Statistical physics Books

Book SynopsisAn Introduction to Statistical Mechanics and Thermodynamics returns with a second edition which includes new chapters, further explorations, and updated information into the study of statistical mechanics and thermal dynamics.The first part of the book derives the entropy of the classical ideal gas, using only classical statistical mechanics and an analysis of multiple systems first suggested by Boltzmann. The properties of the entropy are then expressed as postulates of thermodynamics in the second part of the book. From these postulates, the formal structure of thermodynamics is developed. The third part of the book introduces the canonical and grand canonical ensembles, which are shown to facilitate calculations for many model systems. An explanation of irreversible phenomena that is consistent with time-reversal invariance in a closed system is presented. The fourth part of the book is devoted to quantum statistical mechanics, including black-body radiation, the harmonic solid, Bose-Einstein and Fermi-Dirac statistics, and an introduction to band theory, including metals, insulators, and semiconductors. The final chapter gives a brief introduction to the theory of phase transitions. Throughout the book, there is a strong emphasis on computational methods to make abstract concepts more concrete.Trade ReviewReview from previous edition In his innovative new text, Carnegie Mellon University physics professor Robert Swendsen presents the foundations of statistical mechanics with, as he puts it, a detour through thermodynamics. That's a desirable strategy because the statistical approach is more fundamental than the classical thermodynamics approach and has many applications to current research problems. [] The mathematical notation is carefully introduced and useful; the selected mathematical techniques are clearly explained in a conversational style that both graduate and advanced undergraduate students will find easy to follow. The author's subject organization and conceptual viewpoint address some of the shortcomings of conventional developments of thermal physics and will be helpful to students and researchers seeking a deep appreciation of statistical physics. * Physics Today, August 2013 *Bob Swendsen's book is very well thought out, educationally sound, and more original than other texts. * Jan Tobochnik, Kalamazoo College, USA *Robert Swendsen is a well-respected researcher who has developed many novel algorithms that illustrate his deep understanding of statistical mechanics. His textbook reflects his deep understanding and will likely have a major impact on the way statistical mechanics and thermodynamics is taught. Particularly noteworthy is Swendsen's treatment of entropy, following Boltzmann's original definition in terms of probability, and his comprehensive discussion of the fundamental principles and applications of statistical mechanics and thermodynamics. Students and instructors will enjoy reading the book as much as Swendsen obviously enjoyed writing it. * Harvey Gould, Clark University, USA *In this reader-friendly, excellent text, the author provides a unique combination of the best of two worlds: traditional thermodynamics (following Callen's footsteps) and modern statistical mechanics (including VPython codes for simulations). * Royce Zia, Virginia Polytechnic Institute and State University, USA *Swendsen is famous for developing Monte Carlo algorithms which dramatically speed up the simulation of many systems near a phase transition. The ideas for those algorithms required deep understanding of statistical mechanics, an understanding which is now fully applied to this excellent textbook. * Peter Young, University of California, USA *Table of ContentsPreface Introduction1: Part 1 Entropy 2: The Classical Ideal Gas 3: Discrete Probability Theory 4: The Classical Ideal Gas: Configurational Entropy 5: Continuous Random Numbers 6: The Classical Ideal Gas: Energy-Dependence of Entropy 7: Classical Gasses: Ideal and Otherwise 8: Temperature Pressure, Chemical Potential, and All That Part 2 Thermodynamics 9: The Postulates and Laws of Thermodynamics 10: Perturbations of Thermodynamic State Functions 11: Thermodynamics Processes 12: Thermodynamic Potentials 13: The Consequences of Extensivity 14: Thermodynamic Identities 15: Extremum Principles 16: Stability Conditions 17: Phase Transitions 18: The Nernst Postulate: the Third Law of Thermodynamics Part 3 Classical Statistical Mechanics 19: Ensembles in Classical Statistical Mechanics 20: Classical Ensembles: Grand and Otherwise 21: Refining the Definition of Entropy 22: Irreversibility Part 4 Quantum Statistical Mechanics 23: Quantum Ensembles 24: Quantum Canonical Ensemble 25: Black-Body Radiation 26: The Harmonic Solid 27: Ideal Quantum Gases 28: Bose-Einstein Statistics 29: Fermi-Dirac Statistics 30: Insulators and Semiconductors 31: Phase Transitions and the Ising Model Appendix Appendix: Computer Calculations and VPython Index Index Free

Read more less

Book SynopsisStatistical mechanics is hugely successful when applied to physical systems at thermodynamic equilibrium; however, most natural phenomena occur in nonequilibrium conditions and more sophisticated techniques are required to address this increased complexity. This second edition presents a comprehensive overview of nonequilibrium statistical physics, covering essential topics such as Langevin equations, Lévy processes, fluctuation relations, transport theory, directed percolation, kinetic roughening, and pattern formation. The first part of the book introduces the underlying theory of nonequilibrium physics, the second part develops key aspects of nonequilibrium phase transitions, and the final part covers modern applications. A pedagogical approach has been adopted for the benefit of graduate students and instructors, with clear language and detailed figures used to explain the relevant models and experimental results. With the inclusion of original material and organizational changes throughout the book, this updated edition will be an essential guide for graduate students and researchers in nonequilibrium thermodynamics.

Read more less

Book SynopsisComputational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.Trade ReviewA creative, insightful, and accessible introduction to the theory of computing, written with a keen eye toward the frontiers of the field and a vivid enthusiasm for the subject matter. * Jon Kleinberg, Cornell University *To put it bluntly: this book rocks! It's 900+ pages of awesome. It somehow manages to combine the fun of a popular book with the intellectual heft of a textbook, so much so that I don't know what to call it (but whatever the genre is, there needs to be more of it!). * Scott Aaronson, Massachusetts Institute of Technology *Moore and Mertens guide the reader through the interesting field of computational complexity in a clear, broadly accessible and informal manner, while systematically explaining the main concepts and approaches in this area and the existing links to other disciplines. The book is comprehensive and can be easily used as a textbook, at both advanced undergraduate and postgraduate levels, but is equally useful for researchers in neighbouring disciplines, such as statistical physics [...]. Some of the material covered, such as approximability issues and Probabilistically Checkable Proofs is typically not presented in books of this type, and the authors do an excellent job in presenting them very clearly and convincingly. * David Saad, Aston University, Birmingham *A treasure trove of ideas, concepts and information on algorithms and complexity theory. Serious material presented in the most delightful manner! * Vijay Vazirani, Georgia Instituute of Technology *In a class by itself - in The Nature of Computation, Cristopher Moore and Stephan Mertens have produced one of the most successful attempts to capture the broad scope and intellectual depth of theoretical computer science as it is practiced today. The Nature of Computation is one of those books you can open to a random page and find something amazing, surprising and, often, very funny. * American Scientist *a comprehensive, accessible, and highly enjoyable book that conveys the key intellectual contributions of the theory of computing ... a valuable resource for any educator * Haris Aziz, SIGACT *The book is highly recommended for all interested readers: in or out of courses, students undergraduate or graduate, researchers in other fields eager to learn the subject, or scholars already in the field who wish to enrich their current understanding. It makes for a great textbook in a conventional theory of computing course, as I can testify from recent personal experience (I used it once; Ill use it again!). With its broad and deep wealth of information, it would be a top contender for one of my desert island books.TNoC speaks directly, clearly, convincingly, and entetainingly, but also goes much further: it inspires. * Frederic Green, SIGACT *Table of Contents1. Prologue ; 2. The Basics ; 3. Insights and Algorithms ; 4. Needles in a Haystack: The class NP ; 5. Who is the Hardest One of All: NP-Completeness ; 6. The Deep Question: P vs. NP ; 7. Memory, Paths and games ; 8. Grand Unified Theory of Computation ; 9. Simply the Best: Optimization ; 10. The Power of Randomness ; 11. Random Walks and Rapid Mixing ; 12. Counting, Sampling, and Statistical Physics ; 13. When Formulas Freeze: Phase Transitions in Computation ; 14. Quantum Computing ; 15. Epilogue ; 16. Appendix: Mathematical Tools

