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The mathematical essence of contextuality lies in the similarity of random variables answering the same question in different contexts: contextuality means they are less similar when considered within their respective contexts than when isolated from them. This book presents a principled way of measuring this similarity and distinguishing two forms of context-dependence: contextuality and disturbance. While applicable across a broad range of disciplines, the concept of contextuality in this book is closest to that in quantum physics, where its special forms –in the absence of disturbance – are known as Bell nonlocality and Kochen–Specker contextuality. This systematic introduction requires no prior familiarity with the subject and a very modest mathematical background. Structured as a textbook, complete with exercises and solutions, it is accessible to a broad readership and suitable for teaching. It will be useful to researchers and students in quantum mechanics, philosophy of science, psychology, computer science, linguistics, and probability theory.
Intended for graduate and advanced undergraduate students, this textbook is a thoroughly modern introduction to and a self-contained treatise on the theoretical and mathematical fundamentals of General Relativity. The chapters are organized into three parts, with the first covering Maxwell's theory of electromagnetism, the relativistic Kepler problem, and the systematics of the underlying geometry, with the more abstract notion of the fibre bundle relegated to the Appendix. The second part begins with a derivation of the Einstein equations and leads to topics such as cosmology, black holes, causal structures, and action principles. The third part covers the canonical formulation of field theory in general and General Relativity in particular, leading to the concept of the total energy in General Relativity and quantum phenomena with event horizons. The book minimizes historical references, focuses on modern tools, examples, and applications, and emphasizes the commonalities between relativistic gravity and gauge theory.
Aimed at advanced undergraduate and graduate-level students, this textbook covers the core topics of quantum computing in a format designed for a single-semester course. It will be accessible to learners from a range of disciplines, with an understanding of linear algebra being the primary prerequisite. The textbook introduces central concepts such as quantum mechanics, the quantum circuit model, and quantum algorithms, and covers advanced subjects such as the surface code and topological quantum computation. These topics are essential for understanding the role of symmetries in error correction and the stability of quantum architectures, which situate quantum computation within the wider realm of theoretical physics. Graphical representations and exercises are included throughout the book and optional expanded materials are summarized within boxed 'Remarks'. Lecture notes have been made freely available for download from the textbook's webpage, with instructors having additional online access to selected exercise solutions.
Ordinary chondrites, the most abundant meteorites, constitute about 80% of meteorite falls and are essential to our understanding of cosmochemistry. They provide important information about planetary accretion, the early Solar System, and the geological history of asteroids, including such processes as thermal metamorphism, shock metamorphism, and aqueous alteration. This comprehensive guide begins with meteorite classifications and useful definitions, followed by a discussion of fall phenomena and terrestrial weathering. It provides a detailed overview of the three main ordinary-chondrite groups, which include the most primitive, least-processed meteorites known. Compositional differences among these samples furnish clues to the nature of processes operating in the solar nebula 4.5 billion years ago. These rocks also disclose information on the nature and origin of chondrules, matrix material, and metallic iron-nickel grains. This book is a valuable resource for graduate students and research professionals interested in meteorites and planetary science, as well as amateur meteorite enthusiasts.
Quantum many-body systems are a central feature of condensed matter physics, relevant to important, modern research areas such as ultrafast light-matter interactions and quantum information. This book offers detailed coverage of the contour Green's function formalism – an approach that can be successfully applied to solve the quantum many-body and time-dependent problems present within such systems. Divided into three parts, the text provides a structured overview of the relevant theoretical and practical tools, with specific focus on the Schwinger-Keldysh formalism. Part I introduces the mathematical frameworks that make use of Green's functions in normal phase states. Part II covers fermionic superfluid phases with discussion of topics such as the BCS-BEC crossover and superconducting systems. Part III deals with the application of the Schwinger-Keldysh formalism to various topics of experimental interest. Graduate students and researchers will benefit from the book's comprehensive treatment of the subject matter and its novel arrangement of topics.
'Quantum Cosmology' offers a guided introduction to the quantum aspects of the cosmos. Starting with an overview of early universe cosmology, the book builds up to advanced topics such as the Wheeler–DeWitt equation, gravitational path integrals, and the no-boundary proposal for the wave function of the universe. Readers will explore tunneling processes via Coleman–DeLuccia instantons, the quantum origin of primordial fluctuations, the thermodynamics of horizons, and basic notions of string cosmology. Concepts such as wormholes and semi-classical geometry are introduced with clarity and physical motivation. The book assumes some familiarity with general relativity and quantum mechanics, but little prior knowledge of cosmology. It includes a wide range of exercises, with solutions provided. Written in a pedagogical style, it bridges the gap between undergraduate courses and the research level in this frontier area of theoretical physics.
This two‐volume Element reconstructs and analyzes the historical debates on whether renormalized quantum field theory is a mathematically consistent theory. This volume covers the years the years immediately following the development of renormalized quantum electrodynamics. It begins with the realization that perturbation theory cannot serve as the foundation for a proof of consistency, due to the non-convergence of the perturbation series. Various attempts at a nonperturbative formulation of quantum field theory are discussed, including the Schwinger–Dyson equations, GunnarKällén's nonperturbative renormalization, the renormalization group of MurrayGell-Mann and Francis Low, and, in the last section, early axiomatic quantum field theory. The second volume of this Element covers the establishment of Haag's theorem, which proved that even the Hilbert space of perturbation theory is an inadequate foundation for a consistent theory. This title is also available as Open Access on Cambridge Core.
