The standard cosmological picture of our Universe emerging from a 'big bang' leaves open many fundamental questions which string theory, a unified theory of all forces of nature, should be able to answer. This 2007 text was the first dedicated to string cosmology, and contains a pedagogical introduction to the basic notions of the subject. It describes the possible scenarios suggested by string theory for the primordial evolution of our Universe. It discusses the main phenomenological consequences of these scenarios, stresses their differences from each other, and compares them to the more conventional models of inflation. The book summarises over 15 years of research in this field and introduces advances. It is self-contained, so it can be read by astrophysicists with no knowledge of string theory, and high-energy physicists with little understanding of cosmology. Detailed and explicit derivations of all the results presented provide a deeper appreciation of the subject.

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.

With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach.
In part one, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicas or supersymmetry. Further, all main extensions of the classical Gaussian ensembles of Wigner and Dyson are introduced including sparse, heavy tailed, non-Hermitian or multi-matrix models. In the second and larger part, all major applications are covered, in disciplines ranging from physics and mathematics to biology and engineering. This includes standard fields such as number theory, quantum chaos or quantum chromodynamics, as well as recent developments such as partitions, growth models, knot theory, wireless communication or bio-polymer folding.
The handbook is suitable both for introducing novices to this area of research and as a main source of reference for active researchers in mathematics, physics and engineering.

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.

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.

Statistics links microscopic and macroscopic phenomena, and requires for this reason a large number of microscopic elements like atoms. The results are values of maximum probability or of averaging. This introduction to statistical physics concentrates on the basic principles, and attempts to explain these in simple terms supplemented by numerous examples. These basic principles include the difference between classical and quantum statistics, a priori probabilities as related to degeneracies, the vital aspect of indistinguishability as compared with distinguishability in classical physics, the differences between conserved and non-conserved elements, the different ways of counting arrangements in the three statistics (Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein), the difference between maximization of the number of arrangements of elements, and averaging in the Darwin-Fowler method. Significant applications to solids, radiation and electrons in metals are treated in separate chapters, as well as Bose-Einstein condensation. This revised second edition contains an additional chapter on the Boltzmann transport equation along with appropriate applications. Also, more examples have been added throughout, as well as further references to literature.

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.

Examining important results and analytical techniques, this graduate-level textbook is a step-by-step presentation of the structure and function of complex networks. Using a range of examples, from the stability of the internet to efficient methods of immunizing populations, and from epidemic spreading to how one might efficiently search for individuals, this textbook explains the theoretical methods that can be used, and the experimental and analytical results obtained in the study and research of complex networks. Giving detailed derivations of many results in complex networks theory, this is an ideal text to be used by graduate students entering the field. End-of-chapter review questions help students monitor their own understanding of the materials presented.

Gets right to the point with step-by-step guidance on solving physics problems. Covers all topics in standard general physics courses in the same sequence. Keeps learning about physics fun and engaging through the story of dinosaurs being tested on their knowledge for a final challenge (deflecting an asteroid headed to Earth!). Enables the reader to quickly flip through and locate steps needed for a particular problem. Includes tons of easy to follow diagrams and worked solutions.

Electrons and ions have been used for over 40 years as probes to investigate the fascinating properties of helium liquids. The study of the transport properties of microscopic charge carriers sheds light on superfluidity, on quantum hydrodynamics, and on the interactions with collective excitations in quantum liquids. The structure of the probes themselves depends on their coupling with the liquid environment in a way that gives further insight into the microscopic behavior of the liquid in different thermodynamic conditions, such as in the superfluid phase, in the normal phase, or near the liquid-vapor critical point. This book provides a comprehensive review of the experiments and theories of transport properties of charge carriers in liquid helium. It is a subject about which no other monograph exists to date. The book is intended for graduate and postgraduate students and for condensed matter physicists who will benefit from its completeness and accuracy.

The properties of the harmonic oscillator with random frequency or/and random damping formed the content of the first edition. The second edition includes hundreds of publications on this subject since 2005. The noisy oscillator continues to be the subject of intensive studies in physics, chemistry, biology, and social sciences.The new and the latest type of a stochastic oscillator has also been considered, namely, an oscillator with random mass. Such model describes, among other phenomena, Brownian motion with adhesion, where the molecules of the surrounding medium not only randomly collide, but also stick to the Brownian particle for some (random) time, thereby changing its mass. This edition contains two new chapters, eight new sections and an expanded bibliography. A wide group of researchers, students and teachers will benefit from this book.

This book collects lecture courses and seminars given at the Les Houches Summer School 2010 on "Quantum Theory: From Small to Large Scales." Fundamental quantum phenomena appear on all scales, from microscopic to macroscopic. Some of the pertinent questions include the onset of decoherence, the dynamics of collective modes, the influence of external randomness and the emergence of dissipative behaviour. Our understanding of such phenomena has been advanced by the study of model systems and by the derivation and analysis of effective dynamics for large systems and over long times. In this field, research in mathematical physics has regularly contributed results that were recognized as essential in the physics community. During the last few years, the key questions have been sharpened and progress on answering them has been particularly strong. This book reviews the state-of-the-art developments in this field and provides the necessary background for future studies. All chapters are written from a pedagogical perspective, making the book accessible to master and PhD students and researchers willing to enter this field.