Read more less

Book SynopsisBased on lectures for a statistical mechanics course, this textbook introduces the central concepts and tools of statistical physics including solutions that are available to lecturers at www.cambridge.org/9780521873420. A companion volume, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.Trade Review'In this much-needed modern text, Kardar presents a remarkably clear view of statistical mechanics as a whole, revealing the relationships between different parts of this diverse subject. In two volumes, the classical beginnings of thermodynamics are connected smoothly to a thoroughly modern view of fluctuation effects, stochastic dynamics, and renormalization and scaling theory. Students will appreciate the precision and clarity in which difficult concepts are presented in generality and by example. I particularly like the wealth of interesting and instructive problems inspired by diverse phenomena throughout physics (and beyond!), which illustrate the power and broad applicability of statistical mechanics.' Leon Balents, University of California, Santa Barbara'Statistical Physics of Particles is the welcome result of an innovative and popular graduate course Kardar has been teaching at MIT for almost twenty years. It is a masterful account of the essentials of a subject which played a vital role in the development of twentieth century physics, not only surviving, but enriching the development of quantum mechanics. Its importance to science in the future can only increase with the rise of subjects such as quantitative biology. Statistical Physics of Fields builds on the foundation laid by the Statistical Physics of Particles, with an account of the revolutionary developments of the past 35 years, many of which were facilitated by renormalization group ideas. Much of the subject matter is inspired by problems in condensed matter physics, with a number of pioneering contributions originally due to Kardar himself. This lucid exposition should be of particular interest to theorists with backgrounds in field theory and statistical mechanics.' David R. Nelson, Harvard University'If Landau and Lifshitz were to prepare a new edition of their classic Statistical Physics text they might produce a book not unlike this gem by Mehran Kardar. Indeed, Kardar is an extremely rare scientist, being both brilliant in formalism and an astoundingly careful and thorough teacher. He demonstrates both aspects of his range of talents in this pair of books, which belong on the bookshelf of every serious student of theoretical statistical physics. Kardar does a particularly thorough job of explaining the subtleties of theoretical topics too new to have been included even in Landau and Lifshitz most recent Third Edition (1980), such as directed paths in random media and the dynamics of growing surfaces, which are not in any text to my knowledge. He also provides careful discussion of topics that do appear in most modern texts on theoretical statistical physics, such as scaling and renormalization group.' H. Eugene Stanley, Boston University'This is one of the most valuable textbook I have seen in a long time. Written by a leader in the field, it provides a crystal clear, elegant and comprehensive coverage of the field of statistical physics. I'm sure this book will become 'the' reference for the next generation of researchers, students and practitioners in statistical physics. I wish I had this book when I was a student but I will have the privilege to rely on it for my teaching.' Alessandro Vespignani, Indiana UniversityTable of Contents1. Thermodynamics; 2. Probability; 3. Kinetic theory of gases; 4. Classical statistical mechanics; 5. Interacting particles; 6. Quantum statistical mechanics; 7. Ideal quantum gases; Solutions to selected problems; Index.

Read more less

Book SynopsisThis book covers a vast range of network science techniques that can enhance archaeological research: network data collection and management, exploratory network analysis, sampling issues and sensitivity analysis, spatial networks, and network visualisation. It will be a key educational resource students and teachers.Table of Contents1. Introducing network science for archaeology; 2. Putting network science to work in archaeological research; 3. Network data; 4. Exploratory network analysis; 5. Quantifying uncertainty in archaeological networks; 6. Network visualisation; 7. Spatial networks and networks in space; 8. Uniting theory and method for archaeological network research; Appendix A: Answers for exercises; Appendix B: Software; Glossary.

Read more less

Book SynopsisData assimilation is a hugely important mathematical technique, relevant in fields as diverse as geophysics, data science, and neuroscience. This modern book provides an authoritative treatment of the field as it relates to several scientific disciplines, with a particular emphasis on recent developments from machine learning and its role in the optimisation of data assimilation. Underlying theory from statistical physics, such as path integrals and Monte Carlo methods, are developed in the text as a basis for data assimilation, and the author then explores examples from current multidisciplinary research such as the modelling of shallow water systems, ocean dynamics, and neuronal dynamics in the avian brain. The theory of data assimilation and machine learning is introduced in an accessible and unified manner, and the book is suitable for undergraduate and graduate students from science and engineering without specialized experience of statistical physics.Table of Contents1. Prologue: linking 'The Future' with the present; 2. A data assimilation reminder; 3. Remembrance of things path; 4. SDA variational principles; Euler–Lagrange equations and Hamiltonian formulation; 5. Using waveform information; 6. Annealing in the model precision Rf; 7. Discrete time integration in data assimilation variational principles; Lagrangian and Hamiltonian formulations; 8. Monte Carlo methods; 9. Machine learning and its equivalence to statistical data assimilation; 10. Two examples of the practical use of data assimilation; 11. Unfinished business; Bibliography; Index.

Read more less

Book SynopsisThis open access book offers a concise overview of how data from large scale experiments are analyzed and how technological tools are used in practice, as in the search for new elementary particles. It focuses on interconnects between physics and detector technology in experimental particle physics, and includes descriptions of mathematical approaches. Readers find all the important steps in analysis, including reconstruction of the momentum and energy of particles from detector information, particle identification, and also the general concept of simulating particle production from collisions and detector responses. As the scale of scientific experiments becomes larger and data-intensive science emerges, the techniques used in the data analysis become ever more complicated, making it difficult for beginners to grasp the overall picture. The book provides an explanation of the idea and concepts behind the methods, helping readers understand journal articles on high energy physics. This book is engaging as it does not overemphasize mathematical formalism and it gives a lively example of how such methods have been applied to the Higgs particle discovery in the Large Hadron Collider (LHC) experiments, which led to Englert and Higgs being awarded the Nobel Prize in Physics for 2013.Graduate students and young researchers can easily obtain the required knowledge on how to start data analyses from these notes, without having to spend time in consulting many experts or digesting huge amounts of literature.Table of ContentsIntroduction.- Basic Idea of Measurements in Particle Collisions.- Apparatus.- Statistics.- Detector Calibration.- Particle Identification.- Event Simulation.- Examples of Physics Analysis.

Read more less

Book SynopsisAn understanding of thermal physics is crucial to much of modern physics, chemistry and engineering. This book provides a modern introduction to the main principles that are foundational to thermal physics, thermodynamics and statistical mechanics. The key concepts are carefully presented in a clear way, and new ideas are illustrated with copious worked examples as well as a description of the historical background to their discovery. Applications are presented to subjects as diverse as stellar astrophysics, information and communication theory, condensed matter physics and climate change. Each chapter concludes with detailed exercises.The second edition of this popular textbook maintains the structure and lively style of the first edition but extends its coverage of thermodynamics and statistical mechanics to include several new topics, including osmosis, diffusion problems, Bayes theorem, radiative transfer, the Ising model and Monte Carlo methods. New examples and exercises have been added throughout.Trade ReviewThis is probably the best book I know of thermodynamics and statistical physics. The authors have done really a great job. [...] The contents of the book are organised in such way that it can be used for a standard undergraduate level course in thermodynamics and statistical mechanics, where it is also possible to make the appropriate selection of the topics depending on the level and duration of the course. It could also be very useful as a source reference for lecturers in thermodynamics and statistical physics. * M.A.F. Sanjuan, Contemporary Physics *Table of ContentsI: PRELIMINARIES; II: KINETIC THEORY OF GASES; III: TRANSPORT AND THERMAL DIFFUSION; IV: THE FIRST LAW; V: THE SECOND LAW; VI: THERMODYNAMICS IN ACTION; VII: STATISTICAL MECHANICS; VIII: BEYOND THE IDEAL GAS; IX: SPECIAL TOPICS

Read more less

Book SynopsisProviding a modern introduction to quantum field theory, this comprehensive textbook develops the Standard Model of particle physics and explains state-of-the-art techniques for performing precision theoretical calculations. Intuitive physical discussions of abstract concepts make the subject accessible to students with a variety of backgrounds and interests.Trade Review'This is an excellent graduate-level relativistic quantum field theory text, covering an impressive amount of material often with a very novel presentation. It would be ideal either for courses on relativistic quantum field theory or for courses on the Standard Model of elementary particle interactions. The book provides interesting insights and covers many modern topics not usually presented in current texts such as spinor-helicity methods and on-shell recursion relations, heavy quark effective theory and soft-collinear effective field theory. It is nice to see the modern point of view on the predictive power of non-renormalizable theories discussed. Once in a generation particle physicists elevate a quantum field theory text to the rank of classic. Two such classics are the texts by Bjorken and Drell and Peskin and Schroeder; it wouldn't surprise me if this new book by Schwartz joins this illustrious group.' Mark Wise, California Institute of Technology'A wonderful tour of quantum field theory from the modern perspective, filled with insights on both the conceptual underpinnings and the concrete, elegant calculational tools of the subject.' Nima Arkani-Hamed, Institute for Advanced Study, Princeton'Schwartz has produced a new and valuable introduction to quantum field theory. He has rethought the whole presentation of the subject, from the introductory and foundational concepts to new developments such as effective field theory descriptions of quark dynamics. Students will enjoy viewing quantum field theory from his perspective.' Michael E. Peskin, SLAC National Accelerator Laboratory, Stanford University'Schwartz's book grew out of a popular year long course in quantum field theory at Harvard. Designed primarily for graduate students, this course also attracts and inspires a number of undergraduates each year. The book is unique in its combination of breadth, depth and readability. Schwartz starts at the beginning of the subject and brings us right up to the present. That the book is neither superficial nor impossibly dense is rather remarkable and makes it easy to understand the course's success.' Howard Georgi, Harvard University'In this book, Schwartz gives a thoughtful and modern treatment of many classical and contemporary topics. Students and experienced researchers will find much here of value.' Edward Witten, Institute for Advanced Study, Princeton'Every single one of these pages is packed with information. … this book grew out of lectures Schwartz has given to graduate students at Harvard, and it becomes very clear that he is well aware of possible pitfalls and problems of understanding that students may have. … The first part of the book should be accessible for beginning graduate students who have mastered quantum mechanics, special relativity and electrodynamics. The second part of the book will also be useful for advanced students and researchers who want to learn how to perform calculations in the standard model. … Schwartz has done a great job in presenting his view on this complex matter, and I wish this book had already existed when I learned the subject! I recommend it to anyone dedicated to learning quantum field theory and the physics of the standard model.' Thomas Peters, Contemporary PhysicsTable of ContentsPart I. Field Theory: 1. Microscopic theory of radiation; 2. Lorentz invariance and second quantization; 3. Classical Field Theory; 4. Old-fashioned perturbation theory; 5. Cross sections and decay rates; 6. The S-matrix and time-ordered products; 7. Feynman rules; Part II. Quantum Electrodynamics: 8. Spin 1 and gauge invariance; 9. Scalar QED; 10. Spinors; 11. Spinor solutions and CPT; 12. Spin and statistics; 13. Quantum electrodynamics; 14. Path integrals; Part III. Renormalization: 15. The Casimir effect; 16. Vacuum polarization; 17. The anomalous magnetic moment; 18. Mass renormalization; 19. Renormalized perturbation theory; 20. Infrared divergences; 21. Renormalizability; 22. Non-renormalizable theories; 23. The renormalization group; 24. Implications of Unitarity; Part IV. The Standard Model: 25. Yang–Mills theory; 26. Quantum Yang-Mills theory; 27. Gluon scattering and the spinor-helicity formalism; 28. Spontaneous symmetry breaking; 29. Weak interactions; 30. Anomalies; 31. Precision tests of the standard model; 32. QCD and the parton model; Part V. Advanced Topics: 33. Effective actions and Schwinger proper time; 34. Background fields; 35. Heavy-quark physics; 36. Jets and effective field theory; Appendices; References; Index.

