Best known for his theory of electromagnetism, James Clerk Maxwell (1831–79) was Cambridge University's first Cavendish Professor of Experimental Physics. Albert Einstein described his work as 'the most profound and the most fruitful that physics has experienced since the time of Newton'. He carried out brilliant work in thermodynamics and statistical mechanics, laying the foundation for the kinetic theory of gases. This book, published originally in 1871, summarises his work in this field. It includes the 'Maxwell relations' that still feature in every standard text on thermodynamics. It also outlines his famous thought experiment, later named Maxwell's 'demon'. This idea, which appeared to contradict the second law of thermodynamics, would inspire scientific debate well into the twentieth century. More recently, it has sparked developments in the new sciences of nanotechnology and quantum computing.
Path integrals provide a powerful method for describing quantum phenomena. This book introduces the quantum mechanics of particles that move in curved space by employing path integrals and then using them to compute anomalies in quantum field theories. The authors start by deriving path integrals for particles moving in curved space and their supersymmetric generalizations. They then discuss the regularization schemes essential to constructing and computing these path integrals. This topic is used to introduce regularization and renormalization in quantum field theories in a wider context. These methods are then applied to discuss and calculate anomalies in quantum field theory. Such anomalies provide enormous constraints in the search for physical theories of elementary particles, quantum gravity and string theories. An advanced text for researchers and graduate students of quantum field theory and string theory, the first part is also a stand-alone introduction to path integrals in q
Path integrals provide a powerful method for describing quantum phenomena. This book introduces the quantum mechanics of particles that move in curved space by employing path integrals and then using them to compute anomalies in quantum field theories. The authors start by deriving path integrals for particles moving in curved space and their supersymmetric generalizations. They then discuss the regularization schemes essential to constructing and computing these path integrals. This topic is used to introduce regularization and renormalization in quantum field theories in a wider context. These methods are then applied to discuss and calculate anomalies in quantum field theory. Such anomalies provide enormous constraints in the search for physical theories of elementary particles, quantum gravity and string theories. An advanced text for researchers and graduate students of quantum field theory and string theory, the first part is also a stand-alone introduction to path integrals in q
The First Book on Ultracold MoleculesCold molecules offer intriguing properties on which new operational principles can be based (e.g., quantum computing) or that may allow researchers to study a qual
An original comprehensive guide on computational nanomechanics discussing basic concepts and implications in areas such as computational physics, materials, mechanics and engineering as well as several other interdisciplinary avenues. This book makes the underlying theory accessible to readers without specialised training or extensive background in quantum physics, statistical mechanics, or theoretical chemistry. It combines a careful treatment of theoretical concepts with a detailed tutorial on computer software and computing implementation, including multiscale simulation and computational statistical theory. Multidisciplinary perspectives are provided, yielding a true insight on the applications of computational nanomechanics across diverse engineering fields. The book can serve as a practical guide with step-by-step discussion of coding, example problems and case studies. This book will be essential reading for students new to the subject, as well as an excellent reference for gra
Perceptual organization is the neuro-cognitive process that enables us to perceive scenes as structured wholes consisting of objects arranged in space. Simplicity in Vision explores the intriguing idea that these perceived wholes are given by the simplest organizations of the scenes. Peter A. van der Helm presents a truly multidisciplinary approach to answer fundamental questions such as: Are simplest organizations sufficiently reliable to guide our actions? What is the nature of the regularities that are exploited to arrive at simplest organizations? To account for the high combinatorial capacity and speed of the perceptual organization process, he proposes transparallel processing by hyperstrings. This special form of distributed processing not only gives classical computers the extraordinary computing power that seemed reserved for quantum computers, but also explains how neuronal synchronization relates to flexible self-organizing cognitive architecture in between the relatively ri
Although computation and the science of physical systems would appear to be unrelated, there are a number of ways in which computational and physical concepts can be brought together in ways that illuminate both. This volume examines fundamental questions which connect scholars from both disciplines: is the universe a computer? Can a universal computing machine simulate every physical process? What is the source of the computational power of quantum computers? Are computational approaches to solving physical problems and paradoxes always fruitful? Contributors from multiple perspectives reflecting the diversity of thought regarding these interconnections address many of the most important developments and debates within this exciting area of research. Both a reference to the state of the art and a valuable and accessible entry to interdisciplinary work, the volume will interest researchers and students working in physics, computer science, and philosophy of science and mathematics.
Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG
Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and because of the discovery of surprising and powerful algorithms. As a consequence, algorithmic number theory has gradually emerged as an important and distinct field with connections to computer science and cryptography as well as other areas of mathematics. This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students, written by the leading experts in the field. It includes several articles that cover the essential topics in this area, and in addition, there are contributions pointing in broader directions, including cryptography, computational class field theory, zeta functions and L-series, discrete logarithm algorithms, and quantum computing.
Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and because of the discovery of surprising and powerful algorithms. As a consequence, algorithmic number theory has gradually emerged as an important and distinct field with connections to computer science and cryptography as well as other areas of mathematics. This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students, written by the leading experts in the field. It includes several articles that cover the essential topics in this area, and in addition, there are contributions pointing in broader directions, including cryptography, computational class field theory, zeta functions and L-series, discrete logarithm algorithms, and quantum computing.