This volume presents a collection of original and peer-reviewed articles related with the applications of Statistical Physics dedicated to Professor Dr Leopoldo Garcia-Colin, in commemoration of his 80th birthday in 2010. Professor Garcia-Colin has worked in many different fields of statistical physics, and has applied it to biological physics, solid state physics, relativity and cosmology. These are pioneering works of Prof Garcia-Colin involved in all various fields which have their roots in Mexico. His influence is found in each of these works that cover a wide range of topics including thermodynamics, statistical mechanics and kinetic theory applied to biological systems, cosmology and condensed matter, among others.Papers contributed by important experts in the field, such as J Lebowitz, as well as the latest classical applications of statistical physics can be found in this volume.

This book describes the theory of how processes on the unobservable molecular scale give rise to observable effects such as diffusion and electrical noise on the macroscopic or laboratory scale. It puts the modern theory into historical context, and features new applications, statistical mechanics derivations, and the mathematical background of the topic.

This book is designed for use in an introductory course in thermodynamics. It is aimed at students of Physics, Chemistry, Materials Science, and Engineering. As an undergraduate text, it gives a clear description of the theoretical framework of thermodynamics, while providing specific examples of its use in a wide variety of problems. These examples include topics that are atypical of undergraduate texts, such as biological systems, atmospheric phenomena, and polymers.

The narrative is infused with historical notes on the characters who make up the story of thermodynamics, enlivening the material while keeping the reader engaged.

This book reviews one-dimensional reactions, dynamics, diffusion and adsorption. In studies of complex systems in biology, chemistry and physics, understanding can be gained by analytical and numerical analyses of simple models. This book presents review articles at an advanced research level, describing results for one-dimensional models of dynamical processes such as chemical reactions and catalysis, kinetic ising models, phase separation and cluster growth, monolayer and multilayer adsorption with added relaxation, surface and hard-core particle dynamics, diffusional transport, random systems and experimental results. It also covers experimental results for systems ranging from chemical reactions to adsorption and reactions on polymer chains, steps on crystalline surfaces, and DNA. All chapters are written by leading scientists in the field. They present a self-contained review of this subject that will guide a reader from basic concepts, ideas, methods and models to the forefront of research.

This book provides a comprehensive introduction to the theory of phase transitions and critical phenomena. The content covers a period of more than 100 years of theoretical research of condensed matter phases and phase transitions providing a clear interrelationship with experimental problems. It starts from certain basic University knowledge of thermodynamics, statistical physics and quantum mechanics. The text is illustrated with classic examples of phase transitions. Various types of phase transition and (multi)critical points are introduced and explained. The classic aspects of the theory are naturally related with the modern developments. This interrelationship and the field-theoretical renormalization group method are presented in details. The main applications of the renormalization group methods are presented. Special attention is paid to the description of quantum phase transitions. This edition contains a more detailed presentation of the renormalization group method and its applications to particular systems.

* Explores the exciting and new topic of econophysics * Multidisciplinary approach, that will be of interest to students and researchers from physics, engineering, mathematics, statistics, and other physical sciences * Useful to both students and researchers

This monograph, suitable for use as an advanced text, presents the statistical mechanics of solids from the perspective of the material properties of the solid state.

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chif1ese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics," "CFD," "completely integrable systems," "chaos, synergetics and large-scale order," which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics."

The spectacular success of the scientific enterprise over the last four hundred years has led to the promise of an all encompassing vision of the natural world. In this elegant picture, everything we observe is based upon just a few fundamental processes and entities. The almost infinite variety and complexity of the world is thus the product of emergence. But the concept of emergence is fraught with controversy and confusion. This book ponders the question of how emergence should be understood within the scientific picture, and whether a complete vision of the world can be attained that includes consciousness.

This book provides a comprehensive introduction to the theory of phase transitions and critical phenomena. The content covers a period of more than 100 years of theoretical research of condensed matter phases and phase transitions providing a clear interrelationship with experimental problems. It starts from certain basic University knowledge of thermodynamics, statistical physics and quantum mechanics. The text is illustrated with classic examples of phase transitions. Various types of phase transition and (multi)critical points are introduced and explained. The classic aspects of the theory are naturally related with the modern developments. This interrelationship and the field-theoretical renormalization group method are presented in details. The main applications of the renormalization group methods are presented. Special attention is paid to the description of quantum phase transitions. This edition contains a more detailed presentation of the renormalization group method and its applications to particular systems.

This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.

This third edition of one of the most important and best selling textbooks in statistical physics, is a graduate level text suitable for students in physics, chemistry, and materials science.The discussion of strongly interacting condensed matter systems has been expanded. A chapter on stochastic processes has also been added with emphasis on applications of the Fokker-Planck equation.The modern theory of phase transitions occupies a central place. The chapter devoted to the renormalization group approach is largely rewritten and includes a detailed discussion of the basic concepts and examples of both exact and approximate calculations. The development of the basic tools includes a chapter on computer simulations in which both Monte Carlo method and molecular dynamics are introduced, and a section on Brownian dynamics added.The theories are applied to a number of important systems such as liquids, liquid crystals, polymers, membranes, Bose condensation, superfluidity and superconductivity. There is also an extensive treatment of interacting Fermi and Bose systems, percolation theory and disordered systems in general.

Potts Models and Related Problems in Statistical Mechanics