrophoresis, polymers at interfaces, and dynamics of concentrated solutions of rigid polymers.

The Ising model provides a detailed mathematical description of ferromagnetism and is widely used in statistical physics and condensed matter physics. In this Student's Guide, the author demystifies the mathematical framework of the Ising model and provides students with a clear understanding of both its physical significance, and how to apply it successfully in their calculations. Key topics related to the Ising model are covered, including exact solutions of both finite and infinite systems, series expansions about high and low temperatures, mean-field approximation methods, and renormalization-group calculations. The book also incorporates plots, figures, and tables to highlight the significance of the results. Designed as a supplementary resource for undergraduate and graduate students, each chapter includes a selection of exercises intended to reinforce and extend important concepts, and solutions are also available for all exercises.

Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.

This book presents the statistical theory of complex wave scattering and quantum transport in physical systems which have chaotic classical dynamics, as in the case of microwave cavities and quantum dots, or which possess quenched randomness, as in the case of disordered conductors - with an emphasis on mesoscopic fluctuations. The statistical regularity of the phenomena is revealed in a natural way by adopting a novel maximum-entropy approach. Shannon's information entropy is maximised, subject to the symmetries and constraints which are physically relevant, within the powerful and non-perturbative theory of random matrices; this is a most distinctive feature of the book. Aiming for a self-contained presentation, the quantum theory of scattering, set in the context of quasi-one-dimensional, multichannel systems, and related directly to scattering problems in mesoscopic physics, is introduced in chapters two and three. The linear-response theory of quantum electronic transport, adapted to the context of mesoscopic systems, is discussed in chapter four. These chapters, together with chapter five on the maximum-entropy approach and chapter eight on weak localization, have been written in a most pedagogical style, suitable for use on graduate courses. In chapters six and seven, the problem of electronic transport through classically chaotic cavities and quasi-one-dimensional disordered systems is discussed. Many exercises are included, most of which are worked through in detail, aiding graduate students, teachers, and research scholars interested in the subject of quantum transport through disordered and chaotic systems.

This book is the distilled essence of the author teaching statistical mechanics to juniors, seniors and graduate students for over 50 years in various course settings. It uses a unique approach that leads naturally into the development of all possible ensembles. Much of the later chapters on polymers has previously been available only in the literature. Throughout the book, the assumption is made that the reader is still relatively raw, and mathematical detail is provided that other books leave to the abilities of the reader. While this produces a plethora of equations that mature scientists would regard as unnecessary, it is intended to help those just coming into the field and who want to get the idea without suffering hours of agony wondering, 'where did that come from?'.

This book is the distilled essence of the author teaching statistical mechanics to juniors, seniors and graduate students for over 50 years in various course settings. It uses a unique approach that leads naturally into the development of all possible ensembles. Much of the later chapters on polymers has previously been available only in the literature. Throughout the book, the assumption is made that the reader is still relatively raw, and mathematical detail is provided that other books leave to the abilities of the reader. While this produces a plethora of equations that mature scientists would regard as unnecessary, it is intended to help those just coming into the field and who want to get the idea without suffering hours of agony wondering, 'where did that come from?'.

In this new textbook, a number of unusual applications are discussed in addition to the usual topics covered in a course on Statistical Physics. Examples are: statistical mechanics of powders, Peierls instability, graphene, Bose-Einstein condensates in a trap, Casimir effect and the quantum Hall effect. Superfluidity and super-conductivity (including the physics of high-temperature superconductors) have also been discussed extensively.The emphasis on the treatment of these topics is pedagogic, introducing the basic tenets of statistical mechanics, with extensive and thorough discussion of the postulates, ensembles, and the relevant statistics. Many standard examples illustrate the microcanonical, canonical and grand canonical ensembles, as well as the Bose-Einstein and Fermi-Dirac statistics.A special feature of this text is the detailed presentation of the theory of second-order phase transitions and the renormalization group, emphasizing the role of disorder. Non-equilibrium statistical physics is introduced via the Boltzmann transport equation. Additional topics covered here include metastability, glassy systems, the Langevin equation, Brownian motion, and the Fokker-Planck equation.Graduate students will find the presentation readily accessible, since the topics have been treated with great deal of care and attention to detail.

