Browse

This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on general theory which includes a summary of the basic principles of statistical mechanics; a presentation of the physical phenomena covered and the models used to discuss them; theorems on the existence and uniqueness of partition functions; theorems on order; and critical phenomena and scaling theory. The second part is on series and numerical methods which includes derivations of the Mayer and Ree–Hoover expansions of the low density virial equation of state; Groeneveld's theorems; the application to hard spheres and discs; a summary of numerical studies of systems at high density; and the use of high temperature series expansions to estimate critical exponents for magnets. The third part covers exactly solvable models which includes a detailed presentation of the Pfaffian methods of computing the Ising partition function, magnetization, correlation functions, and susceptibility; the star-triangle (Yang–Baxter equation); functional equations and the free energy for the eight-vertex model; and the hard hexagon and chiral Potts models. All needed mathematics is developed in detail and many open questions are discussed. The goal is to guide the reader to the current forefront of research.

The book integrates agent-based modeling and network science. It is divided into three parts, namely, foundations, primary dynamics on and of social networks, and applications. The book begins with the network origin of agent-based models, known as cellular automata, and introduce a number of classic models, such as Schelling’s segregation model and Axelrod’s spatial game. The essence of the foundation part is the network-based agent-based models in which agents follow network-based decision rules. Under the influence of the substantial progress in network science in late 1990s, these models have been extended from using lattices into using small-world networks, scale-free networks, etc. The book also shows that the modern network science mainly driven by game-theorists and sociophysicists has inspired agent-based social scientists to develop alternative formation algorithms, known as agent-based social networks. The book reviews a number of pioneering and representative models in this family. Upon the given foundation, the second part reviews three primary forms of network dynamics, i.e., diffusions, cascades, and influences. These primary dynamics are further extended and enriched by practical networks in goods-and-service markets, labor markets, and international trade. The book ends with two challenging issues using agent-based models of networks, i.e., network risks and economic growth.

The anomaly, which forms the central part of this book, is the failure of classical symmetry to survive the process of quantization and regularization. The study of anomalies is the key to a deeper understanding of quantum field theory and has played an increasingly important role in the theory over the past twenty years. This book presents all the different aspects of the study of anomalies in an accessible and self-contained way. Much emphasis is now being placed on the formulation of the theory using the mathematical ideas of differential geometry and topology. This approach is followed here, and the derivations and calculations are given explicitly. Topics discussed include the relevant ideas from differential geometry and topology and the application of these paths (path integrals, differential forms, homotopy operators, etc.) to the study of anomalies. Chapters are devoted to abelian and nonabelian anomalies, consistent and covariant anomalies, and gravitational anomalies.

Applied Computational Physics describes methods for solving a vast array of classical and quantum mechanical scientific problems while stressing modern computational paradigms for achieving these solutions. The text develops computational techniques, numerical algorithms, and physics applications in parallel. The goal of the book is to provide students of physics with essential and modern computational skills and to increase the confidence with which they write computer programs within their problem domain. Hundreds of original problems reinforce programming skills and increase the ability to solve real-life physics problems at and beyond the graduate level.

Nonlocality was discovered by John Bell in 1964, in the context of the debates about quantum theory, but is a phenomenon that can be studied in its own right. Its observation proves that measurements are not revealing pre-determined values, falsifying the idea of “local hidden variables” suggested by Einstein and others. One is then forced to make some radical choice: either nature is intrinsically statistical and individual events are unspeakable, or our familiar space-time cannot be the setting for the whole of physics. As phenomena, nonlocality and its consequences will have to be predicted by any future theory, and may possibly play the role of foundational principles in these developments. But nonlocality has found a role in applied physics too: it can be used for “device-independent” certification of the correct functioning of random number generators and other devices. After a self-contained introduction to the topic, this monograph on nonlocality presents the main tools and results following a logical, rather than a chronological, order.

Theoretical physics and foundations of physics have not made much progress in the last few decades. There is no consensus among researchers on how to approach unifying general relativity and quantum field theory (quantum gravity), explaining so-called dark energy and dark matter (cosmology), or the interpretation and implications of quantum mechanics and relativity. In addition, both fields are deeply puzzled about various facets of time including, above all, time as experienced. This book argues that this impasse is the result of the “dynamical universe paradigm,” the idea that reality fundamentally comprises physical entities that evolve in time from some initial state according to dynamical laws. Thus, in the dynamical universe, the initial conditions plus the dynamical laws explain everything else going exclusively forward in time. In cosmology, for example, the initial conditions reside in the Big Bang and the dynamical law is supplied by general relativity. Accordingly, the present state of the universe is explained exclusively by its past. A completely new paradigm (called Relational Blockworld) is offered here whereby the past, present, and future co-determine each other via “adynamical global constraints,” such as the least action principle. Accordingly, the future is just as important for explaining the present as the past is. Most of the book is devoted to showing how Relational Blockworld resolves many of the current conundrums of both theoretical physics and foundations of physics, including the mystery of time as experienced and how that experience relates to the block universe.