The study of magnetism has driven progress in experimental science for centuries, and demonstrates how ground-breaking theoretical advances can be translated directly into essential, transformative technology. Now in an expanded second edition, this popular textbook provides comprehensive coverage of the theory and practical applications of magnetism and magnetic materials. The text has been updated throughout to address significant developments from the last decade, including new theoretical insights, advanced experimental probes, and thin film technology. A new chapter covers the important topic of transverse magnetotransport and effects of topology. The book is extensively illustrated with over 700 figures conveying important experimental data, concepts and applications, and each self-contained chapter concludes with a summary section, a list of further reading and a set of exercises. The text contains a wealth of useful information that will be of interest to graduate students and researchers in physics, materials science and engineering.
This innovative textbook has been designed with approachability and engagement at its forefront, using language reminiscent of a live lecture and interspersing the main text with useful advice and expansions. Striking a balance between theoretical- and experimental-led approaches, this book immediately immerses the reader in charge and neutral currents, which are at the core of the Standard Model, before presenting the gauge field, allowing the introduction of Feynman diagram calculations at an early stage. This novel and effective approach gives readers a head start in understanding the Model's predictions, stoking interest early on. With in-chapter problem sessions which help readers to build their mastery of the subject, clarifying notes on equations, end of chapter exercises to consolidate learning, and marginal comments to guide readers through the complexities of the Standard Model, this is the ideal book for graduate students studying high energy physics.
IAU Symposium 391 showcases cutting-edge research inspired by the James Webb Space Telescope, as presented during the first IAU General Assembly on African soil. This volume captures the pioneering science of galaxy formation, cosmic reionization, stellar evolution, and early universe dynamics, with contributions addressing topics such as metallicity in primordial galaxies, early Lyman-α emitters, and massive quiescent galaxies at high redshifts. Innovative approaches such as nebular emulators and advanced simulations offer fresh insights into clumpy galaxy formation, thin and thick disk structures, and stellar feedback mechanisms. Special focus is given to unexpected findings, such as unusual chemical abundances and insights from the synergy between JWST and complementary observatories like ALMA. These proceedings highlight the latest breakthroughs in astronomy and the collaborative efforts of scientists worldwide to uncover the secrets of our cosmic origins.
Artificial intelligence is transforming industries and society, but its high energy demands challenge global sustainability goals. Biological intelligence, in contrast, offers both good performance and exceptional energy efficiency. Neuromorphic computing, a growing field inspired by the structure and function of the brain, aims to create energy-efficient algorithms and hardware by integrating insights from biology, physics, computer science, and electrical engineering. This concise and accessible book delves into the principles, mechanisms, and properties of neuromorphic systems. It opens with a primer on biological intelligence, describing learning mechanisms in both simple and complex organisms, then turns to the application of these principles and mechanisms in the development of artificial synapses and neurons, circuits, and architectures. The text also delves into neuromorphic algorithm design, and the unique challenges faced by algorithmic researchers working in this area. The book concludes with a selection of practice problems, with solutions available to instructors online.
Offering a detailed account of the key concepts and mathematical apparatus of quantum mechanics, this textbook is an ideal companion to both undergraduate and graduate courses. The formal and practical aspects of the subject are explained clearly alongside examples of modern applications, providing students with the tools required to thoroughly understand the theory and apply it. The authors provide an intuitive conceptual framework that is grounded in a coherent physical explanation of quantum phenomena, established over decades of teaching and research in quantum mechanics and its foundations. The book's educational value is enhanced by the inclusion of examples and exercises, with solutions available online, and an extensive bibliography is provided. Notes throughout the text provide fascinating context on the tumultuous history of quantum mechanics, the people that developed it, and the questions that still remain at its center. This title is also available as Open Access on Cambridge Core.
This introduction to quantum computing from a classical programmer's perspective is meant for students and practitioners alike. More than 50 quantum techniques and algorithms are explained with mathematical derivations and code for simulation, using an open-source code base in Python and C++. New material throughout this fully revised and expanded second edition includes new chapters on Quantum Machine Learning, State Preparation, and Similarity Tests. Coverage includes algorithms exploiting entanglement, black-box algorithms, the quantum Fourier transform, phase estimation, quantum walks, and foundational QML algorithms. Readers will find detailed, easy-to-follow derivations and implementations of Shor's algorithm, Grover's algorithm, SAT3, graph coloring, the Solovay-Kitaev algorithm, Moettoenen's algorithm, quantum mean, median, and minimum finding, Deutsch's algorithm, Bernstein-Vazirani, quantum teleportation and superdense coding, the CHSH game, and, from QML, the HHL algorithm, Euclidean distance, and PCA. The book also discusses productivity issues like quantum noise, error correction, quantum programming languages, compilers, and techniques for transpilation.