Read more less

Book SynopsisTrade Review"Stimulating reading" --New ScientistTable of ContentsFundamental principles of theoretical physics; The Gibbs distribution; Ideal gases; Solids; Non-ideal gases; Solutions; Chemical reactions; Fluctuations; Surfaces.

Read more less

Book SynopsisThe book provides a non-specialist introduction to the reasons why we can make sense of the world around and within us, facing the oceans of complexity which inhabit both. The book provides a scientific and easily accessible description of some of the key physical mechanisms by which the wonderful gift of life materializes in the natural world.Trade ReviewThis book gives a nontechnical survey of complex systems, strongly emphasizing the connection of fundamental physics to biology. Starting with a very nice foundational discussion, the Succi goes on to look at the connection developed by Boltzmann between microscopic physics and macroscopic biology...the thoughtful reader will be rewarded. * Choice *This is an interesting exploration of how the complex macroscopic world is derivable from microscopic physics, and how the non-linearity of complex systems leads to issues of predictability and at the same time accounts for physical structures. The author gives personal comments on his own appreciation of the physics throughout the book, as well as a thought-provoking conclusion suggesting that our experience of time is a consequence of the emergence of complexity. * E. Kincanon, Gonzaga University, CHOICE connect *Complexity is between the two infinities "very big" and "very small" - always a fascinating subject. The author explains things in a very easy-going way, and adds some entertaining stories and thoughts which make it entertaining to read. * Christian Beck, Queen Mary University of London *Complexity science is of critical importance in the modern world, but not on the radar screen of the average reader. This book, designed for the general public, is intended to fix that problem in a very enjoyable and entertaining style. * Bruce Boghosian, Tufts University *A fresh and competent view on a very interesting scientific topic. * Guido Caldarelli, School IMT Alti Studi Lucca *Sauro Succi's new book is both superb and essential. Succi, with clarity and wit, takes us from quarks and Boltzmann to soft matter - precisely the frontier of physics and life. Someone said, “There is no truth beyond magic”. Succi shows us the magic at the edge of life. * Stuart Kauffman, MacArthur Fellow, Fellow of the Royal Society of Canada, Gold Medal Accademia Lincea *Table of ContentsPreface Part 1: COMPLEXITY 1: Introducing Complexity 2: The Guiding Barriers 3: Competition and Cooperation 4: Nonlinearity, The Mother of Complexity 5: The Dark Side of Nonlinearity 6: The Bright Side of Nonlinearity 7: Networks, The Fabric of Complexity Part 2: THE SCIENCE OF CHANGE 8: Good Old Thermodynamics 9: The Man Who Trusted Atoms 10: Biological Escapes 11: Cosmological Escapes 12: Free Energy Part 3: THE PHYSICS-BIOLOGY INTERFACE 13: Survival in Molecular Hyperland, the Ozland Valleys 14: Free Energy Funnels 15: Soft Matter, The Stu that Dreams Are Made Of 16: Water, the Wonderuid Part 4: COMPLEXITY AND THE HUMAN CONDITION 17: Time and the Complexity of the Human Condition 18: Harness the Hybris: Hallelujah! 19: Appendices Epilogue Acknowledgements References

Read more less

Book SynopsisThis book explains the ideas and techniques of statistical mechanics-the theory of condensed matter-in a simple and progressive way. The text starts with the laws of thermodynamics and simple ideas of quantum mechanics. The conceptual ideas underlying the subject are explained carefully; the mathematical ideas are developed in parallel to give a coherent overall view. The text is illustrated with examples not just from solid state physics, but also from recent theories of radiation from black holes and recent data on the background radiation from the Cosmic background explorer. In this second edition, slightly more advanced material on statistical mechanics is introduced, material which students should meet in an undergraduate course. As a result the new edition contains three more chapters on phase transitions at an appropriate level for an undergraduate student. There are plenty of problems at the end of each chapter, and brief model answers are provided for odd-numbered problems. From reviews of the first edition: ''...Introductory Statistical Mechanics is clear and crisp and takes advantage of the best parts of the many approaches to the subject'' Physics Today

Read more less

Book SynopsisThe book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.Table of ContentsPart I: Newtonian Mechanics 1: Introduction 2: Newton's Three Laws 3: Energy and Work 4: Introductory Rotational Dynamics 5: The Harmonic Oscillator 6: Wave Mechanics & Elements of Mathematical Physics Part II: Langrangian Mechanics 7: Introduction 8: Coordinates & Constraints 9: The Stationary Action Principle 10: Constrained Langrangian Mechanics 11: Point Transformations in Langrangian Mechanics 12: The Jacobi Energy Function 13: Symmetries & Langrangian-Hamiltonian-Jacobi Theory 14: Near-Equilibrium Oscillations 15: Virtual Work & d'Alembert's Principle Part III: Canonical Mechanics 16: Introduction 17: The Hamiltonian & Phase Space 18: Hamiltonian's equations & Routhian Reduction 19: Poisson Brackets & Angular momentum 20: Canonical & Gauge Transformations 21: Hamilton-Jacobi Theory 22: Liouville's Theorem & Classical Statistical Mechanics 23: Constrained Hamiltonian Dynamics 24: Autonomous Geometrical Mehcanics 25: The Structure of Phase Space 26: Near-Integrable Systems Part IV: Classical Field Theory 27: Introduction 28: Langrangian Field Theory 29: Hamiltonian Field Theory 30: Clssical Electromagnetism 31: Neother's Theorem for Fields 32: Classical Path-Integrals Part V: Preliminary Mathematics 33: The (Not so?) Basics 34: Matrices 35: Partial Differentiation 36: Legendre Transformations 37: Vector Calculus 38: Differential equations 39: Calculus of Variations Part VI: Advanced Mathematics 40: Linear Algebra 41: Differential Geometry Part VII: Exam Style Questions Appendix A: Noether's Theorem Explored Appendix B: The Action Principle Explored Appendix C: Useful Relations Appendxi D: Poisson & Nambu Brackets Explored Appendix: Canonical Transformations Explored Appendix F: Action-Angle Variables Explored Appendix G: Statistical Mechanics Explored Appendix H: Biographies

Read more less

Book SynopsisQuantum theory (QT) is the best, most useful physics theory ever invented. For example, ubiquitous are cell phones, laser scanners, medical imagers, all inventions depending on QT. However, there is something deeply wrong with QT. It describes the probabilities of what happens, but it does not give a description of what actually happens. Most (but not all) physicists are not worried about this flaw, the probabilities are good enough for them. Other physicists, the author included, believe that is not good enough. The purpose of physics is to describe reality. To not do so is to abandon ''the great enterprise'' (John Bell). This book shows one way to alter QT so that the new theory does describe what actually happens. This theory, created over three decades ago, has been called the ''Continuous Spontaneous Localization'' (CSL) theory.Many experiments over this period have tested CSL, and so far it is neither confirmed nor refuted. This book shows how CSL works, and discusses its consequTrade ReviewA most welcome addition to the physics literature written with extreme care and covering the objective subject matter in a thorough professional and methodical manner. * Daniel Sudarsky, UNAM, Mexico City *A book of very high quality presenting a way of modifying quantum mechanics to remove some of its most serious problems (especially the measurement problem). * Kelvin McQueen, Chapman University, Orange, California *Pearle is the master of this material and writes with beautiful clarity and well-judged occasional witticisms and side-remarks. His experience as teacher, as well as researcher, shows in the vivid explanations, and the careful and consistent level of detail in the exposition. * Jeremy Butterfield, University of Cambridge *Table of Contents1: Introduction 2: Continuous Spontaneous Localization (CSL) Theory 3: CSL Theory Refinements 4: Non-Relativistic CSL 5: Spontaneous Localization (SL) Theory 6: Some Experiments Testing CSL 7: Interpretational Remarks 8: Supplement to Chapter 1 9: Supplement to Chapter 2 10: Supplement to Chapter 3 11: Supplement to Chapter 4 12: Supplement to Chapter 5 13: Supplement to Chapter 6 14: Supplement to Chapter 7 15: A Stochastic Differential Equation Cookbook 16: CSL Expressed as a Schrodinger Stochastic DE 17: Applying the CSL Stratonovich Equation to the Free Particle Undergoing Collapse in Position 18: Applying the CSL Stratonovich Equation to the Harmonic Oscillator Undergoing Collapse in Position Appendix A: Gaussians Appendix B: Random Walk Appendix C: Brownian Motion/Wiener Process Appendix D: White Noise Appendix E: White Noise Field Appendix F: Density Matrix Appendix G: Theoretical Constraint Calculations

