Operational Quantum Physics


Book Description

Operational Quantum Physics offers a systematic presentation of quantum mechanics which makes exhaustive use of the full probabilistic structure of this theory. Accordingly the notion of an observable as a positive operator valued (POV) measure is explained in great detail, and the ensuing quantum measurement theory is developed and applied both to a resolution of long-standing conceptual and interpretational puzzles in the foundations of quantum mechanics, and to an analysis of various recent fundamental experiments. The book, or different parts of it, may be of interest to advanced students or researchers in quantum physics, to philosophers of physics, and to mathematicians working in operator valued measures.




Statistical Structure of Quantum Theory


Book Description

New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.




Essential Astrophysics


Book Description

Essential Astrophysics is a book to learn or teach from, as well as a fundamental reference volume for anyone interested in astronomy and astrophysics. It presents astrophysics from basic principles without requiring any previous study of astronomy or astrophysics. It serves as a comprehensive introductory text, which takes the student through the field of astrophysics in lecture-sized chapters of basic physical principles applied to the cosmos. This one-semester overview will be enjoyed by undergraduate students with an interest in the physical sciences, such as astronomy, chemistry, engineering or physics, as well as by any curious student interested in learning about our celestial science. The mathematics required for understanding the text is on the level of simple algebra, for that is all that is needed to describe the fundamental principles. The text is of sufficient breadth and depth to prepare the interested student for more advanced specialised courses in the future. Astronomical examples are provided throughout the text, to reinforce the basic concepts and physics, and to demonstrate the use of the relevant formulae. In this way, the student learns to apply the fundamental equations and principles to cosmic objects and situations. Astronomical and physical constants and units as well as the most fundamental equations can be found in the appendix. Essential Astrophysics goes beyond the typical textbook by including references to the seminal papers in the field, with further reference to recent applications, results, or specialised literature.




Line Groups in Physics


Book Description

Over last decades low-dimensional materials are in focus of physics and chemistry as well as of material and other natural sciences. Like Vitaly Ginzburg has foreseen 30 years ago, low dimensionality offers physical phenomena and properties unseen in three-dimensional world. To see how thin ?lms and monomolecular layers realize such a prediction it suf?ces only to observe intensity of research devoted to recently synthesized graphene. Still, quasi-one-dimensional compounds are over long period established as the origin of the most important and most interesting discoveries of material science and solid state physics. To mention only deoxyribonucleic acid, the most important molecule in nature, and diversity of nanotubes and nanowires, the cornerstones of the present and future nanotechnology. Line groups, describing symmetry of quasi-one-dimensional materials, offer the deepest insight to their characteristic properties. Underlying many of the laws, they are very useful, but far from simple. This book is intended to explain them, their properties, and their most common applications. In particular, it is important to understand that the line groups are much wider class of symmetries than the well-known rod groups. While the latter describe only translationally periodical objects, line groups include symmetries of incommensurate periodical structures.




Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems


Book Description

The quantum-mechanical few-body problem is of fundamental importance for all branches of microphysics and it has substantially broadened with the advent of modern computers. This book gives a simple, unified recipe to obtain precise solutions to virtually any few-body bound-state problem and presents its application to various problems in atomic, molecular, nuclear, subnuclear and solid state physics. The main ingredients of the methodology are a wave-function expansion in terms of correlated Gaussians and an optimization of the variational trial function by stochastic sampling. The book is written for physicists and, especially, for graduate students interested in quantum few-body physics.




Time in Quantum Mechanics


Book Description

The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the quantum theory. This multi-authored book, written as an introductory guide for newcomers to the subject, as well as a useful source of information for the expert, covers many of the open questions. The book describes the problems, and the attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory.




Nucleation Theory


Book Description

One of the most striking phenomena in condensed matter physics is the occurrence of abrupt transitions in the structure of a substance at certain temperatures or pressures. These are first order phase transitions, and examples such as the freezing of water are familiar in everyday life. The conditions at which the transformation takes place can sometimes vary. For example, the freezing point of water is not always 0°C, but the liquid can be supercooled considerably if it is pure enough and treated carefully. The reason for this phenomenon is nucleation. This monograph covers all major available routes of theoretical research of nucleation phenomena (phenomenological models, semi-phenomenological theories, density functional theories, microscopic and semi-microscopic approaches), with emphasis on the formation of liquid droplets from a metastable vapor. Also, it illustrates the application of these various approaches to experimentally relevant problems. In spite of the familiarity of the involved phenomena, it is still impossible to calculate nucleation accurately, as the properties and the kinetics of the daughter phase are insufficiently well known. Existing theories based upon classical nucleation theory have on the whole explained the trends in behavior correctly. However they often fail spectacularly to account for new data, in particular in the case of binary or, more generally, multi-component nucleation. The current challenge of this book is to go beyond such classical models and provide a more satisfactory theory by using density functional theory and microscopic computer simulations in order to describe the properties of small clusters. Also, semi-phenomenological models are proposed, which attempt to relate the properties of small clusters to known properties of the bulk phases. This monograph is an introduction as well as a compendium to researchers in soft condensed matter physics and chemical physics, graduate and post-graduate students in physics and chemistry starting on research in the area of nucleation, and to experimentalists wishing to gain a better understanding of the efforts being made to account for their data.




Statistical Physics for Cosmic Structures


Book Description

This book has its roots in a series of collaborations in the last decade at the interface between statistical physics and cosmology. The speci?c problem which initiated this research was the study of the clustering properties of galaxies as revealed by large redshift surveys, a context in which concepts of modern statistical physics (e. g. scale-invariance, fractality. . ) ?nd ready application. In recent years we have considerably broadened the range of problems in cosmology which we have addressed, treating in particular more theoretical issues about the statistical properties of standard cosmological models. What is common to all this research, however, is that it is informed by a perspective and methodology which is that of statistical physics. We can say that, beyond its speci?c scienti?c content, this book has an underlying thesis: such interdisciplinary research is an exciting playground for statistical physics, and one which can bring new and useful insights into cosmology. The book does not represent a ?nal point, but in our view, a marker in the development of this kind of research, which we believe can go very much further in the future. Indeed as we complete this book, new developments - which unfortunately we have not been able to include here - have been made on some of the themes described here. Our focus in this book is on the problem of structure in cosmology.




A First Course in Topos Quantum Theory


Book Description

In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory’s unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity. The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory? A possible way to overcome critical issues in present-day quantum physics – such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility of talking about systems without reference to an external observer – is through a reformulation of quantum theory in terms of a different mathematical framework called topos theory. This course-tested primer sets out to explain to graduate students and newcomers to the field alike, the reasons for choosing topos theory to resolve the above-mentioned issues and how it brings quantum physics back to looking more like a “neo-realist” classical physics theory again.




Spacetime


Book Description

One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities". add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.