This thesis offers a comprehensive introduction to surface acoustic waves in the quantum regime. It addresses two of the most significant technological challenges in developing a scalable quantum information processor based on spins in quantum dots: (i) decoherence of the electronic spin qubit due to the surrounding nuclear spin bath, and (ii) long-range spin-spin coupling between remote qubits. Electron spins confined in quantum dots (QDs) are among the leading contenders for implementing quantum information processing. To this end, the author pursues novel strategies that turn the unavoidable coupling to the solid-state environment (in particular, nuclear spins and phonons) into a valuable asset rather than a liability.

The essays in this volume concern the points of intersection between analytic philosophy and the philosophy of the exact sciences. More precisely, it concern connections between knowledge in mathematics and the exact sciences, on the one hand, and the conceptual foundations of knowledge in general. Its guiding idea is that, in contemporary philosophy of science, there are profound problems of theoretical interpretation-- problems that transcend both the methodological concerns of general philosophy of science, and the technical concerns of philosophers of particular sciences. A fruitful approach to these problems combines the study of scientific detail with the kind of conceptual analysis that is characteristic of the modern analytic tradition. Such an approach is shared by these contributors: some primarily known as analytic philosophers, some as philosophers of science, but all deeply aware that the problems of analysis and interpretation link these fields together.

This thesis presents a study of the scalar sector in the standard model (SM), as well as various searches for an extended scalar sector in theories beyond the SM (BSM). The first part of the thesis details the search for an SM Higgs boson decaying to taus, and produced by gluon fusion, vector boson fusion, or associated production with a vector boson, leading to evidence for decays of the Higgs boson to taus. In turn, the second part highlights several searches for an extended scalar sector, with scalar boson decays to taus. In all of the analyses presented, at least one scalar boson decays to a pair of taus. The results draw on data collected by the Compact Muon Solenoid (CMS) detector during proton-proton collisions with a center-of-mass energy of 7 or 8 TeV.

This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field-antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. All topics are well illustrated with examples emphasizing points of central interest. The book should enable graduate students to follow the literature on this subject without much problems, and to perform research in this field.

This book is an introduction to quantum mechanics for undergraduates and interested lay persons. The presentation is both reader-friendly and complete. The first four chapters cover the conceptual and philosophical aspects of quantum mechanics, before the next eleven chapters gently present the mathematics underlying the subject. After a chapter on the history of the theory, the whole of quantum mechanics is then presented. This is followed by applications of the theory and a revision chapter, before we briefly look ahead at relativistic quantum theory.

This book uses less strict yet still formal mathematical language to clarify a variety of concepts in Quantum Field Theory that remain somewhat "fuzzy" in many books designed for undergraduates and fresh graduates. The aim is not to replace formal books on Quantum Field Theory, but rather to offer a helpful complementary tool for beginners in the field. Features include a reader-friendly introduction to tensor calculus and the concept of manifolds; a simple and robust treatment for dimensional regularization; a consistent explanation of the renormalization procedure, step by step and in a transparent manner at all orders, using the QED Lagrangian; and extensive treatment of infrared as well as ultraviolet divergences. The most general (Lorentz invariant) form of Noether's theorem is presented and applied to a few simple yet relevant examples in Quantum Field Theory. These and further interesting topics are addressed in a way that will be accessible for the target readership. Some familiarity with basic notions of Quantum Field Theory and the basics of Special Relativity is assumed.

The production of heavy quarks in high-energy experiments offers a rich field to study, both experimentally and theoretically. Due to the additional quark mass, the description of these processes in the framework of perturbative QCD is much more demanding than it is for those involving only massless partons. In the last two decades, a large amount of precision data has been collected by the deep inelastic HERA experiment. In order to make full use of these data, a more precise theoretical description of charm quark production in deep inelastic scattering is needed. This work deals with the first calculation of fixed moments of the NNLO heavy flavor corrections to the proton structure function F2 in the limit of a small charm-quark mass. The correct treatment of these terms will allow not only a more precise analysis of the HERA data, but starting from there also a more precise determination of the parton distribution functions and the strong coupling constant, which is an essential input for LHC physics. The complexity of this calculation requires the application and development of technical and mathematical methods, which are also explained here in detail.

This book is aimed at those readers who already have some knowledge of mathematical methods and have also been introduced to the basic ideas of quantum optics. It should be attractive to students who have already explored one of the more introductory texts such as Loudon's The quantum theory of light (2/e, 1983, OUP) and are seeking to acquire the mathematical skills used in real problems. This book is not primarily about the physics of quantum optics but rather presents the mathematical methods widely used by workers in this field. There is no comparable book which covers either the range or the depth of mathematical techniques.