Read more less

Book SynopsisThis classic graduate lecture note volume on statistical mechanics focuses on Physics, rather than mathematics. It provides a concise introduction to basic concepts and a clear presentation of difficult topics, while challenging the student to reflect upon as yet unanswered questions.Table of ContentsFront Matter -- INTRODUCTION TO STATISTICAL MECHANICS -- DENSITY MATRICES -- PATH INTEGRALS -- CLASSICAL SYSTEM OF N PARTICLES -- ORDER-DISORDER THEORY -- CREATION AND ANNIHILATION OPERATORS -- SPIN WAVES -- POLARON PROBLEM -- ELECTRON GAS IN A METAL -- SUPERCONDUCTIVITY -- SUPERFLUIDITY

Read more less

Book SynopsisComplex networks are typically not homogeneous, as they tend to display an array of structures at different scales. A feature that has attracted a lot of research is their modular organisation, i.e., networks may often be considered as being composed of certain building blocks, or modules. In this Element, the authors discuss a number of ways in which this idea of modularity can be conceptualised, focusing specifically on the interplay between modular network structure and dynamics taking place on a network. They discuss, in particular, how modular structure and symmetries may impact on network dynamics and, vice versa, how observations of such dynamics may be used to infer the modular structure. They also revisit several other notions of modularity that have been proposed for complex networks and show how these can be related to and interpreted from the point of view of dynamical processes on networks.Table of Contents1. Introduction; 2. Background Material; 3. Modularity, community detection and clustering in networks; 4. Time scale separation and dynamics on modular networks; 5. Symmetries and dynamics on modular networks; 6. Dynamical methods for assortative communities; 7. Dynamical methods for disassortative communities and general block structures; 8. Perspectives; References.

Read more less

This book presents an innovative unified approach to the statistical foundations of entropy and the fundamentals of equilibrium statistical mechanics. These intimately related subjects are often developed in a fragmented historical manner which obscures the essential simplicity of their logical structure. In contrast, this book critically reassesses and systematically reorganizes the basic concepts into a simpler sequential framework which reveals more clearly their logical relationships. The inherent indistinguishability of identical particles is emphasized, and the resulting unification of classical and quantum statistics is discussed in detail.The discussion is focused entirely on fundamental concepts, so applications are omitted. The book is written at the advanced undergraduate or beginning graduate level, and will be useful as a concise supplement to conventional books and courses in statistical mechanics, thermal physics, and thermodynamics. It is also suitable for self-study by those seeking a deeper and more detailed analysis of the fundamentals.

Read more less

Book SynopsisThe study of networks, including computer networks, social networks, and biological networks, has attracted enormous interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on an unprecedented scale, and the development of new theoretical tools has allowed us to extract knowledge from networks of many different kinds. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.Topics covered include the measurement of networks; methods for analyzing network data, including methods developed in physics, statistics, and sociology; fundamentals of graph theory; computer algorithms; mathematical models of networks, including random graph models and generative models; and theories of dynamical processes taking place on networks.Trade ReviewThis is the definitive book on networks, friendly enough for anyone to read and serious enough for researchers to find their way. [Newman] is one of the founders and leaders of the field and has updated the book with cutting-edge topics. * Professor Cris Moore, Santa Fe Institute *This is the definitive book on network science, by one of its most brilliant researchers and graceful expositors. The second edition of Mark Newman's Networks is clear, comprehensive, and fascinating. * Steven Strogatz, Department of Mathematics, Cornell University, USA *This is an excellent textbook by one of the preeminent scholars in the study of networks. I draw heavily from it when teaching my undergraduate course on networks, and I am very pleased to see a new edition of the book. Newman's clear exposition shines through in this textbook. * Mason Porter, Department of Mathematics, UCLA, USA *An extraordinarily comprehensive and clear exposition of network science from one of the giants in the field. Newman succeeds in making accessible to a broad readership even the most technical content. * Santo Fortunato, School of Informatics and Computing, Indiana University *Reviews from previous edition:Networks accomplishes two key goals: It provides a comprehensive introduction and presents the theoretic backbone of network science. [] The book is balanced in its presentation of theoretical concepts, computational techniques, and algorithms. The level of difficulty increases which each chapter [which] makes the book particularly valuable to physics students who wish to acquire a solid foundation based on their knowledge of basic linear algebra, calculus, and differential equations. * Physics Today *Newman has written a wonderful book that gives an extensive overview of the broadly interdisciplinary network-related developments that have occured in many fields, including mathematics, physics, computer science, biology, and the social sciences ... Overall, a valuable resource covering a wide-randing field. * Choice *Likely to become the standard introductory textbook for the study of networks [...] Overall, this is an excellent textbook for the growing field of networks. It is cleverly written and suitable as both an introduction for undergraduate students (particularly Parts 1 to 3) and as a roadmap for graduate students. [...] Being highly self-contained, computer scientists and professionals from other fields can also use the book - in fact, the author himself is a physicist. In short, this book is a delight for the inquisitive mind. * Computing Reviews *This book brings together, for the first time, the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong connections between work in different subject areas. * CERN Courier *Table of Contents1: Introduction Part I: The empirical study of networks 2: Technological networks 3: Networks of information 4: Social networks 5: Biological networks Part II: Fundamentals of network theory 6: Mathematics of networks 7: Measures and metrics 8: Computer algorithms 9: Network statistics and measurement error 10: The structure of real-world networks Part III: Network models 11: Random graphs 12: The configuration model 13: Models of network formation Part IV: Applications 14: Community structure 15: Percolation and network resilience 16: Epidemics on networks 17: Dynamical systems on networks 18: Network search

Read more less

Book SynopsisReplaces the contrived application of the quantum master equation with a satisfactory treatment of quantum fluctuations. This work covers the fluctuations and stochastic methods for describing them. It is of interest to students and researchers in applied mathematics, physics and physical chemistry.Table of ContentsI. Stochastic variablesII. Random eventsIII. Stochastic processesIV. Markov processesV. The master equationVI. One-step processesVII. Chemical reactionsVIII. The Fokker-Planck equationIX. The Langevin approachX. The expansion of the master equationXI. The diffusion typeXII. First-passage problemsXIII. Unstable systemsXIV. Fluctuations in continuous systemsXV. The statistics of jump eventsXVI. Stochastic differential equationsXVII. Stochastic behavior of quantum systems

Read more less

Book SynopsisThermal physics deals with collections of large numbers of particles - typically 10 to the 23rd power or so. Examples include the air in a balloon, the water in a lake, the electrons in a chunk of metal, and the photons given off by the sun. We can''t possibly follow every detail of the motions of so many particles. So in thermal physics we assume that these motions are random, and we use the laws of probability to predict how the material as a whole ought to behave. Alternatively, we can measure the bulk properties of a material, and from these infer something about the particles it is made of.This book will give you a working understanding of thermal physics, assuming that you have already studied introductory physics and calculus. You will learn to apply the general laws of energy and entropy to engines, refrigerators, chemical reactions, phase transformations, and mixtures. You will also learn to use basic quantum physics and powerful statistical methods to predict in detail how teTrade ReviewI am a great admirer of Schroeder's book. While writing a graduate textbook in the subject, I studied many books in statistical mechanics, at various levels of sophistication. Of these, Schroeder's text stood out. Indeed, it was the only one I envied -- his sense of fun, his vivid explanations, and his deep insights into conceptual issues. * James P. Sethna, Cornell University, author of 'Statistical Mechanics: Entropy, Order Parameters, and Complexity', Second Edition, OUP 2021 *Table of ContentsPreface Part I: Fundamentals 1: Energy in Thermal Physics 2: The Second Law 3: Interactions and Implications Part II: Thermodynamics 4: Engines and Refrigerators 5: Free Energy and Chemical Thermodynamics Part III: Statistical Mechanics 6: Boltzmann Statistics 7: Quantum Statistics 8: Systems of Interacting Particles Appendix A: Elements of Quantum Mechanics Appendix B: Mathematical Results Suggested Reading Reference Data Index

