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Although the field of celestial dynamics – the application of Newtonian dynamics to systems with a relatively small number of celestial bodies – is centuries old, it has been reinvigorated by the discovery of thousands of exoplanetary systems orbiting other stars. This textbook uses the properties of planetary systems, including own Solar System, to illustrate the rich variety of behavior permitted by Newton's law of gravity. The textbook then expands its view to examine stellar dynamics – the study of systems containing a very large number of stars or other celestial bodies. The different techniques used for celestial dynamics and stellar dynamics are compared and contrasted. However, throughout the text, emphasis is placed on the underlying physics that applies on scales as small as the Earth–Moon system and as large as a cluster of galaxies. It is ideal for a 1-semester astrophysical dynamics course for upper-level undergraduates and starting graduate students.
This book explores the fractionalization of particles in physics, how interactions between individual particles and with their background can modify their fundamental quantum states. Covering a large breadth of topics with an example-driven approach, this comprehensive text explains why phases of matter must be described in terms of both symmetries and their topology. The majority of important results are derived in full with explanations provided, while exercises at the end of each section allow readers to extend and develop their understanding of key topics. The first part presents polyacetylene as the paradigmatic material in which electric charge can be fractionalized, while the second part introduces the notion of invertible topological phases of matter. The final part is devoted to the 'ten-fold way', a classification of topological insulators or superconductors. The text requires a solid understanding of quantum mechanics and is a valuable resource for graduate students and researchers in physics.
The Green's function method is among the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. With entirely new chapters and updated example problems, the second edition of this popular text continues to provide an ideal introduction to nonequilibrium many-body quantum systems and ultrafast phenomena in modern science. Retaining the unique and self-contained style of the original, this new edition has been thoroughly revised to address interacting systems of fermions and bosons, simplified many-body approaches like the GKBA, the Bloch equations and the Boltzmann equations and the connection between Green's functions and newly developed time-resolved spectroscopy techniques. Small gaps in the theory have been filled, and frequently overlooked subtleties have been systematically highlighted and clarified. With an abundance of illustrative examples, insightful discussions and modern applications, this book remains the definitive guide for students and researchers alike.
Bacteria are the most ubiquitous life-forms on Earth, and are studied extensively to gain insight into their function and understand how they interact with their environment. In recent years, bacterial biophysics has added a new dimension to this research by using the tools of physics to investigate the quantitative principles that underpin these cellular systems. This book provides a modern and cohesive introduction to bacterial biophysics, with a focus on biofilms, slimes and capsules. In the first of three sections, key techniques and models from the physical sciences that can be applied to bacterial problems are presented. Section 2 then provides a bacterial microbiology primer for physical scientists and an examination of single-cell phenomena. The final section explores interacting bacteria and biofilms from a physical perspective. Ideal for physics graduates interested in this important field, this book is also relevant for researchers in physical chemistry, bioengineering, mathematics and microbiology.
For the engineer or scientist using spectroscopic laser diagnostics to investigate gas-phase media or plasmas, this book is an excellent resource for gaining a deeper understanding of the physics of radiative transitions. While a background in quantum mechanics is beneficial, the book presents a comprehensive review of the relevant aspects, extensively covering atomic and molecular structure alongside radiative transitions. The author employs effective Hamiltonians and Hund's case (a) basis wavefunctions to develop the energy level structure of diatomic molecules. These techniques also form the basis for treating radiative transitions in diatomic molecules. Recent advancements in quantum chemistry, enabling readers to calculate absolute single-photon and Raman transition strengths, are also presented. Illustrated with detailed example calculations of molecular structure and transition rates, this self-contained reference for spectroscopic data analysis will appeal to professionals in mechanical, aerospace, and chemical engineering, and in applied physics and chemistry.
This book is for anyone enthralled by the romantic dream of a voyage 'to the stars.' From our current viewpoint in the twenty-first century, crewed interstellar travel will be an exceptionally difficult undertaking. It will require building a spacecraft on a scale never before attempted, at vast cost, relying on unproven technologies. Yet somehow, through works of science fiction, TV and movies, the idea of human interstellar travel being easy or even inevitable has entered our popular consciousness. In this book, Ed Regis critically examines whether humankind is bound for distant stars, or if instead we are bound to our own star, for the indefinite future. How do we overcome the main challenge that even the nearest stars are unimaginably far away? He explores the proposed technologies and the many practical aspects of undertaking an interstellar journey, finishing with his reflections on whether such a journey should be planned for.