This thesis sheds new light on the fascinating properties of composite quantum systems. Quantum systems of different sizes, ranging from small bipartite systems to large many-body ensembles, can be studied with the help of modern quantum optical experiments. These experiments make it possible to observe a broad variety of striking features, including nonclassical correlations, complex dynamics and quantum phase transitions. By adopting the complementary perspectives of quantum information theory, quantum chemistry and many-body theory, the thesis develops new methods for the efficient characterization and description of interacting, composite quantum systems.

Quantum mechanics is one of the great success stories of modern physics, making sense of the very small just as Einstein's theory of relativity made sense of the very large. But, for most students, the ideas that make quantum mechanics powerful can be confusing and counterintuitive. This volume in the Greenwood Guides to Great Ideas in Science series provides a history of quantum mechanics from the early breakthroughs of Planck and Einstein, at the beginning of the 20th century, to the present frontiers of quantum computing and quantum gravity. The approach is entirely non-technical, and is aimed at the general reader who may not have much mathematical background but who has a strong curiosity about some of the most important developments in modern science. Quantum Mechanics: A Historical Perspective traces the history of this powerful theory, including: BLThe early discoveries by Max Planck and Albert Einstein regarding the quantization of radiation BLThe "early quantum theory," including Neils Bohr's theory of the atom BLThe birth of modern quantum mechanics through the work of Heisenberg, Schrodinger, Born, Dirac and others BLApplications of quantum mechanics in chemistry, nuclear physics, electronics, and many other areas BLRecent work in quantum computation and quantum information theory The book emphasizes the fact that despite the great success of quantum mechanics, many exciting intellectual frontiers remain open for further researchers to explore. It includes a glossary, a timeline, and a bibliography of accessible resources for further research.

There are many approaches to noncommutative geometry and its use in physics, the ? operator algebra and C -algebra one, the deformation quantization one, the qu- tum group one, and the matrix algebra/fuzzy geometry one. This volume introduces and develops the subject by presenting in particular the ideas and methods recently pursued by Julius Wess and his group. These methods combine the deformation quantization approach based on the - tion of star product and the deformed (quantum) symmetries methods based on the theory of quantum groups. The merging of these two techniques has proven very fruitful in order to formulate ?eld theories on noncommutative spaces. The aim of the book is to give an introduction to these topics and to prepare the reader to enter the research ?eld himself/herself. This has developed from the constant interest of Prof. W. Beiglboeck, editor of LNP, in this project, and from the authors experience in conferences and schools on the subject, especially from their interaction with students and young researchers. In fact quite a few chapters in the book were written with a double purpose, on the one hand as contributions for school or conference proceedings and on the other handaschaptersforthepresentbook.Thesearenowharmonizedandcomplemented by a couple of contributions that have been written to provide a wider background, to widen the scope, and to underline the power of our methods.

Towards Solid-State Quantum Repeaters: Ultrafast, Coherent Optical Control and Spin-Photon Entanglement in Charged InAs Quantum Dots summarizes several state-of-the-art coherent spin manipulation experiments in III-V quantum dots. Both high-fidelity optical manipulation, decoherence due to nuclear spins and the spin coherence extraction are discussed, as is the generation of entanglement between a single spin qubit and a photonic qubit. The experimental results are analyzed and discussed in the context of future quantum technologies, such as quantum repeaters. Single spins in optically active semiconductor host materials have emerged as leading candidates for quantum information processing (QIP). The quantum nature of the spin allows for encoding of stationary, memory quantum bits (qubits), and the relatively weak interaction with the host material preserves the spin coherence. On the other hand, optically active host materials permit direct interfacing with light, which can be used for all-optical qubit manipulation, and for efficiently mapping matter qubits into photonic qubits that are suited for long-distance quantum communication.

This thesis exploits the ability of the linear-scaling quantum mechanical code ONETEP to analyze systems containing many thousands of atoms. By implementing an electron transport capability to the code, it also investigates a range of phenomena associated with electrical conduction by nanotubes and, in particular, the process of transport electrons between tubes. Extensive work has been done on the conductivity of single carbon nanotubes. However, any realistic wire made of nanotubes will consist of a large number of tubes of finite length. The conductance of the resulting wire is expected to be limited by the process of transferring electrons from one tube to another.These quantum mechanical calculations on very large systems have revealed a number of incorrect claims made previously in the literature. Conduction processes that have never before been studied at this level of theory are also investigated.

