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.

Random walks often provide the underlying mesoscopic mechanism for transport phenomena in physics, chemistry and biology. In particular, anomalous transport in branched structures has attracted considerable attention. Combs are simple caricatures of various types of natural branched structures that belong to the category of loopless graphs. The comb model was introduced to understand anomalous transport in percolation clusters. Comb-like models have been widely adopted to describe kinetic processes in various experimental applications in medical physics and biophysics, chemistry of polymers, semiconductors, and many other interdisciplinary applications.The authors present a random walk description of the transport in specific comb geometries, ranging from simple random walks on comb structures, which provide a geometrical explanation of anomalous diffusion, to more complex types of random walks, such as non-Markovian continuous-time random walks. The simplicity of comb models allows to perform a rigorous analysis and to obtain exact analytical results for various types of random walks and reaction-transport processes.

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 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.

This book provides a comprehensive review of the theory of phase transitions and its modern applications, based on the five pillars of the modern theory of phase transitions: the Ising model, mean field, scaling, renormalization group and universality. This expanded second edition includes, along with a description of vortices and high temperature superconductivity, a discussion of phase transitions in chemical reactions and moving systems. The book covers the close connection between phase transitions and small world phenomena as well as scale-free systems such as the stock market and the Internet.

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.

Flocks of birds, schools of fish and swarms of locusts display amazing forms of collective motion, while huge numbers of glow worms can emit light signals with almost unbelievable synchronization. These and many other collective phenomena in animal societies take place according to laws very similar to those governing the collective behavior in the inanimate nature, such as the magnetization of iron and the light radiation of lasers. During recent years, this has led to the study of swarm behavior as a challenging new field of science, in which ideas from the physical world are applied in order to understand the formation and structure of animal swarms. From these studies, it has become clear that such collective behavior of animals emerges in a self-organized way, without any need of overall coordination. In this book, we present different swarm phenomena of the animal world and compare them to their counterparts in physics, in a conceptual and non-technical way, addressed to a general readership.

Multilayer networks, in particular multilayer social networks, where users belong to and interact on different networks at the same time, are an active research area in social network analysis, computer science, and physics. These networks have traditionally been studied within these separate research communities, leading to the development of several independent models and methods to deal with the same set of problems. This book unifies and consolidates existing practical and theoretical knowledge on multilayer networks including data collection and analysis, modeling, and mining of multilayer social network systems, the evolution of interconnected social networks, and dynamic processes such as information spreading. A single real dataset is used to illustrate the concepts presented throughout the book, demonstrating both the practical utility and the potential shortcomings of the various methods. Researchers from all areas of network analysis will learn new aspects and future directions of this emerging field.

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.

Application of New Cybernetics in Physics describes the application of new cybernetics to physical problems and the resolution of basic physical paradoxes by considering external observer influence. This aids the reader in solving problems that were solved incorrectly or have not been solved. Three groups of problems of the new cybernetics are considered in the book: (a) Systems that can be calculated based on known physics of subsystems. This includes the external observer influence calculated from basic physical laws (ideal dynamics) and dynamics of a physical system influenced even by low noise (observable dynamics). (b) Emergent systems. This includes external noise from the observer by using the black box model (complex dynamics), external noise from the observer by using the observer's intuition (unpredictable dynamics), defining boundaries of application of scientific methods for system behavior prediction, and the role of the observer's intuition for unpredictable systems. (c) Methods for solution of basic physical paradoxes by using methods of the new cybernetics: the entropy increase paradox, Schroedinger's cat paradox (wave package reduction in quantum mechanics), the black holes information paradox, and the time wormholes grandfather paradox. All of the above paradoxes have the same resolution based on the principles of new cybernetics. Indeed, even a small interaction of an observer with an observed system results in their time arrows' alignment (synchronization) and results in the paradox resolution and appearance of the universal time arrow.

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.

Key features: Presents a theoretical outline for each chapter. Motivates the students with standard mechanics problems with step-by-step explanations. Challenges the students with more complex problems with detailed solutions.

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.

"A Modern Course in Statistical Physics" is a textbook that illustrates the foundations of equilibrium and non-equilibrium statistical physics, and the universal nature of thermodynamic processes, from the point of view of contemporary research problems. The book treats such diverse topics as the microscopic theory of critical phenomena, superfluid dynamics, quantum conductance, light scattering, transport processes, and dissipative structures, all in the framework of the foundations of statistical physics and thermodynamics. It shows the quantum origins of problems in classical statistical physics. One focus of the book is fluctuations that occur due to the discrete nature of matter, a topic of growing importance for nanometer scale physics and biophysics. Another focus concerns classical and quantum phase transitions, in both monatomic and mixed particle systems. This fourth edition extends the range of topics considered to include, for example, entropic forces, electrochemical processes in biological systems and batteries, adsorption processes in biological systems, diamagnetism, the theory of Bose-Einstein condensation, memory effects in Brownian motion, the hydrodynamics of binary mixtures. A set of exercises and problems is to be found at the end of each chapter and, in addition, solutions to a subset of the problems is provided. The appendices cover Exact Differentials, Ergodicity, Number Representation, Scattering Theory, and also a short course on Probability.

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.

Brownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian diffusion is one of the ways in which key reactant molecules move about inside a living cell. This book focuses on the four simplest models of Brownian diffusion: the classical Fickian model, the Einstein model, the discrete-stochastic (cell-jumping) model, and the Langevin model. The authors carefully develop the theories underlying these models, assess their relative advantages, and clarify their conditions of applicability. Special attention is given to the stochastic simulation of diffusion, and to showing how simulation can complement theory and experiment. Two self-contained tutorial chapters, one on the mathematics of random variables and the other on the mathematics of continuous Markov processes (stochastic differential equations), make the book accessible to researchers from a broad spectrum of technical backgrounds.

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.