Advances in Quantum Chemistry publishes articles and invited reviews by leading international researchers in quantum chemistry. Quantum chemistry deals particularly with the electronic structure of atoms, molecules, and crystalline matter and describes it in terms of electron wave patterns. It uses physical and chemical insight, sophisticated mathematics and high-speed computers to solve the wave equations and achieve its results. Advances highlights these important, interdisciplinary developments.

Structured singular light is an ubiquitous phenomenon. It is not only created when light refracts at a water surface but can also be found in the blue daytime sky. Such light fields include a spatially varying amplitude, phase, or polarization, enabling the occurrence of optical singularities. As structurally stable units of the light field, these singularities are particularly interesting since they determine its topology. In this excellent book, the author presents a pioneering study of structured singular light, thereby contributing many original approaches. Especially in the field of polarization and its rich number of different types of singularities the book defines and drives a completely new field. The work demonstrates how to control complex polarization singularity networks and their propagation. Additionally, the author pioneers tightly focusing vectorial beams, also developing an urgently needed detection scheme for three-dimensional nanoscale polarization structures. She also studies classical spatial entanglement using structured light, introducing entanglement beating and paraxial spin-orbit-coupling. The book is hallmarked by its comprehensive and thorough way of describing a plethora of different approaches to structure light by amplitude, phase and polarization, as well as the important role of optical singularities.

Quantum theory is one of the most fascinating and successful constructs in the intellectual history of mankind. Nonetheless, the theory has very shaky philosophical foundations. This book contains thoughtful discussions by eminent researchers of a spate of experimental techniques newly developed to test some of the stranger predictions of quantum physics. The advances considered include recent experiments in quantum optics, electron and ion interferometry, photon down conversion in nonlinear crystals, single trapped ions interacting with laser beams, atom-field coupling in micromaser cavities, quantum computation, quantum cryptography, decoherence and macroscopic quantum effects, the quantum state diffusion model, quantum gravity, the quantum mechanics of cosmology and quantum non-locality along with the continuing debate surrounding the interpretation of quantum mechanics. Audience: The book is intended for physicists, philosophers of science, mathematicians, graduate students and those interested in the foundations of quantum theory.

As miniaturisation deepens, and nanotechnology and its machines become more prevalent in the real world, the need to consider using quantum mechanical concepts to perform various tasks in computation increases. Such tasks include: the teleporting of information, breaking heretofore "unbreakable" codes, communicating with messages that betray eavesdropping, and the generation of random numbers. This is the first book to apply quantum physics to the basic operations of a computer, representing the ideal vehicle for explaining the complexities of quantum mechanics to students, researchers and computer engineers, alike, as they prepare to design and create the computing and information delivery systems for the future. Both authors have solid backgrounds in the subject matter at the theoretical and more practical level. While serving as a text for senior/grad level students in computer science/physics/engineering, this book has its primary use as an up-to-date reference work in the emerging interdisciplinary field of quantum computing - the only prerequisite being knowledge of calculus and familiarity with the concept of the Turing machine.

An introduction to how the mathematical tools from quantum field theory can be applied to economics and finance, providing a wide range of quantum mathematical techniques for designing financial instruments. The ideas of Lagrangians, Hamiltonians, state spaces, operators and Feynman path integrals are demonstrated to be the mathematical underpinning of quantum field theory, and which are employed to formulate a comprehensive mathematical theory of asset pricing as well as of interest rates, which are validated by empirical evidence. Numerical algorithms and simulations are applied to the study of asset pricing models as well as of nonlinear interest rates. A range of economic and financial topics are shown to have quantum mechanical formulations, including options, coupon bonds, nonlinear interest rates, risky bonds and the microeconomic action functional. This is an invaluable resource for experts in quantitative finance and in mathematics who have no specialist knowledge of quantum field theory.

This is the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.

The main unique feature of Nonrelativistic Quantum Mechanics is its discussion of Hilbert space and rigged Hilbert space. This invaluable book is suitable for advanced undergraduate students as well as graduate students.

