This thesis focuses on the theoretical foundation of the Standard Model valid up to the Planck scale, based on the current experimental facts from the Large Hadron Collider. The thesis consists of two themes: (1) to open up a new window of the Higgs inflation scenario, and (2) to explore a new solution to the naturalness problem in particle physics. In the first area, on the Higgs inflation scenario, the author successfully improves a large value problem on a coupling constant relevant to the Higgs mass in the Standard Model, in which the coupling value of the order of 105 predicted in a conventional scenario is reduced to the order of 10. This result makes the Higgs inflation more attractive because the small value of coupling is natural in the context of ultraviolet completion such as string theory. In the second area, the author provides a new answer to the naturalness problem, of why the cosmological constant and the Higgs mass are extremely small compared with the Planck scale. Based on the baby universe theory originally proposed by Coleman, the smallness of those quantities is successfully explained without introducing any additional new particles relevant at the TeV energy scale.

Quantum dots, often denoted artificial atoms, are the exquisite tools by which quantum behavior can be probed on a scale appreciably larger than the atomic scale, that is on the nanometer scale. In this way, the physics of the devices is closer to classical physics than that of atomic physics but they are still sufficiently small to clearly exhibit quantum phenomena. The present volume is devoted to an introduction to some of these fascinating aspects, addressing in particular graduate students and young researchers in the field. In the first lecture by R. Shankar, the general theoretical aspects of Fermi liquids are addressed, in particular the renormalization group approach. This is then aptly applied to large quantum dots. A completely different approach is encountered in the second contribution by J.M. Elzerman et al., in that it is a thorough experimental expose of what can be done or expected in the study of small quantum dots. Here the emphasis lies on the electron spin to be used as a qubit. In the third lecture series by M. Pustilnik and Leonid I. Glazman, mechanisms of low-temperature electronic transport through a quantum dot a" weakly coupled to two conducting leads a" are reviewed. The fourth series of lectures, by C.W.J. Beenakker, deals with a very interesting aspect of nanophysics: a peculiar property of superconducting mirrors discovered by Andreev about forty years ago and still a challenge to experimental physicists.

This book is written to conclude the NATO Advanced Research Workshop "Quantum Noise in Mesoscopic Physics" held in Delft, the Netherlands, on June 2-4, 2002. The workshop was co-directed by M. Reznikov of Israel Institute of Technology, and me. The members of the organizing committee were Yaroslav Blanter (Delft), Chirstopher Glattli (Saclay and ENS Paris) and R. Schoelkopf (Yale). The workshop was very successful, and we hope that the reader will be satisfied with the scientific level of the present book. Before addressing scientific issues I find it suitable to address several non-scientific ones. The workshop was attended by researchers from many countries. Most of them perform their activities in academic institutions, where one usually finds the necessary isolation from the problems and sores of the modem world. However, there was a large group of participants for which such isolation was far from perfect. War, hatred, and violence rage just several miles away of their campuses and laboratories, poisoning everyday life in the land of Israel.

This thesis describes experimental work in the field of trapped-ion quantum computation. It outlines the theory of Raman interactions, examines the various sources of error in two-qubit gates, and describes in detail experimental explorations of the sources of infidelity in implementations of single- and two-qubit gates. Lastly, it presents an experimental demonstration of a mixed-species entangling gate.

This thesis reports on the search for dark matter in data taken with the ATLAS detector at CERN's Large Hadron Collider (LHC). The identification of dark matter and the determination of its properties are among the highest priorities in elementary particle physics and cosmology. The most likely candidate, a weakly interacting massive particle, could be produced in the high energy proton-proton collisions at the LHC. The analysis presented here is unique in looking for dark matter produced together with a Higgs boson that decays into its dominant decay mode, a pair of b quarks. If dark matter were seen in this mode, we would learn directly about the production mechanism because of the presence of the Higgs boson. This thesis develops the search technique and presents the most stringent production limit to date.

In 1905, Albert Einstein offered a revolutionary theory--special relativity--to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborate to gain objective knowledge of the world. To encompass both the general and special theory, he uses the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.

In this monograph, group-theoretical approaches are used to build a system of hadrons and qualitatively describe the properties of chemical compounds. This serves as a complement to numerically and approximately solve the many-electron Schroedinger equation, in order to understand the behavior of chemical elements. Besides general theory, specific results are compared with experimentally measured chemical properties. Content: Symmetries of a quantum system Observables of a quantum system Lie groups and Lie algebras The principles of particle classification The symmetry group of chemical elements Classification and chemical properties of elements Appendix A. Fock's energy spectrum of the hydrogen atom Appendix B. Representations of some groups

The successes of the standard models of particle physics and cosmology are many, but have proven incapable of explaining all the phenomena that we observe. This book investigates the potentially important role of quantum physics, particularly quantum anomalies, in various aspects of modern cosmology, such as inflation, the dynamical generation of the visible and dark matter in the universe, and gravitational waves. By doing so, the authors demonstrate that exploring the links between cosmology and particle physics is key to helping solve the mysteries of our Universe.