Read more less

Book SynopsisThis book provides a critical update of the most recent and innovative developments of avalanche science. It aims at re-founding avalanche science on clear scientific bases, from field observations and experiments up to mathematical and physical analysis and modeling. In this respect, it stands in a still unoccupied but fundamental niche amidst the abundant avalanche literature.In the current context of a accelerated climate warming, the book also discusses possible evolutions of snow cover extent and stability. It also shows how the present analysis can be extended, in mountainous areas, to other gravitationally induced phenomena that are likely to take over from avalanches under specific circumstances.The text is supported by online links to field experiments and lectures on triggering mechanisms, risk management, and decision making.Trade ReviewProvides the best overall understanding of avalanche science in the most practical way. * Henry Schniewind, Director of Henry's Avalanche Talk (HAT), London and Val d'Isère *Table of ContentsINTRODUCTION SNOW, AN INTRIGUING, COMPLEX AND CHANGEABLE SOLID 2.1: From ice to snow 2.2: Snow crystals 2.3: From snowfalls to snow layers 2.4: Snow as a granular medium 2.5: Snow as a porous medium: the concept of percolation BASICS OF DEFORMATION, FRACTURE AND FRICTION PROCESSES 3.1: Deformation of solids 3.2: Fracture initiation and extension 3.3: Griffith's criterion 3.4: The brittle to ductile transition 3.5: Coulomb's law of friction SLAB AVALANCHE RELEASE: DATA AND FIELD EXPERIMENTS 4.1: Geometry and dynamical characteristics 4.2: Statistical aspects: scale invariance 4.3: The weak layer, starting point for slab avalanche release 4.4: Stability and Bridging indexes SLAB AVALANCHE MODELING 5.1: Old myths and beliefs to shoot down 5.2: Basis for modeling 5.3: Statistical approach: Playing with cellular 5.4: Sliding or sticking? 5.5: Slab avalanche release in four steps SUPERFICIAL AND FULL-DEPTH AVALANCHES 6.1: Loose snow avalanches 6.2: Full depth avalanches 6.3: Summary SNOW AND AVALANCHES IN A CLIMATE WARMING CONTEXT 7.1: Climate change 7.2: Possible consequences on avalanching SUMMARY AND CONCLUSION APPENDIX A COMPLEXITY AND CRITICAL PHENOMENA A1: From simple to complex systems A2: Scale invariance and self-organized criticality APPENDIX B MODELING A FLUID TO SOLID PHASE TRANSITION IN SNOW WEAK-LAYERS. B1: A fluid to solid phase transition in healable granular materials B2: Application to slab avalanche release APPENDIX C STABILITY OF A SINTERED WEAK LAYER DISK SURROUNDED BY A RING-SHAPED FLUID WEAK LAYER ZONE

Read more less

Book SynopsisA thoroughly modern graduate-level introduction to the theory of critical behaviour.Trade Review' … a short but very intelligible textbook well equilibrated by a variety of material.' V. Zagrebnov, Zentralblatt Math'Supported with interesting exercises at the end of each chapter, Cardy's book is likely to prove a popular introduction to this demanding but extraordinarily successful method for probing many complex phenomena.' Robert Matthews New ScientistTable of ContentsPreface; 1. Phase transitions in simple systems; 2. Mean field theory; 3. The renormalization group idea; 4. Phase diagrams and fixed points; 5. The perturbative renormalization group; 6. Near two dimensions; 7. Surface critical behaviour; 8. Random systems; 9. Polymer statistics; 10. Critical dynamics; 11. Conformal symmetry; Appendix: Gaussian integration; Selected bibliography; Index.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

Book Synopsis

Read more less

Book SynopsisBased on Prof. Lüst's Masters course at the University of Munich, this book begins with a short introduction to general relativity. It then presents black hole solutions, and discusses Penrose diagrams, black hole thermodynamics and entropy, the Unruh effect, Hawking radiation, the black hole information problem, black holes in supergravity and string theory, the black hole microstate counting in string theory, asymptotic symmetries in general relativity, and a particular quantum model for black holes. The book offers an up-to-date summary of all the pertinent questions in this highly active field of physics, and is ideal reading for graduate students and young researchers.Table of ContentsSpecial relativity.- Riemannian geometry.- Introduction to general relativity.- General relativity.- Einstein's equations.- Black holes.- Kruskal-Szekeres coordinates and geodesics of the Schwarzschild black hole.- Conformal compactifications and Penrose diagrams.- Penrose diagrams of charged & rotating black holes.- Rotating black holes and black hole mechanics.- Black hole mechanics and thermodynamics.- Black hole thermodynamics .- Black holes and entropy.- Hawking and Unruh radiation.- Quantum field theory in curved space-time backgrounds.- Unruh und Hawking effect.- Information loss paradox.- Solitons in String Theory.- Brane solutions.- Dimensional reduction and black holes.- Black holes in string theory from p/D-branes.- Black hole microstate counting.- Asymptotic symmetries in general relativity and black hole hair.- Asymptotic symmetries of 4D space-time geometries.- BMS charges.- The gravitational memory effect.- Current research on BMS-like transformations and charges of black holes.- Quantum hair and quantum black hole vacua.

Read more less

Book SynopsisThis book offers an informal, easy-to-understand account of topics in modern physics and mathematics. The focus is, in particular, on statistical mechanics, soft matter, probability, chaos, complexity, and models, as well as their interplay. The book features 28 key entries and it is carefully structured so as to allow readers to pursue different paths that reflect their interests and priorities, thereby avoiding an excessively systematic presentation that might stifle interest. While the majority of the entries concern specific topics and arguments, some relate to important protagonists of science, highlighting and explaining their contributions. Advanced mathematics is avoided, and formulas are introduced in only a few cases. The book is a user-friendly tool that nevertheless avoids scientific compromise. It is of interest to all who seek a better grasp of the world that surrounds us and of the ideas that have changed our perceptions.Trade Review“Each topic is discussed in a brief chapter, at a technical level that could be followed by first-year students of physics and mathematics, but also by wider parts of the public. Each chapter contains a statement of the topic, a brief history, and describes a number of examples … . The book makes a pleasant reading, full of wit and of surprising turns. I think that it can be useful to the general reader … motivate students … .” (Luca Peliti, Journal of Statistical Physics, Vol. 185, 2021)Table of ContentsChapter 1 - Introduction.- Chapter 2 - Atoms, Irreversibility, Probability, Statistical Mechanics, Entropy.- Chapter 3 - Probability, Entropy, Chaos.- Chapter 4 - Chaos, Prediction.- Chapter 5 - Prediction, Turbulence, Models.- Chapter 6 - Models, Richardson.- Chapter 7 - Boltzmann, Statistical Mechanics, Brownian Motion.- Chapter 8 - Boltzmann, Atoms, Statistical Mechanics, Mesoscale Systems.- Chapter 9 - Prediction: Chaos, Poincaré, Richardson, Models, Big data.- Chapter 10 - Statistical Mechanics: Atoms, Boltzmann, Maxwell.