This new edition of College Physics Essentials provides a streamlined update of a major textbook for algebra-based physics. The first volume covers topics such as mechanics, heat, and thermodynamics. The second volume covers electricity, atomic, nuclear, and quantum physics. The authors provide emphasis on worked examples together with expanded problem sets that build from conceptual understanding to numerical solutions and real-world applications to increase reader engagement. Including over 900 images throughout the two volumes, this textbook is highly recommended for students seeking a basic understanding of key physics concepts and how to apply them to real problems.

This book is a compilation of selected reviews by Professor Michael E Fisher. Fisher's major contributions to physics have been in equilibrium statistical mechanics, and have spanned the entire range of that subject. He has been credited with bringing together, and teaching a common language to chemists and physicists working on diverse problems of phase transitions.About the Book by the AuthorTalking informally in a clear way came naturally once intrigued by a field of science; that helped me accept the invitation to publish a collection of review articles. And working actively in an area has led me to express what is new in basic terms, with lots of figures framed, typically, via two- or three-dimensional images. Also encouraging was that my reviews - with crucial references - were recognized in 1983 by the U.S. National Academy of Sciences through their James Murray Luck Award for 'excellence in scientific reviewing.'However, the first article in this collection is by my postdoctoral mentor, Cyril Domb, whose inaugural lecture at King's College London was entitled: 'Statistical Physics and its Problems.' This provides readers with a context for some of the topics later reviewed in greater depth. Among the aspects then explained, are the various critical exponents: , , , and - the special exponents and for the correlation functions, and the scaling relations. Phase diagrams are examined thoroughly along with tricritical and bicritical points, Kosterlitz-Thouless points, protocriticality, etc. Random walks along with vicious walkers and their reunions are introduced. Biophysics is touched upon. The final article: 'Statistical Physics in the Oeuvre of Chen Ning Yang,' stems from the 2015 Conference on 60 Years of Yang-Mills Gauge Field Theories.In conclusion, it is hoped that a wide range of readers (and some experts also!) will enjoy dipping into the variety of reviews collected here.

This book is a compilation of selected reviews by Professor Michael E Fisher. Fisher's major contributions to physics have been in equilibrium statistical mechanics, and have spanned the entire range of that subject. He has been credited with bringing together, and teaching a common language to chemists and physicists working on diverse problems of phase transitions.About the Book by the AuthorTalking informally in a clear way came naturally once intrigued by a field of science; that helped me accept the invitation to publish a collection of review articles. And working actively in an area has led me to express what is new in basic terms, with lots of figures framed, typically, via two- or three-dimensional images. Also encouraging was that my reviews - with crucial references - were recognized in 1983 by the U.S. National Academy of Sciences through their James Murray Luck Award for 'excellence in scientific reviewing.'However, the first article in this collection is by my postdoctoral mentor, Cyril Domb, whose inaugural lecture at King's College London was entitled: 'Statistical Physics and its Problems.' This provides readers with a context for some of the topics later reviewed in greater depth. Among the aspects then explained, are the various critical exponents: , , , and - the special exponents and for the correlation functions, and the scaling relations. Phase diagrams are examined thoroughly along with tricritical and bicritical points, Kosterlitz-Thouless points, protocriticality, etc. Random walks along with vicious walkers and their reunions are introduced. Biophysics is touched upon. The final article: 'Statistical Physics in the Oeuvre of Chen Ning Yang,' stems from the 2015 Conference on 60 Years of Yang-Mills Gauge Field Theories.In conclusion, it is hoped that a wide range of readers (and some experts also!) will enjoy dipping into the variety of reviews collected here.