This book provides an elementary introduction to chaos and fractals. It introduces the key phenomena of chaos — aperiodicity, sensitive dependence on initial conditions, bifurcations — via simple iterated functions. Fractals are introduced as self-similar geometric objects and analysed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia sets and the Mandelbrot set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations.

This book introduces the full range of activity in the rapidly growing field of nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, this book includes a thorough treatment of both differential equation models and iterated map models (including a detailed derivation of the famous Feigenbaum numbers). It includes the increasingly important field of pattern formation and a survey of the controversial question of quantum chaos. Important tools such as Lyapunov exponents, fractal dimensions, and correlation dimensions are treated in detail. Several appendices provide a detailed derivation of the Lorenz model from the Navier-Stokes equation, a summary of bifurcation theory, and some simple computer programs to study nonlinear dynamics. Each chapter includes an extensive, annotated bibliography.

This book provides a practical guide to molecular dynamics and Monte Carlo simulation techniques used in the modelling of simple and complex liquids. Computer simulation is an essential tool in studying the chemistry and physics of condensed matter, complementing and reinforcing both experiment and theory. Simulations provide detailed information about structure and dynamics, essential to understand the many fluid systems that play a key role in our daily lives: polymers, gels, colloidal suspensions, liquid crystals, biological membranes, and glasses. The second edition of this pioneering book aims to explain how simulation programs work, how to use them, and how to interpret the results, with examples of the latest research in this rapidly evolving field. Accompanying programs in Fortran and Python provide practical, hands-on, illustrations of the ideas in the text.

The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more ‘utilitarian’ treatments of the subject. The book is divided into four parts, which look in turn at origins, dynamics, symmetries, and scales. The emphasis is conceptual — the aim is to build the theory up systematically from some clearly stated foundational concepts — and therefore to a large extent anti-historical, but two historical chapters are included to situate quantum field theory in the larger context of modern physical theories. The three remaining sections of the book follow a step by step reconstruction of this framework beginning with just a few basic assumptions: relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The second section of the book lays out the basic structure of quantum field theory arising from the sequential insertion of quantum-mechanical, relativistic and locality constraints. The central role of symmetries in relativistic quantum field theories is explored in the third section of the book, while in the final section the book explores in detail the feature of quantum field theories most critical for their enormous phenomenological success — the scale separation property embodied by the renormalization group properties of a theory defined by an effective local Lagrangian.

Quantum phase transitions describe the violent rearrangement of electrons or atoms as they evolve from well defined excitations in one phase to a completely different set of excitations in another. The book chapters give insights into how a coherent metallic or superconducting state can be driven into an incoherent insulating state by increasing disorder, magnetic field, carrier concentration and inter-electron interactions. They illustrate the primary methods employed to develop a multi-faceted theory of many interacting particle systems. They describe how recent experiments probing the microscopic structure, transport, charge and spin dynamics have yielded guiding insights. What sets this book apart is this strong dialog between experiment and theory, which reveals the recent progress and emergent opportunities to solve some major problems in many body physics. The pedagogical style of the chapters has been set for graduate students starting in this dynamic field.

This book seeks to answer the question “What explains CPT invariance and the spin–statistics connection (SSC)?” These properties play foundational roles in relativistic quantum field theories (RQFTs), are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and spin–statistics theorems; but these theorems cannot be said to explain these properties, at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work toward an understanding of CPT invariance and the SSC by first providing an analysis of the necessary and sufficient conditions for these properties, and second by advocating a particular account of explanation appropriate for this context. Under this account, the explanatory work is done in part by an appeal to intertheoretic relations, and in part by means of a derivation, within a more fundamental theory, of a property expressed in a less fundamental theory.

Technological progress comes with a dark side where good ideas and intentions produce undesirable results (extreme downsides include atomic and biological weapons). The many and various unexpected outcomes of technology span humorous to bizarre, to situations that threaten human survival. Development can be positive for some, but negative and isolating for others (e.g. older or poorer people). Progress is often transient, as faster electronics and computers dramatically shorten retention time of data, knowledge, and information loss (e.g. even photos may be unreadable within a generation). Progress and globalization are also destroying past languages and cultures. Advances cut across all areas of science and life, and the scope is vast from biology, medicine, agriculture, transport, electronics, computers, long-range communications, to a global economy. Reliance on technology causes unexpected technology-driven vulnerability to natural events (e.g. intense sunspot activity) that could annihilate advanced societies by destroying satellites or power grid distribution. Similarly, progress of electronics and communication has produced a boom industry in cybercrime, and cyberterrorism. Medical technology offers improvements in health, but can include many drug-related side effects and mutagenic changes. Over enthusiasm in creating a global food economy is devastating the environment and causing extinction of species, just to support an excessive human population. A diverse coverage of such consequences is consciously presented at a level designed for an intelligent, but non-scientific, readership. It includes suggestions for positive future progress with essential planning, investment, and political commitment. Failure to respond implies human extinction.