Although the debate about the true nature of the quantum behavior of atomic systems has never ceased, there are two periods during which it has been particularly intense: the years that saw the founding of quantum mechanics and, increasingly, these modern times. In 1954 Max Born, on accepting the Nobel Prize for his 'fundamental researches in quantum mechanics', recalled the depth of the disagreements that divided celebrated quantum theorists of those days into two camps: . . . when I say that physicists had accepted the way of thinking developed by us at that time, r am not quite correct: there are a few most noteworthy exceptions - namely, among those very workers who have contributed most to the building up of quantum theory. Planck himself belonged to the sceptics until his death. Einstein, de Broglie, and Schriidinger have not ceased to emphasize the unsatisfactory features of quantum mechanics . . . . This dramatic disagreement centered around some of the most funda mental questions in all of science: Do atomic objects exist il1dependently of human observations and, if so, is it possible for man to understand correctly their behavior? By and large, it can be said that the Copenhagen and Gottingen schools - led by Bohr, Heisenberg, and Born, in particula- gave more or less openly pessimistic answers to these questions."

This book reviews selected topics charterized by great progress and covers the field from theoretical areas to experimental ones. It contains fundamental areas, quantum query complexity, quantum statistical inference, quantum cloning, quantum entanglement, additivity. It treats three types of quantum security system, quantum public key cryptography, quantum key distribution, and quantum steganography. A photonic system is highlighted for the realization of quantum information processing.

A mind-blowing glimpse into the near future, where quantum computing will have world-transforming effects.
The quantum computer is no longer the stuff of science fiction. Pioneering physicists are on the brink of unlocking a new quantum universe which provides a better representation of reality than our everyday experiences and common sense ever could. The birth of quantum computers - which, like Schrodinger's famous "dead and alive" cat, rely on entities like electrons, photons, or atoms existing in two states at the same time - is set to turn the computing world on its head.
In his fascinating study of this cutting-edge technology, John Gribbin updates his previous views on the nature of quantum reality, arguing for a universe of many parallel worlds where "everything is real." Looking back to Alan Turing's work on the Enigma machine and the first electronic computer, Gribbin explains how quantum theory developed to make quantum computers work in practice as well as in principle. He takes us beyond the arena of theoretical physics to explore their practical applications - from machines which learn through "intuition" and trial and error to unhackable laptops and smartphones. And he investigates the potential for this extraordinary science to create a world where communication occurs faster than light and teleportation is possible.
This is an exciting insider's look at the new frontier of computer science and its revolutionary implications.

This book will be useful to anyone who wants to understand the use of quantum theory for the description of physical processes. It is a graduate level text, ideal for independent study, and includes numerous figures, exercises, bibliographical references, and even some computer programs. The first chapters introduce formal tools: the mathematics are precise, but not excessively abstract. The physical interpretation too is rigorous. It makes no use of the uncertainty principle of other ill-defined notions. The central part of the book is devoted to Bell's theorem and to the Kochen-Specker theorem. It is here that quantum phenomena depart most radically from classical physics. There has recently been considerable progress on these issues, and the latest developments have been included. The final chapters discuss further topics of current research: spacetime symmetries, quantum thermodynamics and information theory, semiclassical methods, irreversibility, quantum chaos, and especially the measuring process. In particular, it is shown how modern techniques allow the extraction of more information from a physical system than traditional measurement methods. For physicists, mathematicians and philosophers of science with an interest in the applications and foundations of quantum theory. The volume is suitable as a supplementary graduate textbook.

Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous contributions; this book arose from an international symposium held in honour of Bros on the occasion of his 70th birthday. Key topics in this volume include: Analytic structures of Quantum Field Theory (QFT), renormalization group methods, gauge QFT, stability properties and extension of the axiomatic framework, QFT on models of curved spacetimes, QFT on noncommutative Minkowski spacetime.