While an understanding of electronic principles is vitally important for scientists and engineers working across many disciplines, the breadth of the subject can make it daunting. This textbook offers a concise and practical introduction to electronics, suitable for a one-semester undergraduate course as well as self-guided students. Beginning with the basics of general circuit laws and resistor circuits to ease students into the subject, the textbook then covers a wide range of topics, from passive circuits to semiconductor-based analog circuits and basic digital circuits. Exercises are provided at the end of each chapter, and answers to select questions are included at the end of the book. The complete solutions manual is available for instructors to download, together with eight laboratory exercises that parallel the text. Now in its second edition, the text has been updated and expanded with additional topic coverage and exercises.
This concise and self-contained book opens completely novel areas of research by directly implementing concepts from quantum physics into areas of social science. It constructs compelling arguments originating from fundamental concepts in physics and the philosophy of science, including key developments in economics and finance, then surveys the important work which has been performed to date through applying the formalism of quantum mechanics to decision making and finance. The book is accessible to graduate students and researchers in social science and physics, as well as avid interdisciplinary readers. This title is part of the Flip it Open Programme and may also be available Open Access. Check our website Cambridge Core for details.
'Quasar Absorption Lines' is a comprehensive, detailed exposition on the science and analysis of quasar spectra in two volumes, for both aspiring and seasoned astronomers. This Volume 2: 'Astrophysics, Analysis, and Modeling' describes atomic transitions of hydrogenic and multi-electron ions, the theoretical foundation and practical application of the ΛCDM cosmological model, and radiative transfer from cosmological sources. The theory of spectrographs and the mathematical formalism and quantitative analysis of spectral absorption lines and ionization breaks are treated in detail, including column density measurements, line deblending, and Voigt profile fitting. The philosophies, methods, and techniques of large absorption line surveys are presented, including methods for correcting incompleteness and for measuring accurate absorber population statistics. Gas physics, heating/cooling, and ionization are also covered, followed by detailed methods for undertaking multi-component, multiphase chemical-ionization modeling.
The intersection of statistical mechanics and mathematical analysis has proved a fertile ground for mathematical physics and probability, and in the decades since lattice gases were first proposed as a model for describing physical systems at the atomic level, our understanding of them has grown tremendously. A book that provides a comprehensive account of the methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models has been long overdue. This book, written by one of the masters of the subject, is just that. Topics covered include correlation inequalities, Lee-Yang theorems, the Peierls method, the Hohenberg-Mermin-Wagner method, infrared bounds, random cluster methods, random current methods and BKT transition. The final section outlines major open problems to inspire future work. This is a must-have reference for researchers in mathematical physics and probability and serves as an entry point, albeit advanced, for students entering this active area.
'Quasar Absorption Lines' is a comprehensive, detailed exposition on the science and analysis of quasar spectra in two volumes, for both aspiring and seasoned astronomers. This Volume 1: 'Introduction, Discoveries, and Methods' covers the evolution of the field of quasar spectroscopy over the six decades since quasars were discovered, including the development and application of observational methods and the knowledge gained from them. The broad treatment includes studies of the Ly α forest, Lyman limit systems, damped Ly α absorbers, deuterium (D/H), 21-cm absorbers, HI and HeII reionization, the warm/hot intergalactic medium, and the multiple ionization phases of metal lines. The connections between these absorbers and galaxies (the circumgalactic medium), galaxy groups (the intragroup medium), and clusters of galaxies (the intracluster medium) are treated in depth. Also covered are the taxonomy and classifications of AGN/quasar spectra, black hole accretion, broad and narrow associated absorption lines, and the quasar circumgalactic medium.
The theory of causal fermion systems represents a novel approach to fundamental physics and is a promising candidate for a unified physical theory. This book offers a comprehensive overview of the theory, structured in four parts: the first lays the necessary mathematical and physical foundations; the second offers an introduction to the theory and the causal action principle; the third describes the mathematical tools for analyzing causal fermion systems; and the fourth gives an outlook on the key physical applications. With relevance across mathematical and theoretical physics, the book is aimed at graduate students and researchers interested in novel approaches to the structure of spacetime and alternative perspectives to the more established quantum field theories. It can be used for advanced courses in the subject or as a reference for research and self-guided study. Exercises are included at the end of each chapter to build and develop key concepts.
Living systems consist of diverse components and constitute a hierarchy, from molecules to cells to organisms, which adapt to external perturbations and reproduce stably. This book describes the statistical and physical principles governing cell growth and reproduction, and the mechanisms for adaptation through noise, kinetic memory, and robust cell differentiation through cell to cell interaction and epigenetics. The laws governing rate, direction, and constraints of phenotypic evolution are examined from the perspective of microscopic units (molecules) and macroscopic states (cells), with a focus on maintaining consistency between these length and temporal scales. By integrating theoretical, computational, and experimental approaches, this book offers novel insights into biology from a physicist's perspective and provides a detailed picture of the universal characteristics of living systems. It is indispensable for students and researchers in physics, biology and mathematics interested in understanding the nature of life and the physical principles it is based upon.