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.

It has been said that String theorists talk to string theorists and everyone else wonders what they are saying'. This book will be a great help to those researchers who are challenged by modern quantum field theory. Quantum field theory experienced a renaissance in the late 1960s. Here, participants in the Les Houches sessions of 1970/75, now key players in quantum field theory and its many impacts, assess developments in their field of interest and provide guidance to young researchers challenged by these developments, but overwhelmed by their complexities. The book is not a textbook on string theory, rather it is a complement to Polchinski's book on string theory. It is a survey of current problems which have their origin in quantum field theory.

Waves represent a classic topic of study in physics, mathematics, and engineering. Many modern technologies are based on our understanding of waves and their interaction with matter. In the past thirty years there have been some revolutionary developments in the study of waves. The present volume is the only available source which details these developments in a systematic manner, with the aim of reaching a broad audience of non-experts. It is an important resource book for those interested in understanding the physics underlying nanotechnology and mesoscopic phenomena, as well as for bridging the gap between the textbooks and research frontiers in any wave related topic. A special feature of this volume is the treatment of classical and quantum mechanical waves within a unified framework, thus facilitating an understanding of similarities and differences between the two.

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."

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.

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.

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.

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.

This book is a distillation of Prof T Y Wu's fifty years of experience teaching quantum theory to many generations of physicists. Starting with chapters on classical physics and the old quantum theory, Prof Wu quickly develops Heisenberg's matrix mechanics and the Schroedinger equation. After a detailed treatment of the general formulation of quantum theory, standard discussions on Perturbation Theory and the Hydrogen Atom follow. A fairly exhaustive treatment of the Zeeman effect is to be found in these chapter. Many electron atoms are treated expertly. The former is treated with great depth; the latter is a good introduction to the subject.

This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts. Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows special case-studies from queueing theory (in particular, the famous problem of Joining the Shorter of Two Queues) and enumerative combinatorics (Counting, Asymptotics). Researchers and graduate students should find this book very useful.

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 correlations between physical systems provide significant information about their collective behaviour - information that is used as a resource in many applications, e.g. communication protocols. However, when it comes to the exploitation of such correlations in the quantum world, identification of the associated 'resource' is extremely challenging and a matter of debate in the quantum community. This dissertation describes three key results on the identification, detection, and quantification of quantum correlations. It starts with an extensive and accessible introduction to the mathematical and physical grounds for the various definitions of quantum correlations. It subsequently focusses on introducing a novel unified picture of quantum correlations by taking a modern resource-theoretic position. The results show that this novel concept plays a crucial role in the performance of collaborative quantum computations that is not captured by the standard textbook approaches. Further, this new perspective provides a deeper understanding of the quantum-classical boundary and paves the way towards establishing a resource theory of quantum computations.

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.

These lecture notes are based on special courses on Field Theory and Statistical Mechanics given for graduate students at the City College of New York. It is an ideal text for a one-semester course on Quantum Field Theory.

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.

The first part of this thesis presents the measurement of the inclusive cross-section for electron production from heavy-flavour decays in the electron transverse momentum range 7 GeV < pT < 26 GeV using 1.3 pb 1 of 7 TeV proton-proton collision data collected by the ATLAS experiment at the Large Hadron Collider in 2010. The measured value of the cross-section within the fiducial range of the analysis is _e^HF = 0.946 +/- 0.020(stat.) +/- 0.146(syst.) +/- 0.032(lumi.) b. Theoretical predictions are in good agreement with the measurement. The second part of this thesis is a search for compressed supersymmetric scenarios in events with missing transverse energy, jets and one isolated low-pT lepton in the final state using 4.7 fb-1 of ATLAS data collected at 7 TeV center-of-mass energy in 2011. No significant excess of events over the Standard Model expectation is observed and exclusion limits are derived for a number of supersymmetric models.

This book contains lectures given at the Institute for Scientific Interchange (I.S.I., Turin) in 1983 - 1984 on the exact solution of the 8-vertex and related models and extensions of the Baxter model to 3 dimensions.

This book contains lectures given at the Institute for Scientific Interchange (I.S.I., Turin) in 1983 - 1984 on the exact solution of the 8-vertex and related models and extensions of the Baxter model to 3 dimensions.

Based on a series of university lectures on nonrelativistic quantum mechanics, this textbook covers a wide range of topics, from the birth of quantum mechanics to the fine-structure levels of heavy atoms. The author sets out from the crisis in classical physics and explores the seminal ideas of Einstein, Bohr, and de Broglie and their vital importance for the development of quantum mechanics. There follows a bottom-up presentation of the postulates of quantum mechanics through real experiments (such as those of neutron interferometry), with consideration of their most important consequences, including applications in the field of atomic physics. A final chapter is devoted to the paradoxes of quantum mechanics, and particularly those aspects that are still open and hotly debated, to end up with a mention to Bell's theorem and Aspect's experiments. In presenting the principles of quantum mechanics in an inductive way, this book has already proved very popular with students in its Italian language version.It complements the exercises and solutions book "Problems in Quantum Mechanics", by E. d'Emilio, L.E. Picasso (Springer).

Quantum machine learning investigates how quantum computers can be used for data-driven prediction and decision making. The books summarises and conceptualises ideas of this relatively young discipline for an audience of computer scientists and physicists from a graduate level upwards. It aims at providing a starting point for those new to the field, showcasing a toy example of a quantum machine learning algorithm and providing a detailed introduction of the two parent disciplines. For more advanced readers, the book discusses topics such as data encoding into quantum states, quantum algorithms and routines for inference and optimisation, as well as the construction and analysis of genuine ``quantum learning models''. A special focus lies on supervised learning, and applications for near-term quantum devices.

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.