This thesis casts new light on quantum entanglement of photons with complex spatial patterns due to direct coincidence imaging. It demonstrates novel methods to generate, investigate, and verify entanglement of complex spatial structures. Quantum theory is one of the most successful and astonishing physical theories. It made possible various technical devices like lasers or mobile phones and, at the same time, it completely changed our understanding of the world. Interestingly, such counterintuitive features like entanglement are an important building block for future quantum technologies. In photonic experiments, the transverse spatial degree of freedom offers great potential to explore fascinating phenomena of single photons and quantum entanglement. It was possible to verify the entanglement of two photons with very high quanta of orbital angular momentum, a property of photons connected to their spatial structure and theoretically unbounded. In addition, modern imaging technology was used to visualize the effect of entanglement even in real-time and to show a surprising property: photons with complex spatial patterns can be both entangled and not entangled in polarization depending on their transverse spatial position.

This volume is an outgrowth of the Second International Workshop on Macroscopic Quantum Coherence and Computing held in Napoli, Italy, in June 2000. This workshop gathered a number of experts from the major Universities and Research Institutions of several countries. The choice of the location, which recognizes the role and the traditions of Naples in this field, guaranteed the participants a stimulating atmosphere. The aim of the workshop has been to report on the recent theoretical and experimental results on the macroscopic quantum coherence of macroscopic systems. Particular attention was devoted to Josephson devices. The correlation with other atomic and molecular systems, exhibiting a macroscopic quantum behaviour, was also discussed. The seminars provided both historical overview and recent theoretical ground on the topic, as well as information on new experimental results relative to the quantum computing area. The first workshop on this topic, held in Napoli in 1998, has been ennobled by important reports on observations of Macroscopic Quantum Coherence in mesoscopic systems. The current workshop proposed, among many stimulating results, the first observations of Macroscopic Quantum Coherence between macroscopically distinct fluxoid states in rf SQUIDs, 20 years after the Leggett's proposal to experimentally test the quantum behavior of macroscopic systems. Reports on observations of quantum behaviour in molecular and magnetic systems, small Josephson devices, quantum dots have also been particularly stimulating in view of the realization of several possible q-bits.

Ever since its invention in 1929 the Dirac equation has played a fundamental role in various areas of modern physics and mathematics. Its applications are so widespread that a description of all aspects cannot be done with sufficient depth within a single volume. In this book the emphasis is on the role of the Dirac equation in the relativistic quantum mechanics of spin-1/2 particles. We cover the range from the description of a single free particle to the external field problem in quantum electrodynamics. Relativistic quantum mechanics is the historical origin of the Dirac equation and has become a fixed part of the education of theoretical physicists. There are some famous textbooks covering this area. Since the appearance of these standard texts many books (both physical and mathematical) on the non relativistic Schrodinger equation have been published, but only very few on the Dirac equation. I wrote this book because I felt that a modern, comprehensive presentation of Dirac's electron theory satisfying some basic requirements of mathematical rigor was still missing."

Waves are everywhere in our daily life. We all experience sound and light with our ears and eyes, we use microwaves to cook, and radio waves are transmitted from and are received by our cell phones. These are just some examples of waves that carry energy from point A to B. However, we may not know details of the physics underlying all these waves. It is important to understand the mechanisms that generate wave dynamics for a given system. It is not straightforward to explain how an electromagnetic i eld becomes oscillatory and propagates as a wave. Waves sometimes represent the underlying dynamics of observed phenomena at a fundamental level of physics. This book is designed to explore these mechanisms by discussing various aspects of wave dynamics from as many perspectives as possible. The target audiences are undergraduate students majoring in engineering science and graduate students majoring in general engineering. Going beyond the typical approach to learning science, this book discusses wave dynamics and related concepts at various levels of mathematics and physics, sometimes touching on profound physics behind them. This book was written to help readers learn wave dynamics on a deep physical level, and develop innovative ideas in their own fields.

Faithful communication is a necessary precondition for large-scale quantum information processing and networking, irrespective of the physical platform. Thus, the problems of quantum-state transfer and quantum-network engineering have attracted enormous interest over the last years, and constitute one of the most active areas of research in quantum information processing. The present volume introduces the reader to fundamental concepts and various aspects of this exciting research area, including links to other related areas and problems. The implementation of state-transfer schemes and the engineering of quantum networks are discussed in the framework of various quantum optical and condensed matter systems, emphasizing the interdisciplinary character of the research area. Each chapter is a review of theoretical or experimental achievements on a particular topic, written by leading scientists in the field. The volume aims at both newcomers as well as experienced researchers.

Quantum many-body theories have become an essential tool for all physicists. The field is interdisciplinary, predicting the properties of macroscopic matter based on the fundamental interactions between the elementary constituents. This book presents a systematic and pedagogical approach to the coupled cluster method, correlated basis function theory and Monte Carlo methods. These topics are widely recognized and provide the most powerful and widely applicable theories of all available formulations of QMBT. As the future evolution of QMBT depends to a large measure on establishing links between these different methods, the authors discuss hyprid procedures that can build even further upon the huge strengths and great advantages of each theory.

