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This book provides a comprehensive introduction to equilibrium and non-equilibrium Green's function methods in many-body physics. It begins with a derivation of second quantisation for relativistic systems based on the many-body relativistic Dirac equation and its non-relativistic limit. The properties of equilibrium Green's functions are then described, with discussion of the two-time and Matsubara function methods. The coverage of non-equilibrium Green's function methods includes the diagrammatic techniques applicable to electrons and phonons using both the perturbation and variational approaches. Specific applications to steady-state and time-dependent quantum transport are presented in the final chapters. The book's accessible explanations, detailed derivations, and systematic treatment of the underlying theory make it a valuable resource for graduate students and early-career researchers. More than 200 problems have been included to support learning, with selected solutions available at the end of each chapter. Instructors benefit from access to the full solutions manual.
Spontaneous symmetry breaking lies at the heart of modern physics, shaping our understanding of matter, forces, and even the universe itself. From condensed matter physics to particle physics and cosmology, spontaneous symmetry breaking unifies phenomena that at first seem worlds apart. This graduate-level text offers a comprehensive yet accessible guide to the conceptual theory and practical consequences of spontaneous symmetry breaking. It introduces topics ranging from Noether's theorem, thermodynamic limits, and gauge freedoms to Nambu–Goldstone modes, topological defects, effective field theory, the Mermin–Wagner–Hohenberg–Coleman theorem, and the Anderson–Higgs mechanism within the Standard Model. Packed with exercises, with solutions available online, in-depth projects, and a myth-busting FAQ section addressing common pitfalls, this book equips readers to master both the fundamentals and modern frontiers of spontaneous symmetry breaking, making it an indispensable resource for students, teachers, and researchers.
The study of periodic partial differential equations has experienced significant growth in recent decades, driven by emerging applications in fields such as photonic crystals, metamaterials, fluid dynamics, carbon nanostructures, and topological insulators. This book provides a uniquely comprehensive overview for mathematicians, physicists, and material scientists engaged in the analysis and construction of periodic media. It describes all the mathematical objects, tools, problems, and techniques involved. Topics covered are central for areas such as spectral theory of PDEs, homogenization, condensed matter physics and optics. Although it is not a textbook, some basic proofs, background material, and references to an extensive bibliography providing pointers to the wider literature are included to allow graduate students to access the content.
Bubbles have unique properties that make them of great importance in disparate fields such as energy production, acoustics, chemical engineering, material processing, biomedicine, food science and a host of others which, on the surface, appear to have little in common. Bringing together information scattered in many hundreds of sources, this book provides a unified treatment of the subject, illustrating the roots of this surprising versatility with a wealth of examples. The emphasis is on physics, explained with words and images before introducing a limited mathematical apparatus. Building on the foundation of the compressible and incompressible Rayleigh-Plesset equation, the treatment continues with the volume oscillations of gas bubbles and associated scattering and emission of sound, the diffusion of dissolved gases and of heat, boiling, nucleation and the behavior of bubbles in elastic and visco-elastic media. The book concludes with chapters on biomedical applications, sonochemistry, acoustic and flow cavitation and bubbly liquids.
This graduate-level volume is a coherent and self-contained introduction to Quantum Field Theory, uniquely focused on geometric and non-perturbative aspects. The first part covers quantum fields and Euclidean path integral, Yang-Mills field theories, and Wilsonian renormalization. Wilson's notion of the effective field theory and its heavy implication for the QFT framework itself are given particular attention. Next, geometrical and topological aspects are thoroughly treated, accompanied by a healthy dose of underlying mathematics. Anomalies, or quantum failures of classical symmetries, follow as crucial litmus tests for self-consistency, which are delineated in unprecedented detail, spanning decades of development. In the final part, the book asks how relativistic gravity, known to resist standard quantization schemes, may reconcile with the quantum world. This question is approached by invoking d=2 Weyl anomaly, Hawking effects, black hole partition functions, and the renormalization of fundamental strings, with a view toward quantum gravity and superstring theory.