This thesis presents a qualitative advance in our understanding of quantum effects in layered magnetic materials. The nearest neighbor Heisenberg ferromagnetic ranks among the oldest and most fundamental models of quantum many body effects. It has long been established that in one dimension quantum fluctuations lead to a quantum disordered ground state with fractional excitations called spinons." In two dimensions, the ground state of the Heisenberg model displays static order and to first approximation the dynamics can be described as semi-classical spin waves. Through theoretical advances the author demonstrates that at high energy around particular points in reciprocal space these semi-classical spin-waves deconfine into fractional excitations akin to the one-dimensional spinons. He thereby provides the first explanation of a long-standing experimental observation. In the second half of his thesis Bastien Dalla Piazza develops a unified description of the magnetic excitation spectra of a range of cuprate parent compounds to the high temperature superconductors.

The Theoretical Foundations of Quantum Mechanics addresses fundamental issues that are not discussed in most books on quantum mechanics. This book focuses on analyzing the underlying principles of quantum mechanics and explaining the conceptual and theoretical underpinning of quantum mechanics. In particular, the concepts of quantum indeterminacy, quantum measurement and quantum superposition are analyzed to clarify the concepts that are implicit in the formulation of quantum mechanics. The Schrodinger equation is never solved in the book. Rather, the discussion on the fundamentals of quantum mechanics is treated in a rigorous manner based on the mathematics of quantum mechanics. The new concept of the interplay of empirical and trans-empirical constructs in quantum mechanics is introduced to clarify the foundations of quantum mechanics and to explain the counter-intuitive construction of nature in quantum mechanics. The Theoretical Foundations of Quantum Mechanics is aimed at the advanced undergraduate and assumes introductory knowledge of quantum mechanics. Its objective is to provide a solid foundation for the reader to reach a deeper understanding of the principles of quantum mechanics.

Homological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years. The present volume bridges a gap in the literature by providing a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives. With contributions by K. Fukaya, M. Herbst, K. Hori, M. Huang, A. Kapustin, L. Katzarkov, A. Klemm, M. Kontsevich, D. Page, S. Quackenbush, E. Sharpe, P. Seidel, I. Smith and Y. Soibelman, this volume will be a reference on the topic for everyone starting to work or actively working on mathematical aspects of quantum field theory.

Quantum mechanics and the Schrodinger equation are the basis for the de scription of the properties of atoms, molecules, and nuclei. The development of reliable, meaningful solutions for the energy eigenfunctions of these many is a formidable problem. The usual approach for obtaining particle systems the eigenfunctions is based on their variational extremum property of the expectation values of the energy. However the complexity of these variational solutions does not allow a transparent, compact description of the physical structure. There are some properties of the wave functions in some specific, spatial domains, which depend on the general structure of the Schrodinger equation and the electromagnetic potential. These properties provide very useful guidelines in developing simple and accurate solutions for the wave functions of these systems, and provide significant insight into their physical structure. This point, though of considerable importance, has not received adequate attention. Here we present a description of the local properties of the wave functions of a collection of particles, in particular the asymptotic properties when one of the particles is far away from the others. The asymptotic behaviour of this wave function depends primarily on the separation energy of the outmost particle. The universal significance of the asymptotic behaviour of the wave functions should be appreciated at both research and pedagogic levels. This is the main aim of our presentation here."

These proceedings gather invited and contributed talks presented at the XXI DAE-BRNS High Energy Physics Symposium, which was held at the Indian Institute of Technology Guwahati in December 2014. The contributions cover many of the most active research areas in particle physics, namely (i) Electroweak Physics; (ii) QCD and Heavy Ion Physics; (iii) Heavy Flavour Physics and CP Violation; (iv) Neutrino Physics; (v) Astro-particle Physics and Cosmology; (vi) Formal Theory; (vii) Future Colliders and New Machines; and (viii) BSM Physics: SUSY, Extra Dimensions, Composites etc. The DAE-BRNS High Energy Physics Symposium, widely considered to be one of the premiere symposiums organised in India in the field of elementary particle physics, is held every other year and supported by the Board of Research in Nuclear Sciences, Department of Atomic Energy, India. Roughly 250 physicists and researchers participated in the 21st Symposium, discussing the latest advancements in the field in 18 plenary review talks, 15 invited mini-review talks and approximately 130 contributed presentations. Bringing together the essential content, the book offers a valuable resource for both beginning and advanced researchers in the field.