* Which problems do arise within relativistic enhancements of the Schrodinger theory, especially if one adheres to the usual one-particle interpretation? * To what extent can these problems be overcome? * What is the physical necessity of quantum field theories? In many textbooks, only insufficient answers to these fundamental questions are provided by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this book emphasizes particularly this point of view (relativistic quantum mechanics in the ''narrow sense''): it extensively discusses the relativistic one-particle view and reveals its problems and limitations, therefore illustrating the necessity of quantized fields in a physically comprehensible way. The first two chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always with a view to the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the Feynman rules from propagator techniques. This is where the indispensability of quantum field theory reasoning becomes apparent and basic quantum field theory concepts are introduced. This textbook addresses undergraduate and graduate Physics students who are interested in a clearly arranged and structured presentation of relativistic quantum mechanics in the "narrow sense" and its connection to quantum field theories. Each section contains a short summary and exercises with solutions. A mathematical appendix rounds out this excellent textbook on relativistic quantum mechanics."

The NATO Advanced Study Institute and EC Summer School "Progress in String Field and Particle Theory" was held in Cargse from June 25th till July 11th 2002. The main focus of the school was the recent progress in the very ac tive areas of superstring theory, quantum gravity and the theory of elementary particles. It covered topical problems in domains such as duality between gravity and gaugeinteractions, string field theory, tachyon condensation, non-commutative field theory, string cosmology and string phenomenology. The School featured daily introductory lectures and topical seminars. An informal Gong Show session allowed young post-doctoral researchers and senior graduate students to make a concise presentation oftheir current work. The School gave an excellent opportunity to the youngest researchers to establish a close relationship with their seniors and with the lecturers. These proceedings will further serve in fixing the acquired knowledge, and hopefully, become a useful reference for anyone working in this fascinating do main of physics. Some of the contributions provide an elementary introduction to their subject, while other ones are more geared to the specialist. We are deeply indebted to the NATO Division for Scientific Affairs for funding, and for their constant attention for our meetings, and to the European Commission for a High-Level Scientific Conference grant HPCFCT 2001-00298."

The first NATO Advanced Workshop on Quantum Tunneling of Magnetization (QTM) was organized and co-directed by Bernard Barbara, Leon Gunther, Nicolas Garcia, and Anthony Leggett and was held from June, 27 through July 1, 1994 in Grenoble and Chichilianne, France. These Proceedings include twenty-nine articles that represent the contributions of the participants in the Workshop. Quantum Tunneling of Magnetization is not only interesting for purely academic reasons. It was pointed out in the review article by L. Gunther in the December, 1990 issue of Physics World, that QTM may be destined to play a significant role within the next two decades in limiting the density of information storage in magnetic systems. Recent advances have indicated that this limitation may well be reached even earlier than first predicted. Furthermore, the number of people who have entered the field of study of QTM during these past few years has increased many fi)ld. The time was therefore opportune to hold a Workshop to bring together for the first time the leading researchers of QTM, both theoretical and experimental, so as to discuss the current status of the field. The most controversial issue at the time of the Workshop was how to establish r.eliable criteria for determining whether experimental results do indeed reveal manifestations of QTM. We believe that much progress was made at the Workshop on this issue.

This book reflects our own struggle to understand the semiclassical behaviour of quantized fields in the presence of boundaries. Along many years, motivated by the problems of quantum cosmology and quantum field theory, we have studied in detail the one-loop properties of massless spin-l/2 fields, Euclidean Maxwell the ory, gravitino potentials and Euclidean quantum gravity. Hence our book begins with a review of the physical and mathematical motivations for studying physical theories in the presence of boundaries, with emphasis on electrostatics, vacuum v Maxwell theory and quantum cosmology. We then study the Feynman propagator in Minkowski space-time and in curved space-time. In the latter case, the corre sponding Schwinger-DeWitt asymptotic expansion is given. The following chapters are devoted to the standard theory of the effective action and the geometric im provement due to Vilkovisky, the manifestly covariant quantization of gauge fields, zeta-function regularization in mathematics and in quantum field theory, and the problem of boundary conditions in one-loop quantum theory. For this purpose, we study in detail Dirichlet, Neumann and Robin boundary conditions for scalar fields, local and non-local boundary conditions for massless spin-l/2 fields, mixed boundary conditions for gauge fields and gravitation. This is the content of Part I. Part II presents our investigations of Euclidean Maxwell theory, simple super gravity and Euclidean quantum gravity.