Leading young scientists, many holding prestigious Royal Society Research Fellowships, describe their research and give their visions of the future. Re-written in a popular and well illustrated style, the articles are derived from scholarly and authoritative papers published in a special Millennium Issue of the Royal Society's Philosophical Transactions (used by Newton, this is the world's longest running scientific journal). Carefully selected by the journal's editor, Professor J. M. T. Thompson FRS, topics include quantum physics and its relation to relativity theory and human consciousness; electronics for the future; exotic quantum computing and data storage; telecommunications and the internet. The book conveys the excitement and enthusiasm of the young authors for their work in Physics and Electronics. Two companion books cover Astronomy and Earth Science, and Chemistry and Life Science. All are definitive reviews for anyone with a general interest in the future directions of sci
The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups (both finite and infinite). In the text Dr Martin gives a full, self-contained account of this algebra and these links, covering both the basic theory of Schur algebras and related areas. He discusses the usual representation-theoretic topics such as constructions of irreducible modules, the blocks containing them, their modular characters and the problem of computing decomposition numbers; moreover deeper properties such as the quasi-hereditariness of the Schur algebra are discussed. The opportunity is taken to give an account of quantum versions of Schur algebras and their relations with certain q-deformations of the coordinate rings of the general linear group. The approach is combinatorial where possible, making the presentation accessible to graduate students. This is the first comprehensive text in this important and active area of research; it wi
Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG
Information retrieval, IR, the science of extracting information from any potential source, can be viewed in a number of ways: logical, probabilistic and vector space models are some of the most important. In this book, the author, one of the leading researchers in the area, shows how these views can be reforged in the same framework used to formulate the general principles of quantum mechanics. All the usual quantum-mechanical notions have their IR-theoretic analogues, and the standard results can be applied to address problems in IR, such as pseudo-relevance feedback, relevance feedback and ostensive retrieval. The relation with quantum computing is also examined. To keep the book self-contained appendices with background material on physics and mathematics are included. Each chapter ends with bibliographic remarks that point to further reading. This is an important, ground-breaking book, with much new material, for all those working in IR, AI and natural language processing.
A year of HBR's essential thinking on tech—all in one place.From quantum computing to VR training and from 3D printing to brain-computer interface, new technologies are reshaping business on the factory floor and in the C-suite. What should you and your company be doing now to take advantage of the new opportunities these technologies are creating—and to avoid falling victim to disruption?The Year in Tech, 2022: The Insights You Need from Harvard Business Review will help you understand what the latest and most important tech innovations mean for your organization and how you can use them to compete and win in today's turbulent business environment.Business is changing. Will you adapt or be left behind?Get up to speed and deepen your understanding of the topics that are shaping your company's future with the Insights You Need from Harvard Business Review series. Featuring HBR's smartest thinking on fast-moving issues—blockchain, cybersecurity, AI, and more—each book provides the founda
From Jim Holt, the New York Times bestselling author of Why Does the World Exist?, comes an entertaining and accessible guide to the most profound scientific and mathematical ideas of recent centuries in When Einstein Walked with Gödel: Excursions to the Edge of Thought.Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? In this scintillating collection, Holt explores the human mind, the cosmos, and the thinkers who’ve tried to encompass the latter with the former. With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, f
Although computation and the science of physical systems would appear to be unrelated, there are a number of ways in which computational and physical concepts can be brought together in ways that illuminate both. This volume examines fundamental questions which connect scholars from both disciplines: is the universe a computer? Can a universal computing machine simulate every physical process? What is the source of the computational power of quantum computers? Are computational approaches to solving physical problems and paradoxes always fruitful? Contributors from multiple perspectives reflecting the diversity of thought regarding these interconnections address many of the most important developments and debates within this exciting area of research. Both a reference to the state of the art and a valuable and accessible entry to interdisciplinary work, the volume will interest researchers and students working in physics, computer science, and philosophy of science and mathematics.
Magnetism in carbon nanostructures is a rapidly expanding field of current materials science. Its progress is driven by the wide range of applications for magnetic carbon nanosystems, including transmission elements in spintronics, building blocks of cutting-edge nanobiotechnology, and qubits in quantum computing. These systems also provide novel paradigms for basic phenomena of quantum physics, and are thus of great interest for fundamental research. This comprehensive survey emphasizes both the fundamental nature of the field, and its groundbreaking nanotechnological applications, providing a one-stop reference for both the principles and the practice of this emerging area. With equal relevance to physics, chemistry, engineering and materials science, senior undergraduate and graduate students in any of these subjects, as well as all those interested in novel nanomaterials, will gain an in-depth understanding of the field from this concise and self-contained volume.
That everyone has a human right to enjoy the benefits of the progress of science and its applications comes as a surprise to many. Nevertheless, this right is pertinent to numerous issues at the intersection of science and society: open access; 'dual use' science; access to ownership and dissemination of data, knowledge, methods and the affordances and applications thereof; as well as the role of international co-operation, human dignity and other human rights in relation to science and its products. As we advance towards superintelligence, quantum computing, drone swarms, and life-extension technology, serious policy decisions will be made at the national and international levels. The human right to science provides an ideal tool to do so, backed up as it is by international law, political heft, and normative weight. This book is the first sustained attempt at turning this wonder of foresight into an actionable and justiciable right. This title is also available as Open Access on Camb
Topological Phases of Matter are an exceptionally dynamic field of research: several of the most exciting recent experimental discoveries and conceptual advances in modern physics have originated in this field. These have generated new, topological, notions of order, interactions and excitations. This text provides an accessible, unified and comprehensive introduction to the phenomena surrounding topological matter, with detailed expositions of the underlying theoretical tools and conceptual framework, alongside accounts of the central experimental breakthroughs. Among the systems covered are topological insulators, magnets, semimetals, and superconductors. The emergence of new particles with remarkable properties such as fractional charge and statistics is discussed alongside possible applications such as fault-tolerant topological quantum computing. Suitable as a textbook for graduate or advanced undergraduate students, or as a reference for more experienced researchers, the book ass