This book provides a comprehensive yet short description of the basic concepts of complex network theory and the code to implement this theory. Differently from other books, we present these concepts starting from real cases of study. The application topics span from food webs, to the Internet, the World Wide Web, and social networks, passing through the international trade web and financial time series. The final part is devoted to definition and implementation of the most important network models. We provide information on the structure of the data and on the quality of available datasets. Furthermore, we provide a series of codes to implement instantly what is described theoretically in the book. People knowing the basis of network theory could learn the art of coding in Python by checking our codes and using the online material. In particular, the interactive Python notebook format is used so that the reader can immediately experiment by themselves with the codes present in the manuscript. To this purpose we have set up a dedicated web site where readers can download and test the codes. The whole project is finalised to allow scientists and practitioners the possibility of working instantly in the field of complex networks.

The investigation of discrete symmetries is a fascinating subject which has been central to the agenda of physics research for fifty years, and has been the target of many experiments, ongoing and in preparation, all over the world. This book approaches the subject from a somewhat less traditional angle: it puts more emphasis on the experimental aspects of the field, trying to provide a wider picture than usual and to convey the intellectual challenge of experimental physics. The book includes the related connection to phenomenology, a purpose for which the precision experiments in this field — often rather elegant and requiring a good amount of ingenuity — are very well suited. The book discusses discrete symmetries (parity, charge conjugation, time reversal, and of course CP symmetry) in microscopic (atomic, nuclear, and particle) physics, and includes a detailed description of some key or representative experiments. The book discusses their principles and challenges more than the historical development. The main past achievements and the most recent developments are both included.

Most of the solid materials we use in everyday life, from plastics to cosmetic gels exist in a non-crystalline, amorphous form: they are glasses. Yet, we are still seeking a fundamental explanation as to what glasses really are, why they form, and what their properties are. This book surveys the most recent theoretical and experimental research dealing with the physics of glassy and disordered materials, from molecular fluids to colloidal glasses, granular media and foams. Chapters present broad and original perspectives on one of the deepest mystery of condensed matter physics, with a particular emphasis on the key role played by dynamic heterogeneities to understand from a unified viewpoint phenomena occurring in scores of disordered materials. The book covers both fundamental aspects, and reviews extensively several recent theoretical developments in the field of the glass transition that have changed our view of the glass transition. It also provides an up-to-date perspective on new experimental tools that have been developed to study with unprecedented resolution the structural relaxation of systems like molecular and polymer liquids, colloidal glasses, foams and granular materials. It also confronts, discusses, compares, and challenges the different perspectives actively promoted by different research groups and communities in a very active area of condensed-matter and statistical physics.

An understanding of the behaviour of financial assets and the evolution of economies has never been as important as it is today. This book looks at these complex systems from the perspective of the physicist. So-called ‘econophysics’ and its application to finance have made great strides in recent years. Less emphasis has been placed on the broader subject of macroeconomics, and many economics students are still taught traditional neo-classical economics. The reader is given a general primer in statistical physics, probability theory, and use of correlation functions. Much of the mathematics that is developed is frequently no longer included in undergraduate physics courses. The statistical physics of Boltzmann and Gibbs is one of the oldest disciplines within physics and it can be argued that it was first applied to ensembles of molecules as opposed to being applied to social agents only by way of historical accident. The authors argue by analogy that the theory can be applied directly to economic systems comprising assemblies of interacting agents. The necessary tools and mathematics are developed in a clear and concise manner. The body of work, now termed econophysics, is then developed. The authors show where traditional methods break down and how the probability distributions and correlation functions can be properly understood using high-frequency data. Recent work by the physics community on risk and market crashes are discussed together with new work on betting markets, as well as studies of speculative peaks that occur in housing markets.

Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.

Relativity is a set of remarkable insights into the way space and time work. The basic notion of relativity, first articulated by Galileo, explains why we do not feel Earth moving as it orbits the Sun and was successful for hundreds of years. We present thinking tools that elucidate Galilean relativity and prepare us for the more modern understanding. We then show how Galilean relativity breaks down at speeds near the speed of light, and follow Einstein’s steps in working out the unexpected relationships between space and time that we now call special relativity. These relationships give rise to time dilation, length contraction, and the twin “paradox” which we explain in detail. Throughout, we emphasize how these effects are tightly interwoven logically and graphically. Our graphical understanding leads to viewing space and time as a unified entity called spacetime whose geometry differs from that of space alone, giving rise to these remarkable effects. The same geometry gives rise to the energy?momentum relation that yields the famous equation E = mc², which we explore in detail. We then show that this geometric model can explain gravity better than traditional models of the “force” of gravity. This gives rise to general relativity, which unites relativity and gravity in a coherent whole that spawns new insights into the dynamic nature of spacetime. We examine experimental tests and startling predictions of general relativity, from everyday applications (GPS) to exotic phenomena such as gravitomagnetism, gravitational waves, Big Bang cosmology, and especially black holes.

This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic governs all of the thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs — dating from the 19th century and extended considerably over the following 100 years — is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-20th Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.