This book is devoted to the scientific legacy of Professor Victor Ambartsumian - one of the distinguished scientists of the last century. He obtained very essential results not only in astrophysics, but also in mathematics and theoretical physics. One can recall his fundamental results concerning the Sturm-Liouville inverse problem, quantum field theory, structure of atomic nuclei etc. Nevertheless, his revolutionary ideas in astrophysics and corresponding results are known more widely and have predetermined the further development of this science. The concept about the activity phenomena and objects' evolution, particularly, determination of the age of our Galaxy, ideas about the stars' formation nowadays in stellar associations, the activity of galactic nuclei appeared to be exceptionally fruitful. These directions are being elaborated at many astronomical centers all over the world.

This book systematically introduces the nonlinear adiabatic evolution theory of quantum many-body systems. The nonlinearity stems from a mean-field treatment of the interactions between particles, and the adiabatic dynamics of the system can be accurately described by the nonlinear Schroedinger equation. The key points in this book include the adiabatic condition and adiabatic invariant for nonlinear system; the adiabatic nonlinear Berry phase; and the exotic virtual magnetic field, which gives the geometric meaning of the nonlinear Berry phase. From the quantum-classical correspondence, the linear and nonlinear comparison, and the single particle and interacting many-body difference perspectives, it shows a distinct picture of adiabatic evolution theory. It also demonstrates the applications of the nonlinear adiabatic evolution theory for various physical systems. Using simple models it illustrates the basic points of the theory, which are further employed for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.

The understanding in science implies insights from several different points of view. Alternative modern outlooks on electronic structure of atoms and molecules, all rooted in quantum mechanics, are presented in a single text. Together these complementary perspectives provide a deeper understanding of the localization of electrons and bonds, the origins of chemical interaction and reactivity behavior, the interaction between the geometric and electronic structure of molecules, etc. In the opening two parts the basic principles and techniques of the contemporary computational and conceptual quantum chemistry are presented, within both the wave-function and electron-density theories. This background material is followed by a discussion of chemical concepts, including stages of the bond-formation processes, chemical valence and bond-multiplicity indices, the hardness/softness descriptors of molecules and reactants, and general chemical reactivity/stability principles. The insights from Information Theory, the basic elements of which are briefly introduced, including the entropic origins and Orbital Communication Theory of the chemical bond, are the subject of Part IV. The importance of the non-additive (interference) information tools in exploring patterns of chemical bonds and their covalent and ionic components will be emphasized.

This work was nominated as an outstanding PhD thesis by the LPSC, Universite Grenoble Alpes, France. The LHC Run 1 was a milestone in particle physics, leading to the discovery of the Higgs boson, the last missing piece of the so-called "Standard Model" (SM), and to important constraints on new physics, which challenge popular theories like weak-scale supersymmetry. This thesis provides a detailed account of the legacy of the LHC Run 1 Yregarding these aspects. First, the SM and the need for its extension are presented in a concise yet revealing way. Subsequently, the impact of the LHC Higgs results on scenarios of new physics is assessed in detail, including a careful discussion of the relevant uncertainties. Two approaches are considered: generic modifications of the Higgs couplings, possibly arising from extended Higgs sectors or higher-dimensional operators; and tests of specific new physics models. Lastly, the implications of the null results of the searches for new physics are discussed with a particular focus on supersymmetric dark matter candidates. Here as well, two approaches are presented: the "simplified models" approach, and recasting by event simulation. This thesis stands out for its educational approach, its clear language and the depth of the physics discussion. The methods and tools presented offer readers essential practical tools for future research.

The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell's inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell's theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed.

This is the first scientic book devoted to the Pauli exclusion principle, which is a fundamental principle of quantum mechanics and is permanently applied in chemistry, physics, and molecular biology. However, while the principle has been studied for more than 90 years, rigorous theoretical foundations still have not been established and many unsolved problems remain. Following a historical survey in Chapter 1, the book discusses the still unresolved questions around this fundamental principle. For instance, why, according to the Pauli exclusion principle, are only symmetric and antisymmetric permutation symmetries for identical particles realized, while the Schrodinger equation is satisfied by functions with any permutation symmetry? Chapter 3 covers possible answers to this question. The construction of function with a given permutation symmetry is described in the previous Chapter 2, while Chapter 4 presents effective and elegant methods for finding the Pauli-allowed states in atomic, molecular, and nuclear spectroscopy. Chapter 5 discusses parastatistics and fractional statistics, demonstrating that the quasiparticles in a periodical lattice, including excitons and magnons, are obeying modified parafermi statistics. With detailed appendices, The Pauli Exclusion Principle: Origin, Verifications, and Applications is intended as a self-sufficient guide for graduate students and academic researchers in the fields of chemistry, physics, molecular biology and applied mathematics. It will be a valuable resource for any reader interested in the foundations of quantum mechanics and its applications, including areas such as atomic and molecular spectroscopy, spintronics, theoretical chemistry, and applied fields of quantum information.