The N-body problem has been investigated since Isaac Newton, however vast tracts of the problem remain open. Showcasing the vibrancy of the problem, this book describes four open questions and explores progress made over the last 20 years. After a comprehensive introduction, each chapter focuses on a different open question, highlighting how the stance taken and tools used vary greatly depending on the question. Progress on question one, 'Are the central configurations finite?', uses tools from algebraic geometry. Two, 'Are there any stable periodic orbits?', is dynamical and requires some understanding of the KAM theorem. The third, 'Is every braid realised?', requires topology and variational methods. The final question, 'Does a scattered beam have a dense image?', is quite new and formulating it precisely takes some effort. An excellent resource for students and researchers of mathematics, astronomy, and physics interested in exploring state-of-the-art techniques and perspectives on this classical problem.
Research applications of complex systems and nonlinear physics are rapidly expanding across various scientific disciplines. A common theme among them is the concept of “self-organized criticality systems”, which this volume presents in detail for observed astrophysical phenomena, such as solar flares, coronal mass ejections, solar energetic particles, solar wind, stellar flares, magnetospheric events, planetary systems, galactic and black-hole systems. The author explores fundamental questions: Why do power laws, the hallmarks of self-organized criticality, exist? What power law index is predicted for each astrophysical phenomenon? Which size distributions have universality? What can waiting time distributions tell us about random processes? This is the first monograph that tests comprehensively astrophysical observations of self-organized criticality systems for students, post-docs, and researchers. A highlight is a paradigm shift from microscopic concepts, such as the traditional cellular automaton algorithms, to macroscopic concepts formulated in terms of physical scaling laws.
This book contains more than 300 problems in quantum mechanics with accompanying solutions, covering topics that are commonly taught in first-year graduate physics programs. Special care is given to each problem's formulation, with detailed and extensive solutions provided to support understanding. The problems span a range of difficulties, from basic exercises to more challenging applications and extensions of the standard material. Students are required to think critically and incorporate physics and mathematical techniques learned previously or concurrently to solve the more challenging problems. Each chapter begins by framing the particular topic being examined with a short theory section that sets the context for and motivates the problems that follow. This text is well suited for self-study or as a useful supplement to the existing quantum mechanics textbooks for upper-undergraduate and graduate students, and their instructors.
Neoclassical economics is heavily based on a formalistic method, primarily centred on mathematical deduction. Consequently, mainstream economists became overfocused on describing the states of an economy rather than understanding the processes driving these states. However, many phenomena arise from the intricate interactions among diverse elements, eluding explanation solely through micro-level rules. Such systems, characterised by emergent properties arising from interactions, are defined as complex. This Element delves into the complexity approach, portraying the economy as an evolving system undergoing structural changes over time.
The global race to build the world's first quantum computer has attracted enormous investment from government and industry, and it attracts a growing pool of talent. As with many cutting-edge technologies, the optimal implementation is not yet settled. This important textbook describes four of the most advanced platforms for quantum computing: nuclear magnetic resonance, quantum optics, trapped ions, and superconducting systems. The fundamental physical concepts underpinning the practical implementation of quantum computing are reviewed, followed by a balanced analysis of the strengths and weaknesses inherent to each type of hardware. The text includes more than 80 carefully designed exercises with worked solutions available to instructors, applied problems from key scenarios, and suggestions for further reading, facilitating a practical and expansive learning experience. Suitable for senior undergraduate and graduate students in physics, engineering, and computer science, Building Quantum Computers is an invaluable resource for this emerging field.
An indispensable resource for readers in physics and mathematics seeking a solid grasp of the mathematical tools shaping modern theoretical physics, this book comprises a practical introduction to the mathematical theory of modular forms and their application to the physics of string theory and supersymmetric Yang-Mills theory. Suitable for adventurous undergraduates, motivated graduate students, and researchers wishing to navigate the intersection of cutting-edge research in physics and mathematics, it guides readers from the theory of elliptic functions to the fascinating mathematical world of modular forms, congruence subgroups, Hecke theory, and more. Having established a solid basis, the book proceeds to numerous applications in physics, with only minimal prior knowledge assumed. Appendices review foundational topics, making the text accessible to a broad audience, along with exercises and detailed solutions that provide opportunities for practice. After working through the book, readers will be equipped to carry out research in the field.
Orbital motions have always been used to test gravitational theories which, from time to time, have challenged the then-dominant paradigms. This book provides a unified treatment for calculating a wide variety of orbital effects due to general relativity and modified models of gravity, to its first and second post-Newtonian orders, in full generality. It gives explicit results valid for arbitrary orbital configurations and spin axes of the sources, without a priori simplifying assumptions on either the orbital eccentricity or inclination. These general results apply to a range of phenomena, from Earth's artificial satellites to the S-stars orbiting the supermassive black hole in the Galactic Centre to binary and triple pulsars, exoplanets, and interplanetary probes. Readers will become acquainted with working out a variety of orbital effects other than the time-honoured perihelion precession, designing their own space-based tests, performing effective sensitivity analyses, and assessing realistic error budgets.