Phase transitions take place when a substance changes from one physical state to another, and they are of fundamental importance in science and engineering with applications ranging from superconductivity to climate science. This Student's Guide coherently examines the underlying dynamics of phase transitions, beginning with a detailed description of phase diagrams and their graphical interpretation, before introducing the Van der Waals equations of state. It progresses to more advanced topics such as mean-field theory in magnetic systems, phase transitions in binary mixtures, and other more exotic types of phase transitions in liquid crystals, superconductors, and superfluids. A separate chapter covers the unique and subtle phase transition dynamics of water. The book includes numerous worked examples and problems, with full solutions available online. It will be a valuable resource for students and life-long learners in physical science and engineering.
The culmination of years of teaching experience, this book provides a modern introduction to the mathematical theory of interacting particle systems. Assuming a background in probability and measure theory, it has been designed to support a one-semester course at a Master or Ph.D. level. It also provides a useful reference for researchers, containing several results that have not appeared in print in this form before. An emphasis is placed on graphical representations, which are used to give a construction that is intuitively easier to grasp than the traditional generator approach. Also included is an extensive look at duality theory, along with discussions of mean-field methods, phase transitions and critical behaviour. The text is illustrated with the results of numerical simulations and features exercises in every chapter. The theory is demonstrated on a range of models, reflecting the modern state of the subject and highlighting the scope of possible applications.
This comprehensive and up-to-date manual accompanies the third edition of Bernard Schutz's A First Course in General Relativity. It offers step-by-step guidance through more than 200 selected exercises, providing detailed solutions and explanatory comments which are cross-referenced to the relevant equations and sections in Schutz's text. The material is further extended by the inclusion of 168 supplementary problems that highlight conceptual challenges and direct readers to the most useful supporting literature. A comprehensive index with bolded keywords allows for quick navigation, while an appendix of useful results makes the book a lasting reference for advanced undergraduate and graduate students, instructors, and self-directed learners seeking a deeper understanding of the subject. A Mathematica notebook and tables of exercises and supplementary problems are freely available as online resources, with instructors benefiting from access to solutions to selected exercises and problems.
Recent observations of the afterglow of the Big Bang, commonly referred to as the Cosmic Microwave Background radiation, have greatly advanced our understanding of the early Universe and have helped reinforce the observational foundations of modern cosmology. This volume provides a comprehensive pedagogical overview of all aspects of the Cosmic Microwave Background radiation. Topics covered include theory, current observations, instrumentation, statistical analyses and the astrophysics of Galactic and other microwave foregrounds. These latter topics are important as much of the contemporary work in cosmology focuses on perfecting experimental techniques and on mitigating and assessing sources of error. Bringing together the latest research and scientific developments from the primary literature into one book, this is a go-to resource for graduate students and researchers working in cosmology and astrophysics.
Philosophical problems fundamentally infuse the theory and practice of astronomy. Bringing together fifteen historians, eleven philosophers, and four pioneering scientists, this volume provides a rigorous yet largely accessible examination of the conceptual and methodological challenges that lie at the intersection of philosophy and astronomy – broadly construed to include astrophysics, cosmology, space science, and astrobiology. Drawing largely on interdisciplinary advances from the past two centuries, the book's chapters tackle metaphysical inquiries into the fundamental nature of reality, the limits of reasoning, the problematic nature of observation and inference, the role of technology, and the epistemology of concepts such as space, time, life, and intelligence. Discussions are anchored to fascinating theories and examples from the 'canals' of Mars to exoplanets, black holes, dark matter, and the multiverse. Written primarily for practicing scientists, this volume will also serve historians and philosophers of science, as well as the curious general reader.
Driven by advances in data science and machine learning, photonics has evolved rapidly in recent years and has transformed into a highly interdisciplinary field, connecting fundamental research with cutting-edge applications. Inspired by recent Nobel Prizes in Physics in 2021 and 2024, Conti highlights the interplay between photonics and spin glasses, a key concept for understanding the link between photon propagation and complex systems. Beginning with a study of black-body radiation, the book then revisits laser theory using techniques from non-equilibrium statistical mechanics. Through a step-by-step exploration of important photonic experiments, it bridges foundational concepts and advances in optical computing, with a focus on developing efficient hardware for classical and quantum artificial intelligence. This reveals the profound ties between complexity, photonics, and the future of AI technologies. The book will be a valuable resource for advanced undergraduate and graduate students and more practised researchers.