Read more less

Book SynopsisThis book offers an introduction to statistical mechanics, special relativity, and quantum physics. It is based on the lecture notes prepared for the one-semester course of "Quantum Physics" belonging to the Bachelor of Science in Material Sciences at the University of Padova.The first chapter briefly reviews the ideas of classical statistical mechanics introduced by James Clerk Maxwell, Ludwig Boltzmann, Willard Gibbs, and others. The second chapter is devoted to the special relativity of Albert Einstein. In the third chapter, it is historically analyzed the quantization of light due to Max Planck and Albert Einstein, while the fourth chapter discusses the Niels Bohr quantization of the energy levels and the electromagnetic transitions. The fifth chapter investigates the Schrodinger equation, which was obtained by Erwin Schrodinger from the idea of Louis De Broglie to associate to each particle a quantum wavelength. Chapter Six describes the basic axioms of quantum mechanics, which were formulated in the seminal books of Paul Dirac and John von Neumann. In chapter seven, there are several important application of quantum mechanics: the quantum particle in a box, the quantum particle in the harmonic potential, the quantum tunneling, the stationary perturbation theory, and the time-dependent perturbation theory. Chapter Eight is devoted to the study of quantum atomic physics with special emphasis on the spin of the electron, which needs the Dirac equation for a rigorous theoretical justification. In the ninth chapter, it is explained the quantum mechanics of many identical particles at zero temperature, while in Chapter Ten the discussion is extended to many quantum particles at finite temperature by introducing and using the quantum statistical mechanics. The four appendices on Dirac delta function, complex numbers, Fourier transform, and differential equations are a useful mathematical aid for the reader.Table of ContentsTable of Contents1 Classical Statistical Mechanics1.1 Kinetic Theory of Gases 1.1.1 Maxwell Distribution of Velocities1.1.2 Maxwell-Boltzmann Distribution of Energies 1.1.3 Single-Particle Density of States 1.2 Statistical Ensembles of Gibbs 1.2.1 Microcanonical Ensemble 1.2.2 Canonical Ensemble 1.2.3 Grand Canonical Ensemble 1.2.4 Many-Particle Density of States 2 Special Relativity 2.1 Lorentz Transformations 2.2 Einstein Postulates 2.2.1 Gedanken Experiment of Einstein 2.3 Relativistic Mechanics 2.3.1 Relativistic Kinematics 2.3.2 Relativistic Dynamics 3 Quantum Properties of Light 3.1 Black-Body Radiation 3.1.1 Ideal Black Body 3.1.2 Derivation of the Planck Law 3.2 Photoelectric E ect 3.2.1 Experimental Data 3.2.2 Theoretical Explanation 3.3 Energy and Linear Momentum of a Photon 3.4 Compton E ect 3.4.1 Theoretical Explanation 4 Quantum Energy Levels of Atoms 4.1 Energy Spectra 4.1.1 Energy Spectrum of Hydrogen Atom 4.2 Hydrogen Atom of Bohr4.2.1 Derivation of the Bohr Results 4.3 Energy Levels and Photons 4.4 Electromagnetic Transitions 5 Wave Properties of Matter 5.1 De Broglie Wavelength 5.1.1 Explaining the Bohr Quantization 5.2 Experiment of Davisson and Germer 5.3 Double-Slit Experiment with Light5.4 Double-Slit Experiment with Electrons 5.5 Old Quantum Mechanics of Bohr, Wilson and Sommerfeld5.6 Matrix Quantum Mechanics of Heisenberg, Born and Jordan 5.7 Wave Quantum Mechanics of Schrodinger 5.7.1 Derivation of the Schr odinger Equation 5.8 Formal Quantization Rules5.8.1 Schrodinger Equation for a Free Particle 5.8.2 Schrodinger Equation for a Particle in an External Potential 5.9 Stationary Schr odinger Equation6 Axioms of Quantum Mechanics 6.1 Matrix Mechanics 6.2 Axioms of Quantum Mechanics7 Applications of Quantum Mechanics 7.1 Quantum Particle in a One-Dimensional Box Potential7.2 Quantum Particle in a One-Dimensional Harmonic Potential8 Quantum Physics of Atoms 8.1 Quantum Particle in a Separable Potential 8.1.1 Quantum Particle in the Harmonic Potential 8.2 Dirac Notation for a Quantum State8.3 Electron in the Hydrogen Atom 8.3.1 Schrodinger Equation in Spherical Polar Coordinates 8.3.2 Selection Rules 8.4 Pauli Exclusion Principle and the Spin8.5 Semi-Integer and Integer Spin: Fermions and Bosons8.6 The Dirac Equation 8.6.1 The Pauli Equation and the Spin8.6.2 Dirac Equation with a Central Potential 8.6.3 Relativistic Hydrogen Atom and Fine Splitting 8.6.4 Relativistic Corrections to the Schrodinger Hamiltonian9 Quantum Mechanics of Many-Body Systems 9.1 Identical Quantum Particles 9.1.1 Spin-Statistics Theorem9.2 Non-Interacting Identical Particles9.2.1 Atomic Shell Structure and the Periodic Table of the Elements 9.3 Interacting Identical Particles9.3.1 Variational Principle9.3.2 Electrons in Atoms and Molecules10 Quantum Statistical Mechanics 10.1 Quantum Statistical Ensembles 10.1.1 Quantum Microcanonical Ensemble 10.1.2 Quantum Canonical Ensemble 10.1.3 Quantum Grand Canonical Ensemble 10.2 Bosons and Fermions at Finite Temperature 10.2.1 Gas of Photons at Thermal Equlibrium10.2.2 Gas of Massive Bosons at Thermal Equlibrium 10.2.3 Gas of Non-Interacting Fermions at Zero TemperatureAppendix A Dirac Delta Function A.1 The Heaviside Step Function A.2 The Strange Function of Dirac A.2.1 Dirac Function and the Integrals A.3 Dirac Function in D Spatial Dimensions Appendix B Complex Numbers B.1 Set of Complex Numbers B.2 Gauss Plane B.2.1 Polar Representation B.3 Euler Formula B.3.1 Proof of the Euler Formula B.3.2 De Moivre FormulaB.4 Fundamental Theorem of Algebra B.5 Complex Functions Appendix C Fourier Transform C.1 Geometric and Taylor SeriesC.2 Fourier Series .C.2.1 Complex Representation of the Fourier Series C.3 Fourier Integral C.3.1 Properties of the Fourier Transform C.3.2 Fourier Transform and Uncertanty TheoremC.4 Fourier Transform of Space-Time FunctionsAppendix D Di erential equations D.1 First-Order Ordinary Di erential EquationsD.1.1 Separation of Variables D.2 Second-Order Ordinary Di erential Equations D.3 Newton Law as a Second-Order ODE D.4 Partial Di erential Equations D.4.1 Wave Equation D.4.2 Di usion Equation Bibliography

Read more less

Book SynopsisThis book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.Trade Review“I would say … that the author’s use of an interdisciplinary approach in presenting the field of spatial data modeling is what makes this book truly unique. … I believe anyone who is willing to learn about and understand concepts, assumptions and methods behind spatial data modeling would benefit from having a copy of this outstanding book.” (Sandra De Iaco, Mathematical Geosciences, February 12, 2021)Table of ContentsIntroduction.- Preliminary Remarks.- Why Random Fields?.- Notation and Definitions.- Noise and Errors.- Spatial Data and Basic Processing Procedures.- A Personal Selection of Relevant Books.- Trend Models and Estimation.- Empirical Trend Estimation.- Regression Analysis.- Global Trend Models.- Local Trend Models.- Trend Estimation based on Physical Information.- Trend Based on the Laplace Equation.- Basic Notions of Random Fields.- Introduction.- Single-Point Description.- Stationarity and Statistical Homogeneity.- Variogram versus Covariance.- Permissibility of Covariance Functions.- Permissibility of Variogram Functions.- Additional Topics of Random Field Modeling.- Ergodicity.- Statistical Isotropy.- Anisotropy.- Anisotropic Spectral Densities.- Multipoint Description of Random Fields.- Geometric Properties of Random Fields.- Local Properties.- Covariance Hessian Identity and Geometric Anisotropy.- Spectral Moments.- Length Scales of Random Fields.- Fractal Dimension.- Long-Range Dependence.- Intrinsic Random Fields.- Fractional Brownian Motion.- Classification of Random Fields.- Gaussian Random Fields.- Multivariate Normal Distribution.- Field Integral Formulation.- Useful Properties of Gaussian Random Fields.- Perturbation Theory for Non-Gaussian Probability Densities.- Non-stationary Covariance Functions.- Further Reading.- Random Fields based on Local Interactions.- Spartan Spatial Random Fields.- Two-point Functions and Realizations.- Statistical and Geometric Properties.- Bessel-Lommel Covariance Functions.- Lattice Representations of Spartan Random Fields.- Introduction to Gauss-Markov Random Fields.- From Spartan Random Fields to Gauss-Markov Random Fields.- Lattice Spectral Density.- SSRF Lattice Moments.- SSRF Inverse Covariance Operator on Lattices.- Spartan Random Fields and Langevin Equations.- Introduction to Stochastic Differential Equations.- Classical Harmonic Oscillator.- Stochastic Partial Differential Equations.- Spartan Random Fields and Stochastic Partial Differential Equations.- Covariance and Green’s functions.- Whittle-Matérn Stochastic Partial Differential Equation.- Diversion in Time Series.- Spatial Prediction Fundamentals.- General Principles of Linear Prediction.- Deterministic Interpolation.- Stochastic Methods.- Simple Kriging.- Ordinary Kriging.- Properties of the Kriging Predictor.- Topics Related to the Application of Kriging.- Evaluating Model Performance.- More on Spatial Prediction.- Linear Generalizations of Kriging.- Nonlinear Extensions of Kriging.- Connections with Gaussian Process Regression.- Bayesian Kriging.- Continuum Formulation of Linear Prediction.- The “Local-Interaction” Approach.- Big Spatial Data.- Basic Concepts and Methods of Estimation.- Estimator Properties.- Estimating the Mean with Ordinary Kriging.- Variogram Estimation.- Maximum Likelihood Estimation.- Cross Validation.- More on Estimation.- The Method of Normalized Correlations.- The Method of Maximum Entropy.- Stochastic Local Interactions.- Measuring Ergodicity.- Beyond the Gaussian Models.- Trans-Gaussian Random Fields.- Gaussian Anamorphosis.- Tukey g-h Random Fields.- Transformations based on Kappa Exponentials.- Hermite Polynomials.- Multivariate Student’s t-distribution.- Copula Models.- The Replica Method.- Binary Random Fields.- The Indicator Random Field.- Ising Model.- Generalized Linear Models.- Simulations.- Introduction.- Covariance Matrix Factorization.- Spectral Simulation Methods.- Fast-Fourier-Transform Simulation.- Randomized Spectral Sampling.- Conditional Simulation based on Polarization Method.- Conditional Simulation based on Covariance Matrix Factorization.- Monte Carlo Methods.- Sequential Simulation of Random Fields.- Simulated Annealing.- Karhunen-Loève Expansion.- Karhunen-Loève Expansion of Spartan Random Fields.- Epilogue.- A Jacobi’s Transformation Theorems.- B Tables of SSRF Properties.- C Linear Algebra Facts.- D Kolmogorov-Smirnov Test.- Glossary.- References.- Index.

Read more less

Book SynopsisThe aim of this book is to present Classical Thermodynamics in a unified way, from the most fundamental principles to non-uniform systems, thereby requiring the introduction of coarse graining methods, leading for instance to phase field methods. Solutions thermodynamics and temperature-concentration phase diagrams are covered, plus also a brief introduction to statistical thermodynamics and topological disorder. The Landau theory is included along with a general treatment of multicomponent instabilities in various types of thermodynamic applications, including phase separation and order-disorder transitions. Nucleation theory and spinodal decomposition are presented as extreme cases of a single approach involving the all-important role of fluctuations.In this way, it is hoped that this coverage will reconcile in a unified manner techniques generally presented separately in physics and materials texts.