The quantum information revolution has had a huge impact not only on quantum technologies, including quantum computing and cryptography, but also on the foundations of quantum mechanics. This book presents the information viewpoint on the foundations of quantum physics by highlighting the role of complementarity and contextuality and coupling the ideas of the fathers of quantum mechanics, Bohr and Einstein, with the modern quantum information framework. The classical-quantum dilemma is resolved through an appeal to the Bild conception of scientific theories established in the 19th century by Hertz and Boltzmann. Bell inequalities are treated from the complementarity-contextuality viewpoint, supporting the attempts to discard nonlocality from quantum physics. Philosophical aspects of the topic are explored from a physicist's perspective, balancing accessibility with scientific rigour. This unique approach to quantum foundations will be of interest to graduates, Ph.D. students and researchers in fields ranging from quantum information to philosophy.
This Element works as non-technical overview of Agent-Based Modelling (ABM), a methodology which can be applied to economics, as well as fields of natural and social sciences. This Element presents the introductory notions and historical background of ABM, as well as a general overview of the tools and characteristics of this kind of models, with particular focus on more advanced topics like validation and sensitivity analysis. Agent-based simulations are an increasingly popular methodology which fits well with the purpose of studying problems of computational complexity in systems populated by heterogeneous interacting agents.
How did life originate? Is there life beyond Earth? What is the future of life on our planet? The rapidly growing multidisciplinary field of astrobiology deals with life's big questions. This text harnesses the authors' two decades' experience of teaching acclaimed courses in astrobiology, and adopts a novel quantitative approach towards this emergent discipline. It details the physical principles and chemical processes that have shaped the origins and distribution of molecules, stars, planets, and hence habitable environments, life, and intelligence in the Universe. By synthesising insights from domains as diverse as astronomy and physics to microbiology, biochemistry, and geology, the authors provide a cutting-edge summary of astrobiology, and show how answers to many fundamental questions are drawing closer than ever. Geared towards advanced undergraduates and graduate students in the physical sciences, the text contains more than 150 innovative problems designed to enhance students' knowledge and understanding.
Steven Weinberg shares his candid thoughts, in his own words, on theoretical physics and cosmology, along with personal anecdotes and recollections of the people who helped shape his career. These memoirs of his life as a scientist and public figure cover his student days and early career, through the golden age of particle physics in the 1970s, his being awarded the Nobel prize, through to the end of the twentieth century. In addition to his research insights, Weinberg provides glimpses into his life in academia more broadly: dealing with the 'two-body problem', tenure, international conference travel, his book-writing, advisory work with JASON, and his advocacy for the Superconducting Super Collider. Physicists, historians of science and interested readers will find the presentation engaging and often witty, as Weinberg reflects on his life in physics.
The aim of this Element is to understand how far mathematical theories based on active particle methods have been applied to describe the dynamics of complex systems in economics, and to look forward to further research perspectives in the interaction between mathematics and economics. The mathematical theory of active particles and the theory of behavioural swarms are selected for the above interaction. The mathematical approach considered in this work takes into account the complexity of living systems, which is a key feature of behavioural economics. The modelling and simulation of the dynamics of prices within a heterogeneous population is reviewed to show how mathematical tools can be used in real applications.
Quantum Models of Cognition and Decision, Second Edition presents a fully updated and expanded version of this innovative and path-breaking text. It offers an accessible introduction to the intersection of quantum theory and cognitive science, covering new insights, modelling techniques, and applications for understanding human cognition and decision making. In it, Busemeyer and Bruza delve into such topics as the non-commutative nature of judgments, quantum interference as a general principle governing human decision making, contextuality in modelling human cognition, and thought-provoking speculation about what a quantum approach to cognition might reveal about the ultimate nature of the human mind. Additions include new material on measurement, open systems, and applications to computer science. Requiring no prior background in quantum physics, this book comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.
The population balance methodology provides a powerful framework for studying polydisperse entities such as aerosols, crystals and bubbles. This self-contained and accessible book explains how this theoretical framework can be employed across a wide range of scientific, engineering and environmental problems. The methodology is explained step-by-step, showing readers how to use these techniques by formulating the population balance problem, choosing models and implementing appropriate solution methods. Particular focus is given to the coupling of the population balance with fluid mechanics and computational fluid dynamics (CFD), in both laminar and turbulent flows. Applications of the population balance methodology are explored in case studies including nanoparticle synthesis, soot formation and crystallisation, and sample open-source code is provided. This book will be valuable to researchers across a range of disciplines including chemical and mechanical engineering, physics and environmental science, and can be used as a resource for advanced undergraduate and graduate courses.