This book addresses electron spin-qubit based quantum computing and quantum information processing with a strong focus on the background and applications to EPR/ESR technique and spectroscopy. It explores a broad spectrum of topics including quantum computing, information processing, quantum effects in electron-nuclear coupled molecular spin systems, adiabatic quantum computing, heat bath algorithmic cooling with spins, and gateway schemes of quantum control for spin networks to NMR quantum information. The organization of the book places emphasis on relevant molecular qubit spectroscopy. These revolutionary concepts have never before been included in a comprehensive volume that covers theory, physical basis, technological basis, applications, and new advances in this emerging field. Electron Spin Resonance (ESR) Based Quantum Computing, co-edited by leading and renowned researchers Takeji Takui, Graeme Hanson and Lawrence J Berliner, is an ideal resource for students and researchers in the fields of EPR/ESR, NMR and quantum computing. This book also * Explores methods of harnessing quantum effects in electron-nuclear coupled molecular spin systems * Expertly discusses applications of optimal control theory in quantum computing * Broadens the readers' understanding of NMR quantum information processing

The main focus of this thesis is the mathematical structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related, on the one hand, to Loop Quantum Gravity (LQG) and on the other, to matrix- and tensor models. Background material on these topics, including conceptual and technical aspects, are introduced in the first chapters. The work then goes on to explain how the standard tools of Quantum Field Theory can be generalized to GFTs and exploited to study the large cut-off behaviour and renormalization group transformations of the latter. Among the new results derived in this context are a proof of renormalizability of a three-dimensional GFT with gauge group SU(2), which opens the way to applications of the formalism to quantum gravity.

Focusing on spectroscopic properties of molecular systems, Quantum Modeling of Molecular Materials presents the state-of-the-art methods in theoretical chemistry that are used to determine molecular properties relevant to different spectroscopies. This timely reference gives a basic presentation of response theory and its application to the simulation of spectroscopic properties of molecular materials. This in-depth presentation of time-dependent response theory and its applications in spectroscopy provides an important advance towards a modern vision of theoretical tools for researchers in academia and industry and postgraduate students.

The spectral theory of linear operators in Hilbert spaces is the most important tool in the mathematical formulation of quantum mechanics; in fact, linear ope- tors and quantum mechanics have had a symbiotic relationship. However, typical physicstextbooks on quantum mechanics givejust a roughsketch of operator t- ory, occasionallytreating linear operatorsas matricesin ?nite-dimensional spaces; the implicit justi?cation is that the details of the theory of unbounded operators are involved and those texts are most interested in applications. Further, it is also assumed that mathematical intricacies do not show up in the models to be d- cussedorareskippedby"heuristicarguments. "Inmanyoccasionssomequestions, such as the very de?nition of the hamiltonian domain, are not touched, leaving an open door for controversies, ambiguities and choices guided by personal tastes and ad hoc prescriptions. All in all, sometimes a blank is left in the mathematical background of people interested in nonrelativistic quantum mechanics. Quantum mechanics was the most profound revolution in physics; it is not natural to our common sense (check, for instance, the wave-particle duality) and the mathematics may become crucial when intuition fails. Even some very simple systemspresentnontrivialquestionswhoseanswersneedamathematicalapproach. For example, the Hamiltonian of a quantum particle con?ned to a box involves a choice of boundary conditions at the box ends; since di?erent choices imply di?erentphysicalmodels, studentsshouldbeawareofthebasicdi?cultiesintrinsic tothis(inprinciple)verysimple model, aswellasinmoresophisticatedsituations. The theory of linear operators and their spectra constitute a wide ?eld and it is expected that the selection of topics in this book will help to ?ll this theoretical gap. Ofcoursethisselectionisgreatlybiasedtowardthepreferencesofthe author.

Our current understanding of the fundamental building blocks of the Universe, summarised by the Standard Model of particle physics, is incomplete. For example, it fails to explain why we do not see equal, or almost equal, numbers of particles and their antiparticle partners. To explain this asymmetry requires, among other effects, a mechanism known as charge-parity (CP) violation that causes differences between the rates at which particles and antiparticles decay. CP violation is seen in systems containing bottom and strange quarks, but not in those with up, charm or top quarks. This thesis describes searches for particle-antiparticle asymmetries in the decay rates of charmed mesons. No evidence of CP violation is found. With current sensitivities, an asymmetry large enough to observe probably could not be explained by the Standard Model. Instead an explanation could come from new physics, for example contributions from supersymmetric or other undiscovered heavy particles. In the thesis, the development of new techniques to search for these asymmetries is described. They are applied to data from the LHCb experiment at CERN to make precise measurements of asymmetries in the D^+->K^-K^+pi^+ decay channel. This is the most promising charged D decay for CP violation searches.