Read more less

Book SynopsisUnraveling the mystery of the negative thermal expansion of liquid water has been a challenge for scientists for centuries. Various theories have been proposed so far, but none has been able to solve this mystery. Since the thermodynamic properties of matter are determined by the interaction between particles, the mystery can be solved fundamentally if the thermodynamic physical quantities using the laws of thermodynamics and statistical mechanics are determined, the experimental results are reproduced, and the phenomena in relation to the shape of the interaction between particles are elucidated. In this sense, this book has fundamentally unraveled this mystery. In addition, it discusses the mysteries of isothermal compressibility, structural diversity, as well as liquefaction and boiling points of water in relation to the shape of the interaction between particles. It carefully explains the analysis and calculation methods so that they can be easily understood by the readers. Table of Contents1. Statistical Mechanics and Thermodynamics of Fluids 2. Strange Temperature Change of Water Density 3. Fundamental Clarification of Thermodynamic Phenomena in Water 4. Variety of Shapes of Water-Molecule Interactions 5. Ornstein-Zernike Equation 6. Calculation Procedure of SCOZA 7. Pressure and Chemical Potential 8. Thermodynamic Properties of Subcritical Fluids

Read more less

Book SynopsisZwiebach is once again faithful to his goal of making string theory accessible to undergraduates. This text now includes AdS/CFT correspondence, as well introducing superstrings. With almost 300 problems and exercises it is perfectly suited for introductory courses for students with a background in physics.Trade Review'A refreshingly different approach to string theory that requires remarkably little previous knowledge of quantum theory or relativity. This highlights fundamental features of the theory that make it so radically different from theories based on point-like particles. This book makes the subject amenable to undergraduates but it will also appeal greatly to beginning researchers who may be overwhelmed by the standard textbooks.' Michael Green, University of Cambridge'Barton Zwiebach has written a careful and thorough introduction to string theory that is suitable for a full-year course at the advanced undergraduate level. There has been much demand for a book about string theory at this level, and this one should go a long way towards meeting that demand.' John Schwarz, California Institute of Technology'There is a great curiosity about string theory, not only among physics undergraduates but also among professional scientists outside of the field. This audience needs a text that goes much further than the popular accounts but without the full technical detail of a graduate text. Zwiebach's book meets this need in a clear and accessible manner. It is well-grounded in familiar physical concepts, and proceeds through some of the most timely and exciting aspects of the subject.' Joseph Polchinski, University of California, Santa Barbara'Zwiebach, a respected researcher in the field and a much beloved teacher at MIT, is truly faithful to his goal of making string theory accessible to advanced undergraduates – the test develops intuition before formalism, usually through simplified and illustrative examples … Zwiebach avoids the temptation of including topics that would weigh the book down and make many students rush it back to the shelf and quit the course.' Physics Today'… well-written … takes us through the hottest topics in string theory research, requiring only a solid background in mechanics and some basic quantum mechanics. … This is not just one more text in the ever-growing canon of popular books on string theory …' The Times Higher Education Supplement'… the book provides an excellent basis for an introductory course on string theory and is well-suited for self-study by graduate students or any physicist who wants to learn the basics of string theory.' Zentralblatt MATH'… excellent introduction by Zwiebach… aimed at advanced undergraduates who have some background in quantum mechanics and special relativity, but have not necessarily mastered quantum field theory and general relativity yet … the book … is a very thorough introduction to the subject … Equipped with this background, the reader can safely start to tackle the books by Green, Schwarz and Witten and by Polchinski.' Marcel L. Vonk, Mathematical Reviews ClippingsTable of ContentsForeword; Preface; Acknowledgements; Part I. Basics: 1. A brief introduction; 2. Special relativity and extra dimensions; 3. Electromagnetism and gravitation in various dimensions; 4. Nonrelativistic strings; 5. The relativistic point particle; 6. Relativistic strings; 7. Strong parameterization and classical motion; 8. World-sheet currents; 9. Light-cone relativistic strings; 10. Light-cone fields and particles; 11. The relativistic quantum point particle; 12, Relativistic quantum closed strings; 13. Relativistic quantum closed strings; 14. A look at relativistic superstrings; Part II. Developments: 15. D-branes and gauge fields; 16. String charge and electric charge; 17. T-duality of closed strings; 18. T-duality of open strings; 19. Electromagnetism fields in D-branes; 20. Nonlinear and Born-Infeld electrodynamics; 21. Strong theory and particle physics; 22. String thermodynamics and black holes; 23. Strong interactions and AdS/CFT; 24. Covariant string quantization; 25. String interactions and Riemann surfaces; 26. Loop amplitudes in string theory; References; Index.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

Book Synopsis

Read more less

Book SynopsisSince the early 1990s the atomic pair distribution function (PDF) analysis of powder diffraction data has undergone something of a revolution in its ability to do just that: yield important structural information beyond the average crystal structure of a material. With the advent of advanced sources, computing and algorithms, it is now useful for studying the structure of nanocrystals, clusters and molecules in solution or otherwise disordered in space, nanoporous materials and things intercalated into them, and to look for local distortions and defects in crystals. It can be used in a time-resolved way to study structural changes taking place during synthesis and in operating devices, and to map heterogeneous systems.Although the experiments are somewhat straightforward, there can be a gap in knowledge when trying to use PDF to extract structural information by modelling. This book addresses this gap and guides the reader through a series of real life worked examples that gradually inTable of Contents1: Introduction and review 1.1 What this book is not 1.2 What this book is 1.3 Why PDF? 1.4 Software 2: PDF Primer 2.1 Introduction 2.2 X-ray scattering from materials 2.3 Obtaining the PDF from x-ray total scattering data 2.4 The pair distribution function 2.5 Extracting structural information from the PDF 2.6 Measurement of total scattering data 2.7 It is time to start modelling! 3: PDF modelling of simple crystal structures: Bulk Ni and Pt nanoparticles 3.1 Introduction and overview 3.2 The question 3.3 The result 3.4 The experiment 3.5 What next? 3.6 Wait, what? How do I do that? 3.7 Problems 3.8 Solution 3.9 Diffpy-CMI solution 4: Getting the PDF 4.1 Introduction and overview 4.2 The question 4.3 The result 4.4 The experiment 4.5 What next? 4.6 Wait, what? How do I do that? 4.7 results 4.8 problems 4.9 solution 5: Quantification of sample phase composition: physical mixtures of Si and Ni 5.1 Introduction and overview 5.2 The question 5.3 The result 5.4 The experiment 5.5 What next? 5.6 Wait, what? How do I do that? 5.7 Problems 5.8 Solution 5.9 Diffpy-CMI Solution 6: More advanced crystal structure modeling: the room-temperature structure of crystalline Ba0.7K0.3(Zn0.85Mn0.15)2As2 6.1 Introduction and overview 6.2 The question 6.3 The result 6.4 The experiment 6.5 What next? 6.6 Wait, what? How do I do that? 6.7 Problems 6.8 Solution 6.9 Diffpy-CMI Solution 7: Investigating the tetragonal-to-orthorhombic phase transition in SrFe2As2 7.1 Introduction and overview 7.2 The question 7.3 The result 7.4 The experiment 7.5 What next? 7.6 Wait, what? How do I do that? 7.7 Problems 7.8 Solution 7.9 Diffpy-CMI Solution 8: Simple modeling of nanoparticles: Size-dependent structure, defects and morphology of quantum dot nanoparticles 8.1 Introduction and overview 8.2 The question 8.3 The result 8.4 The experiment 8.5 What next? 8.6 Wait, what? How do I do that? 8.7 Problems 8.8 Solutions 8.9 Diffpy-CMI Solution 9: Local structure in a crystal with short-range ordered lower-symmetry domains: Local iridium dimerization and triclinic distortions in cubic CuIr1.76Cr0.24S4 9.1 Introduction and overview 9.2 The question 9.3 The result 9.4 The experiment 9.5 What next? 9.6 Wait, what? How do I do that? 9.7 Problems 9.8 Solution 9.9 Diffpy-CMI Solution 10: Nano and polycrystalline thin films: Local structure of nanocrystalline TiO2 grown on glass 10.1 Introduction and overview 10.2 The question 10.3 The result 10.4 The experiment 10.5 What next? 10.6 Wait, what? How do I do that? 10.7 Problems 10.8 Solution 10.9 Diffpy-CMI Solution 11: Structure of discrete tetrahedral quantum dots: Atomically precise CdSe tetrahedral nanoclusters 11.1 Introduction and overview 11.2 The question 11.3 The result 11.4 The experiment 11.5 What next? 11.6 Wait, what? How do I do that? 11.7 Problems 11.8 Solution 12: Structure and intercalation environment of disordered layered materials: zirconium phosphonateDSphosphate unconventional MOFs 12.1 Introduction . 12.2 The question 12.3 The result 12.4 The experiment 12.5 What next? 12.6 Wait, what? How do I do that? 12.7 Problems 12.8 Solution 13: Magnetic PDF 13.1 Introduction and overview 13.2 The question 13.3 The result 13.4 The experiment 13.5 What next? 13.6 Wait, what? How do I do that? 13.7 Problems 13.8 Solution 14: Tips and Tricks: PDF measurements 14.1 Introduction and overview 14.2 Basic overview: what are total scattering data? 14.3 What type of radiation should I use? 14.4 Detectors 14.5 Sample geometries 14.6 Samples 14.7 Sample environments 15: More PDF Tips and Tricks 15.1 Introduction 15.2 PXRD or PDF, Q-space or r-space analysis? 15.3 Model-free analysis of PDF 15.4 More options for PDF modelling 15.5 Automated PDF modelling 15.6 Final words 16: Appendix 1: Python 16.1 Introduction 16.2 Installing Python programs 16.3 The terminal and the command prompt 16.4 Python IDE>'s and Jupyter Notebooks 17: Appendix 2: Data processing and integration 17.1 Introduction Bibliography

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

a huge range and FREE tracked UK delivery on ALL orders.