Quantum theory is the most successful of all physical theories: it has a towering mathematical structure, a vast range of accurate predictions, and technological applications. Its interpretation, however, is as unsettled now as in the heroic days of Einstein and Bohr.

This book focuses on quantum non-locality, the curious quantum correlations between spatially separated systems. Quantum non-locality was one subject of the debates between Einstein, Bohr and others such as Schrodinger. The topic was revived in the 1960s as a result of Bell's epoch-making theorems; since then it has been a very active research field, both theoretically and experimentally.

This book contains twenty new papers by eminent researchers, who report recent developments in both the physics of the subject and its philosophy. The physics topics covered include quantum information, the unsharp (positive-operator) approach to observables, the state-space approach, and the pilot-wave theory. The philosophy papers include precise studies of Bohr's reply to the original Einstein-Podolsky-Rosen non-locality paradox, and of non-locality's relation to causation, probability and modality."

A major outstanding problem in physics is understanding the nature of the dark energy that is driving the accelerating expansion of the Universe. This thesis makes a significant contribution by demonstrating, for the first time, using state-of-the-art computer simulations, that the interpretation of future galaxy survey measurements is far more subtle than is widely assumed, and that a major revision to our models of these effects is urgently needed. The work contained in the thesis was used by the WiggleZ dark energy survey to measure the growth rate of cosmic structure in 2011 and had a direct impact on the design of the surveys to be conducted by the European Space Agency's Euclid mission, a 650 million euro project to measure dark energy.

This invaluable book consists of problems in nonrelativistic quantum mechanics together with their solutions. Most of the problems have been tested in class. The degree of difficulty varies from very simple to research-level. The problems illustrate certain aspects of quantum mechanics and enable the students to learn new concepts, as well as providing practice in problem solving.The book may be used as an adjunct to any of the numerous books on quantum mechanics and should provide students with a means of testing themselves on problems of varying degrees of difficulty. It will be useful to students in an introductory course if they attempt the simpler problems. The more difficult problems should prove challenging to graduate students and may enable them to enjoy problems at the forefront of quantum mechanics.

This thesis investigates the structure and behaviour of entanglement, the purely quantum mechanical part of correlations, in many-body systems, employing both numerical and analytical techniques at the interface of condensed matter theory and quantum information theory. Entanglement can be seen as a precious resource which, for example, enables the noiseless and instant transmission of quantum information, provided the communicating parties share a sufficient "amount" of it. Furthermore, measures of entanglement of a quantum mechanical state are perceived as useful probes of collective properties of many-body systems. For instance, certain measures are capable of detecting and classifying ground-state phases and, particularly, transition (or critical) points separating such phases. Chapters 2 and 3 focus on entanglement in many-body systems and its use as a potential resource for communication protocols. They address the questions of how a substantial amount of entanglement can be established between distant subsystems, and how efficiently this entanglement could be "harvested" by way of measurements. The subsequent chapters 4 and 5 are devoted to universality of entanglement between large collections of particles undergoing a quantum phase transition, where, despite the enormous complexity of these systems, collective properties including entanglement no longer depend crucially on the microscopic details.

This book provides a comprehensive view of the contemporary methods for quantum-light engineering. In particular, it addresses different technological branches and therefore allows the reader to quickly identify the best technology - application match. Non-classical light is a versatile tool, proven to be an intrinsic part of various quantum technologies. Its historical significance has made it the subject of many text books written both from theoretical and experimental point of view. This book takes another perspective by giving an insight to modern technologies used to generate and manipulate quantum light.

Traditionally, new materials have been developed by empirically correlating their chemical composition, and the manufacturing processes used to form them, with their properties. Until recently, metallurgists have not used quantum theory for practical purposes. However, the development of modern density functional methods means that today, computational quantum mechanics can help engineers to identify and develop novel materials. Computational Quantum Mechanics for Materials Engineers describes new approaches to the modelling of disordered alloys that combine the most efficient quantum-level theories of random alloys with the most sophisticated numerical techniques to establish a theoretical insight into the electronic structure of complex materials such as stainless steels, Hume-Rothery alloys and silicates. The practical success of these approaches to applications in all of these areas are covered in detail.