This book is an introduction to the arrow of time in thermodynamics and cosmology, and develops a new quantum measurement theory in which the foregoing concepts play an essential role. The first chapter is an overview and 'route map' and is followed by an exposition of irreversibility, the expansion of the Universe and other arrows of time. The author examines the thesis that the thermodynamic arrow follows the cosmological one, and in doing so extends traditional statistical mechanics. The second part of the book presents a new theory of quantum measurement and possible experimental tests. This theory incorporates the extended statistical mechanics in an essential way. The last chapter discusses open experimental and theoretical issues. Written in a lively and accessible style, the text is liberally sprinkled with exercises. Each chapter ends with a resources section that includes notes, further reading, and technical appendices.
This book is an introduction to the arrow of time in thermodynamics and cosmology, and develops a new quantum measurement theory in which the foregoing concepts play an essential role. The first chapter is an overview and 'route map' and is followed by an exposition of irreversibility, the expansion of the Universe and other arrows of time. The author examines the thesis that the thermodynamic arrow follows the cosmological one, and in doing so extends traditional statistical mechanics. The second part of the book presents a new theory of quantum measurement and possible experimental tests. This theory incorporates the extended statistical mechanics in an essential way. The last chapter discusses open experimental and theoretical issues. Written in a lively and accessible style, the text is liberally sprinkled with exercises. Each chapter ends with a resources section that includes notes, further reading, and technical appendices.
This book adopts a novel, physics-first approach to quantum measurement, using physical experiments as the basis to describe the underlying mathematical formalism. Topics covered include weak measurements, quantum measurement reversal, quantum trajectories and the stochastic path integral formalism. The theory of quantum measurement is also covered in detail, including discussion of how it can be tested and demonstrated in a laboratory: how to build quantum-limited amplifiers, fundamental noise limits imposed on measurement by quantum mechanics, and the design of superconducting circuits. This text is an excellent introduction for students with a basic understanding of quantum mechanics wanting to learn more about measurement theory, and the inclusion of a wide selection of end-of-chapter exercises make this book ideal for emerging courses on the topic. Key chapters introducing the foundations of quantum computing and the history of measurement theory are equally accessible to a broader, less specialised audience.
In the last two decades there has been an enormous progress in the experimental investigation of single quantum systems. This progress covers fields such as quantum optics, quantum computation, quantum cryptography, and quantum metrology, which are sometimes summarized as `quantum technologies'. A key issue there is entanglement, which can be considered as the characteristic feature of quantum theory. As disparate as these various fields maybe, they all have to deal with a quantum mechanical treatment of the measurement process and, in particular, the control process. Quantum control is, according to the authors, `control for which the design requires knowledge of quantum mechanics'. Quantum control situations in which measurements occur at important steps are called feedback (or feedforward) control of quantum systems and play a central role here. This book presents a comprehensive and accessible treatment of the theoretical tools that are needed to cope with these situations. It also provides the reader with the necessary background information about the experimental developments. The authors are both experts in this field to which they have made significant contributions. After an introduction to quantum measurement theory and a chapter on quantum parameter estimation, the central topic of open quantum systems is treated at some length. This chapter includes a derivation of master equations, the discussion of the Lindblad form, and decoherence – the irreversible emergence of classical properties through interaction with the environment. A separate chapter is devoted to the description of open systems by the method of quantum trajectories. Two chapters then deal with the central topic of quantum feedback control, while the last chapter gives a concise introduction to one of the central applications – quantum information. All sections contain a bunch of exercises which serve as a useful tool in learning the material. Especially helpful are also various separate boxes presenting important background material on topics such as the block representation or the feedback gain-bandwidth relation. The two appendices on quantum mechanics and phase-space and on stochastic differential equations serve the same purpose. As the authors emphasize, the book is aimed at physicists as well as control engineers who are already familiar with quantum mechanics. It takes an operational approach and presents all the material that is needed to follow research on quantum technologies. On the other hand, conceptual issues such as the relevance of the measurement process for the interpretation of quantum theory are neglected. Readers interested in them may wish to consult instead a textbook such as Decoherence and the Quantum-to-Classical Transition by Maximilian Schlosshauer. Although the present book does not contain applications to gravity, part of its content might become relevant for the physics of gravitational-wave detection and quantum gravity phenomenology. In this respect it should be of interest also for the readers of this journal.