Read more less

Book SynopsisSpectral analysis is widely used to interpret time series collected in diverse areas. This book covers the statistical theory behind spectral analysis and provides data analysts with the tools needed to transition theory into practice. Actual time series from oceanography, metrology, atmospheric science and other areas are used in running examples throughout, to allow clear comparison of how the various methods address questions of interest. All major nonparametric and parametric spectral analysis techniques are discussed, with emphasis on the multitaper method, both in its original formulation involving Slepian tapers and in a popular alternative using sinusoidal tapers. The authors take a unified approach to quantifying the bandwidth of different nonparametric spectral estimates. An extensive set of exercises allows readers to test their understanding of theory and practical analysis. The time series used as examples and R language code for recreating the analyses of the series are aTrade Review'Percival and Walden have written an excellent text for anyone who analyzes or wants to learn how to analyze time series data in the frequency domain. The aims and scope of the text are broad and require the skills that one would acquire in a basic course on mathematical statistics. The authors take a data analysis approach and relegate theoretical material to special sections or problems, and give ample references to the more theoretical details. The authors give philosophical as well as practical guidance in applying spectral techniques to time series data. This book is one of the best texts on the topic and would be useful as a reference for researchers. In addition, the book would be great as a textbook for a one semester/quarter course on the spectral analysis of time series.' David Stoffer, University of Pittsburgh'I used Spectral Analysis for Physical Applications several times for my spectral analysis courses. It was an excellent addition to the literature. This new book, considerably enlarged, will certainly have the same impact. The authors should be congratulated for a most valuable book.' Pedro A. Morettin, Universidade de São Paulo'Spectral Analysis for Univariate Time Series is an excellent step-by-step introduction to using Fourier methods in the statistical analysis of time series. The in-depth material, extensive exercises, practical advice, and illustrative data analyses provide valuable insights to readers of varied backgrounds.' Peter F. Craigmile, Ohio State University'This book will serve scientists and engineers in many fields with a general toolbox for spectral analysis. The fundamentals of non-parametric and parametric methods are presented, together with convincing examples and exercises. I especially appreciate the extensive chapter on combining direct spectral estimators, as todays standard toolbox definitely should include multitaper based spectral analysis.' Maria Sandsten, Lunds universitet'The book constitutes a lot more than an update of the authors' 1993 book Spectral Analysis for Physical Applications. The stand-out features are still the examples and exercises, but all data analysis has been done in R and considerable effort has gone into explanation, and how the methods fit in with alternatives. There is also a new chapter on simulation. The book is suitable not just as a reference for statisticians, engineers and physicists, but also as a graduate level text, particularly because of the chapter summaries and the thought-provoking comments at the section ends.' Barry Quinn, Macquarie University, Sydney'The excellent new textbook by Percival and Walden is an important source of information for anyone interested in time series analysis. Theoretical rigour combined with practical analysis of interesting real world data gives the reader a pedagogical journey into the world of spectral analysis and time series analysis. Highly recommended!' Alfred Hanssen, Universitetet i Tromsø – Norges arktiske universitetTable of Contents1. Introduction to spectral analysis; 2. Stationary stochastic processes; 3. Deterministic spectral analysis; 4. Foundations for stochastic spectral analysis; 5. Linear time-invariant filters; 6. Periodogram and other direct spectral estimators; 7. Lag window estimators; 8. Combining direct spectral estimators; 9. Parametric spectral estimators; 10. Harmonic analysis; 11. Simulation of time series.

Read more less

Book SynopsisThis book presents a modern, interdisciplinary perspective on cities and urban systems that combines new data with tools from statistical physics and urban economics. Analysis of mobility patterns and infrastructure networks, as well as spatial and social organization, provide a quantitative description of cities for scientists interested in modeling these complex systems.Trade Review'Every so often along comes a book that attempts a grand synthesis. Marc Barthelemy has put together many ideas from statistical physics with theory in urban economics, fashioning an approach that demonstrates its essential logic and empirical relevance. A book that must be absorbed by urbanists of every persuasion and used to advance our science of cities.' Michael Batty, University College London'Collective effects are often counterintuitive and defeat our imagination. We need specific models to anticipate financial crashes, traffic jams, mass panics. The spontaneous organization of cities falls in the same category of phenomena created by ourselves, humans, but that -- paradoxically – we struggle to understand. This wonderful book summarizes a large number of data and ideas about how cities grow and self-organize, sometimes not in the most efficient way. In his plea for a new science for cities, Marc Barthelemy musters methods from statistical physics for a problem that concerns an ever-growing fraction of humanity.' Jean-Philippe Bouchaud, Capital Fund Management, Paris'… a multi-disciplinary effort to describe and understand the numerous structural aspects of cities and their evolution … This book makes an effort to bring these different points of view together, to find a common scientific language, and to look at cities as systems that show typical features such as complexity, self-organisation and emergence which can be described in the language of statistical physics. …The whole text is a well-written scientific essay and fully referenced to scientific publications from a broad range of disciplines. The data and models are presented with mathematical rigour and illustrated by numerous black-and-white figures. The book is highly interesting for its multi-disciplinary approach as well as for the data presented, and can be recommended to a wide interested readership with a general understanding of mathematics and statistical physics.' Manuel Vogel, Contemporary Physics'Marc Barthelemy refreshes ideas and opens new avenues for further research in urban/economic quantitative geography. Without ignoring 'Founding Fathers' in geography, he suggests inspiring ideas anchored in physics for modelling urban realities. A path toward multidisciplinary analysis, which has still a long way to go before success.' Isabelle Thomas, Université catholique de LouvainTable of ContentsPreface; Acknowledgements; 1. Urban systems; 2. Models and methods; 3. The spatial organization of cities; 4. Infrastructure networks; 5. Mobility patterns; 6. Multimodality in cities; 7. Socio-economical aspects; 8. Systems of cities; 9. Towards a new science of cities; References; Index.

Read more less

Book SynopsisThis is a Nova Science Publication.

Read more less

Book Synopsis

Read more less

Book Synopsis

Read more less

Book SynopsisAt the time of its original publication this reissued ''classic'' text, co-written by the Nobel Laureate of 1954, Max Born, represented the final account of the subject and in many ways it still does. The book is divided into four sections. The first of these is very general in nature and deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second part deals with the properties of long lattice waves; the third with thermal properties and the fourth with optical properties.Trade Review'extraordinarily general and sound introduction ... a standard work that is indispensable to all working in this field' * Die Naturwissenschaften *'... important mathematical methods which should be of use in other subjects as well' * British Journal of Applied Physics *Table of ContentsPART 1: ELEMENTARY THEORIES ; PART 2: GENERAL THEORIES

Read more less

Book SynopsisRecent developments have led to a good understanding of universality; why phase transitions in systems as diverse as magnets, fluids, liquid crystals, and superconductors can be brought under the same theoretical umbrella and well described by simple models. This book describes the physics underlying universality and then lays out the theoretical approaches now available for studying phase transitions. Traditional techniques, mean-field theory, series expansions, and the transfer matrix, are described; the Monte Carlo method is covered, and two chapters are devoted to the renormalization group, which led to a break-through in the field.The book will be useful as a textbook for a course in `Phase Transitions'', as an introduction for graduate students undertaking research in related fields, and as an overview for scientists in other disciplines who work with phase transitions but who are not aware of the current tools in the armoury of the theoretical physicist.Trade Review'The book will be useful as a textbook for a course in phase transitions; as an introduction in other disciplines who work with phase transitions but who are not aware of the current tools in the armoury of the theoretical physicist. (orig.) Physics Briefs'it is desirable that those who wish to be acquainted with the work being done in the field have access to suitable textbooks ... Such a book is the text under review ... this book will serve as a useful map to novices to the field.' Dr A. Danielian, King's College, London, Contemporary Physics, Volume 33, Number 5, September/October 1992'novices will be provided with an up-to-date map of the field.' Dr. A. Danielian, King's College, London. Contemporary Physics, 1992, Volume 33, Number 5.Table of ContentsIntroduction; Statistical mechanics and thermodynamics; Models; Mean-field theories; The transfer matrix; Series expansions; Monte Carlo simulations; The renormalization group; Implementations of the renormalization group.

Read more less