Statistical mechanics is concerned with defining the thermodynamic properties of a macroscopic sample in terms of the properties of the microscopic systems of which it is composed. The previous book Introduction to Statistical Mechanics provided a clear, logical, and self-contained treatment of equilibrium statistical mechanics starting from Boltzmann's two statistical assumptions, and presented a wide variety of applications to diverse physical assemblies. An appendix provided an introduction to non-equilibrium statistical mechanics through the Boltzmann equation and its extensions. The coverage in that book was enhanced and extended through the inclusion of many accessible problems. The current book provides solutions to those problems. These texts assume only introductory courses in classical and quantum mechanics, as well as familiarity with multi-variable calculus and the essentials of complex analysis. Some knowledge of thermodynamics is also assumed, although the analysis starts with an appropriate review of that topic. The targeted audience is first-year graduate students and advanced undergraduates, in physics, chemistry, and the related physical sciences. The goal of these texts is to help the reader obtain a clear working knowledge of the very useful and powerful methods of equilibrium statistical mechanics and to enhance the understanding and appreciation of the more advanced texts.

The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.

The aim of this book is to give a physical treatment of the kinetic theory of gases and magnetoplasmas, covering the standard material in as simple a way as possible, using mean-free-path arguments when possible and identifying problem areas where received theory has either failed or has fallen short of expectations. Examples are provided by strong shock waves, ultrasonic waves (high Knudsen numbers), and transport across strong magnetic fields. Examples of problem areas provided by strong shock waves, ultrasonic waves (high Knudsen numbers), and transport across strong magnetic fields. One of the paradoxes arising in kinetic theory concerns the fluid pressure. Collisions are necessary for a fluid force to result, yet standard kinetic theory does not entail this, being satisfied to bypass Newton's equations by defining pressure as a momentum flux. This omission usually has no adverse consequences, but with increasing Knudsen number, it leads to errors. This text pays particular attention to pressure, explaining the importance of allowing for its collisional nature from the outset in developing kinetic theory.

This book establishes the foundations of non-equilibrium quantum statistical mechanics in order to support students and academics in developing and building their understanding. The formal theory is derived from first principles by mathematical analysis, with concrete physical interpretations and worked examples throughout. It explains the central role of entropy; its relation to the probability operator and the generalisation to transitions, as well as providing first principles derivation of the von Neumann trace form, the Maxwell-Boltzmann form and the Schroedinger equation.

The aim of this book is to provide the fundamentals of statistical physics and its application to condensed matter. The combination of statistical mechanics and quantum mechanics has provided an understanding of properties of matter leading to spectacular technological innovations and discoveries in condensed matter which have radically changed our daily life.The book gives the steps to follow to understand fundamental theories and to apply these to real materials.

The aim of this book is to provide the fundamentals of statistical physics and its application to condensed matter. The combination of statistical mechanics and quantum mechanics has provided an understanding of properties of matter leading to spectacular technological innovations and discoveries in condensed matter which have radically changed our daily life.The book gives the steps to follow to understand fundamental theories and to apply these to real materials.

The study of network theory is a highly interdisciplinary field, which has emerged as a major topic of interest in various disciplines ranging from physics and mathematics, to biology and sociology. This book promotes the diverse nature of the study of complex networks by balancing the needs of students from very different backgrounds. It references the most commonly used concepts in network theory, provides examples of their applications in solving practical problems, and clear indications on how to analyse their results. In the first part of the book, students and researchers will discover the quantitative and analytical tools necessary to work with complex networks, including the most basic concepts in network and graph theory, linear and matrix algebra, as well as the physical concepts most frequently used for studying networks. They will also find instruction on some key skills such as how to proof analytic results and how to manipulate empirical network data. The bulk of the text is focused on instructing readers on the most useful tools for modern practitioners of network theory. These include degree distributions, random networks, network fragments, centrality measures, clusters and communities, communicability, and local and global properties of networks. The combination of theory, example and method that are presented in this text, should ready the student to conduct their own analysis of networks with confidence and allow teachers to select appropriate examples and problems to teach this subject in the classroom.

In this book we have solved the complicated problem of constructing upper bounds for many-time averages for the case of a fairly broad class of model systems with four-fermion interaction. The methods proposed in this book for solving this problem will undoubtedly find application not only for the model systems associated with the theory of superconductivity considered here. The theoretical methods developed in Chapters 1 and 2 are already applicable to a much broader class of model systems from statistical physics and the theory of elementary particles.