The material contained in this work concerns relativistic quantum mechanics, and as such pertains to classical fields. On the one hand it is meant to serve as a text on the subject, a desire stemming from the author's fruitless searches for an adequate, up-to-date reference when lecturing on these topics. At times the supplementary material was found to exceed by far that in the assigned text. On the other hand, there is some flavor of a monograph to what follows, most particularly in the later chapters, for a major goal is to demonstrate just how far we can advance our understanding of the behavior of stable particles and their interactions without introducing quantized fields. Those wishing to describe the world in this way may view the result as a point of departure, despite the fact that their wish remains unfulfilled. Confirmed quantum-field theorists, however, will doubtless view it as a summary of just why they feel compelled to quantize the fields. Approximately half the book is devoted to the single-particle Dirac equation and its solutions. A great deal of detail is provided in this respect, and the discus sion is reasonably comprehensive. The Dirac equation is extraordinarily important in its own right, particularly as a basis for quantum electrodynamics (QED), and is thus worthy of extensive study."

Volume 2 of this three-part series presents the quantization of classical field theory using the path integral formalism. For this volume the target audience is students who wish to learn about relativistic quantum field theory applied to particle physics, however, it is still very accessible and useful for students of condensed matter. This volume begins with the introduction of the path integral formalism for non-relativistic quantum mechanics and then, using this as a basis, extends the formalism to quantum fields with an infinite number of degrees of freedom. Dr. Strickland then discusses how to quantize gauge fields using the Fadeev-Popov method and fermionic fields using Grassman algebra. He then presents the path integral formulation of quantum chromodynamics and its renormalization. Finally, he discusses the role played by topological solutions in non-abelian gauge theories.

Entanglement was initially thought by some to be an oddity restricted to the realm of thought experiments. However, Bell's inequality delimiting local - havior and the experimental demonstration of its violation more than 25 years ago made it entirely clear that non-local properties of pure quantum states are more than an intellectual curiosity. Entanglement and non-locality are now understood to ?gure prominently in the microphysical world, a realm into which technology is rapidly hurtling. Information theory is also increasingly recognized by physicists and philosophers as intimately related to the foun- tions of mechanics. The clearest indicator of this relationship is that between quantum information and entanglement. To some degree, a deep relationship between information and mechanics in the quantum context was already there to be seen upon the introduction by Max Born and Wolfgang Pauli of the idea that the essence of pure quantum states lies in their provision of probabilities regarding the behavior of quantum systems, via what has come to be known as the Born rule. The signi?cance of the relationship between mechanics and information became even clearer with Leo Szilard's analysis of James Clerk Maxwell's infamous demon thought experiment. Here, in addition to examining both entanglement and quantum infor- tion and their relationship, I endeavor to critically assess the in?uence of the study of these subjects on the interpretation of quantum theory.

This book is a contribution to a problem in foundational studies, the problem of the interpretation of quantum mechanics, in the sense of the theoretical significance of the transition from classical to quantum mechanics. The obvious difference between classical and quantum mechanics is that quantum mechanics is statistical and classical mechanics isn't. Moreover, the statistical character of the quantum theory appears to be irreducible: unlike classical statistical mechanics, the probabilities are not generated by measures on a probability space, i. e. by distributions over atomic events or classical states. But how can a theory of mechanics be statistical and complete? Answers to this question which originate with the Copenhagen inter pretation of Bohr and Heisenberg appeal to the limited possibilities of measurement at the microlevel. To put it crudely: Those little electrons, protons, mesons, etc., are so tiny, and our fingers so clumsy, that when ever we poke an elementary particle to see which way it will jump, we disturb the system radically - so radically, in fact, that a considerable amount of information derived from previous measurements is no longer applicable to the system. We might replace our fingers by finer probes, but the finest possible probes are the elementary particles them selves, and it is argued that the difficulty really arises for these."

The revised edition of this book offers an extended overview of quantum walks and explains their role in building quantum algorithms, in particular search algorithms. Updated throughout, the book focuses on core topics including Grover's algorithm and the most important quantum walk models, such as the coined, continuous-time, and Szedgedy's quantum walk models. There is a new chapter describing the staggered quantum walk model. The chapter on spatial search algorithms has been rewritten to offer a more comprehensive approach and a new chapter describing the element distinctness algorithm has been added. There is a new appendix on graph theory highlighting the importance of graph theory to quantum walks. As before, the reader will benefit from the pedagogical elements of the book, which include exercises and references to deepen the reader's understanding, and guidelines for the use of computer programs to simulate the evolution of quantum walks. Review of the first edition: "The book is nicely written, the concepts are introduced naturally, and many meaningful connections between them are highlighted. The author proposes a series of exercises that help the reader get some working experience with the presented concepts, facilitating a better understanding. Each chapter ends with a discussion of further references, pointing the reader to major results on the topics presented in the respective chapter." - Florin Manea, zbMATH.

One of the major scientific thrusts in recent years has been to try to harness quantum phenomena to increase dramatically the performance of a wide variety of classical information processing devices.