Abstract This book provides the reader with a contemporary and comprehensive introduction to Quantum Mechanics. It is suitable for beginners as well as for more advanced university students. Quantum mechanics is presented in a pedagogical fashion, with a clear logical organization. The various concepts and methods are introduced first in elementary terms, and later developed into more precise formulations. Systematic studies of approximation methods and the discussion of a wide class of physical applications follow. Part I of the book, together with the opening sections of Part II, provide adequate material for an introductory course of one semester at most universities. The rest of the book might be used in an advanced course on Quantum Mechanics. The basic material is fairly standard, even though some discussions such as those on general systems with time-dependent Hamiltonians, on metastable systems, as well as the discussions in some of the Complement sections, may not be found in other textbooks. The book also contains many original observations or new ways of illustrating even well-known subjects. In fact, the authors wish to convey in this book the sense of wonder in the logical simplicity and at the same time the beauty of subtle and far-reaching consequences of Quantum Mechanics, to young physics students in particular. Problem sets are provided at the end of each chapter, to be solved either analytically or by numerical methods. The solutions to both types of problems are given as separate pdf files or as Mathematica notebooks (there are 88 of them), all together on a CD accompanying the textbook. The presence of such a collection of numerical analyses enriches the main text and is one of the characteristic features of the book. With the many interesting systems discussed, the book will also be a useful reference for researchers and teachers. It provides the reader with a unique, enjoyable and rather complete textbook of Quantum Mechanics, destined to set a new standard for many years to come.
Within the general formalism of quantum theory irreversibility and the arrow of time and the in the evolution of various physical systems are studied. Irreversible behavior often manifests itself in the guise of “entropy production.” This motivates me to begin this chapter with a brief review of quantum-mechanical entropy, a subject that Elliott Lieb has made outstanding contributions to, followed by an enumeration of examples of irreversible behavior and of an arrow of time analyzed in later sections. Subsequently, a derivation of the laws of thermodynamics from (quantum) statistical mechanics, and, in particular, of the Second Law of thermodynamics, in the forms given to it by Clausius and Carnot, is presented. In a third part, results on diffusive (Brownian) motion of a quantum particle interacting with a quasi-free quantum-mechanical heat bath are reviewed. This is followed by an outline of a theory of friction by emission of Cherenkov radiation of sound waves in a system consisting of a particle moving through a Bose–Einstein condensate and interacting with it. In what may be the most important section of this chapter, the fundamental arrow of time inherent in Quantum Mechanics is discussed.
The well known theoretical physicist and editor of the Journal of Mathematical Physics has written a handy book, with eight chapters devoted to the broader knowledge of and reflection about physical theories, notably quantum theory. After thinking about what is a physical theory, he addresses the problem of the state in quantum theory (a very central chapter of the book), the power of mathematics, the field - particle issue (the author pleads for the superiority of the field concept - the book is very indebted to Julian Schwinger's ideas), symmetry in physics, the problem of causality and probability, the five different arrows of time (from cause-effect ordering to the cosmological arrow), and finally turns to the presently quite often discussed relation of the quantum-mechanical description to reality. After one has learned that the author is not approaching the questions from a sharper historical point of view, and that he shares the prejudices of a mathematical physicist toward experiment, one thoroughly enjoys his elegant, competent and deep treatment. This reviewer wishes that every graduate student of physics should, at an early stage, read Newton's book (which could be done either at a stroke or piecewise) because it presents the essence of a great deal of modern physical theory in both a condensed and leisurely digestible form.
Quantum physics is believed to be the fundamental theory underlying our understanding of the physical universe. However, it is based on concepts and principles that have always been difficult to understand and controversial in their interpretation. This book aims to explain these issues using a minimum of technical language and mathematics. After a brief introduction to the ideas of quantum physics, the problems of interpretation are identified and explained. The rest of the book surveys, describes and criticises a range of suggestions that have been made with the aim of resolving these problems; these include the traditional, or 'Copenhagen' interpretation, the possible role of the conscious mind in measurement, and the postulate of parallel universes. This new edition has been revised throughout to take into account developments in this field over the past fifteen years, including the idea of 'consistent histories' to which a completely new chapter is devoted.