From genome sequencing to large sky surveys, digital technologies produce massive datasets that promise unprecedented scientific insights. But data, for being good to use and reuse, need people – scientists, technicians, and administrators – as embodied, evaluative, social humans. In this book, anthropologist Götz Hoeppe draws on an ethnography of astronomical research to examine the media and practices that scientists and technicians use to instruct graduate students, make diagrams for data calibration and discovery, organize collaborative work, negotiate the ethics of open access, encode their knowledge in datasets – and do social inquiries along the way. This book offers a reflection on the sociality of data-rich research that will benefit attempts to integrate human and machine learning. It is essential reading for anyone interested in data science, science and technology studies, as well as the anthropology, sociology, history, and philosophy of science. This book is also available Open Access on Cambridge Core.
What is the physics behind getting a spacecraft to the nearest stars? What science can it do when it gets there? How can it send back data over enormous distances? Drawing on established physics, Coryn Bailer-Jones explores the various challenges of getting an uncrewed spacecraft to a nearby star within a human lifetime. In addition to propulsion methods such as nuclear rockets and laser sails, this book examines critical issues such as navigation, communication, and the interstellar medium. Starting from fundamental concepts, readers will learn how a broad spectrum of physics – ranging from relativity to optics, and thermodynamics to astronomy – can be applied to address this demanding problem. Assuming some familiarity with basic physics, this volume is a comprehensive and self-contained introduction to interstellar travel, and an indispensable guide for studying the literature on deep space exploration. This title is also available as open access on Cambridge Core.
'Quantum Engineering' covers the theory, design, fabrication and applications of quantum coherent solid-state structures. This updated and expanded second edition provides a self-contained presentation of the theoretical methods and experimental results in both first and second waves of quantum technology innovation. Topics span the quantum theory of electric circuits, theoretical methods of quantum optics in application to solid-state circuits, the quantum theory of noise, decoherence and measurements, Landauer formalism for quantum transport, the physics of weak superconductivity and the physics of two-dimensional electron gas in semiconductor heterostructures. The author introduces microscopic ion- and defect-based qubits, currently among the most successful platforms for quantum computation and quantum sensing. Reflecting the significant progress of quantum hardware, state-of-the-art implementations such as quantum metamaterials and quantum reservoir computing are also added to the discussion. Written for graduate students in physics, this book also serves electronic engineers working in quantum engineering.
Starting from ancient astronomy, this text follows the development of celestial mechanics culminating in applications of the most recent results concerning stability of planetary orbits: Kolmogorov's and Nekhoroshev's theorems. Key topics covered include: a historical introduction from ancient astronomy to Kepler and Newton; Lagrange's perturbation theory; the problem of three bodies, with a discussion of Levi-Civita regularization and of Sundman's theorem; methods of algebraic calculation of perturbation series, including a discussion of non-convergence due to the accumulation of small divisors; and a complete application of Kolmogorov's and Nekhoroshev's theorems. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students, and for young researchers. Its approach allows students to learn about perturbation methods leading to advanced results.
This volume gathers the contributions of founders, experts and practitioners of supergravity celebrating the 50th anniversary of its birth, discussing the history of the field and its modern applications to high energy physics, mathematics, particle physics and cosmology. Since its discovery in the mid-1970s, fully understanding its symmetries and structures, the physical implications, permitted generalizations and the connections with other theories have been highly nontrivial challenges. Whether supergravity will be proven true by experiments or it remains a mathematical framework, the theory is elegant, intriguing, rich and entertaining. Many agree that it will continue to be an inspiration and theoretical laboratory for quantum gravity, as well as an intellectual achievement that expresses the highest levels of human creativity in our effort to understand the cosmos and its rules. Current and future practitioners, and historians of science, will value both the comprehensive history and future perspectives of the field within.
An impressively comprehensive textbook adopting a phenomenological approach to quantum physics. The chapters cover everything from basic definitions of key concepts to detailed discussions of the underlying theoretical framework, walking students step-by-step through the necessary mathematics and drawing clear connections between the theory and the most important modern research applications including quantum optics, fluids, nanophysics, entanglement, information, and relativity. With this book, students and researchers will have access to hundreds of real-world examples, exercises, and illustrations to support and expand their understanding. Instructors can tailor the content to suit the length and level of their course and will have access to an online solutions manual with fully worked solutions to all 300+ exercises in the book. Other online resources include Python simulations, additional exercises, and detailed appendices.