Analytical Mechanics for Relativity and Quantum Mechanics is an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the introductory graduate level. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity.
This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum mechanics. Comparisons to quantum mechanics appear throughout the text. The extended Hamiltonian theory with time as a coordinate is compared to Dirac's formalism of primary phase space constraints. The chapter on relativistic mechanics shows how to use covariant Hamiltonian theory to write the Klein-Gordon and Dirac equations. The chapter on Hamilton-Jacobi theory includes a discussion of the closely related Bohm hidden variable model of quantum mechanics. Classical mechanics itself is presented with an emphasis on methods, such as linear vector operators and dyadics, that will familiarize the student with similar techniques in quantum theory. Several of the current fundamental problems in theoretical physics - the development of quantum information technology, and the problem of quantizing the gravitational field, to name two - require a rethinking of the quantum-classical connection.
Graduate students preparing for research careers will find a graduate mechanics course based on this book to be an essential bridge between their undergraduate training and advanced study in analytical mechanics, relativity, and quantum mechanics.
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This book gives a general introduction to theoretically understand thermodynamic properties and response to applied fields of mesoscopic systems that closely relate to experiments. The book clarifies many conceptual and practical problems associated with the Larmor clock and thus makes it a viable approach to study these properties. The book is written pedagogically so that a graduate or undergraduate student can follow it. This book also opens up new research areas related to the unification of classical and quantum theories and the meaning of time. It provides a scientific mechanism for time travel which is of immense fascination to science as well as society. It is known that developments in mesoscopic physics can lead to downscaling of device sizes. So, new or experienced researchers can have a quick introduction to various areas in which they might contribute in the future. This book is expected to be a valuable addition to the subject of mesoscopic physics.

The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations. Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science.

Quantum logic gates are the crucial information-processing operation of quantumcomputers. Two crucial performance metrics for logic gates are their precision andspeed. Quantum processors based on trapped ions have always been the touchstonefor gate precision, but have suffered from slow speed relative to other quantum logicplatforms such as solid state systems. This thesis shows that it is possible to acceleratethe logic "clock speed" from kHz to MHz speeds, whilst maintaining a precision of99.8%. This is almost as high as the world record for conventional trapped-ion gates,but more than 20 times faster. It also demonstrates entanglement generation in atime (480ns) shorter than the natural timescale of the ions' motion in the trap, whichstarts to probe an interesting new regime of ion trap physics. In separate experiments, some of the first "mixed-species" quantum logic gates areperformed, both between two different elements, and between different isotopes.The mixed-isotope gate is used to make the first test of the quantum-mechanical Bellinequality between two different species of isolated atoms.

The Second Edition of Quantum Information Processing, Quantum Computing, and Quantum Error Correction: An Engineering Approach presents a self-contained introduction to all aspects of the area, teaching the essentials such as state vectors, operators, density operators, measurements, and dynamics of a quantum system. In additional to the fundamental principles of quantum computation, basic quantum gates, basic quantum algorithms, and quantum information processing, this edition has been brought fully up to date, outlining the latest research trends. These include: Key topics include: Quantum error correction codes (QECCs), including stabilizer codes, Calderbank-Shor-Steane (CSS) codes, quantum low-density parity-check (LDPC) codes, entanglement-assisted QECCs, topological codes, and surface codes Quantum information theory, and quantum key distribution (QKD) Fault-tolerant information processing and fault-tolerant quantum error correction, together with a chapter on quantum machine learning. Both quantum circuits- and measurement-based quantum computational models are described The next part of the book is spent investigating physical realizations of quantum computers, encoders and decoders; including photonic quantum realization, cavity quantum electrodynamics, and ion traps In-depth analysis of the design and realization of a quantum information processing and quantum error correction circuits This fully up-to-date new edition will be of use to engineers, computer scientists, optical engineers, physicists and mathematicians.

This thesis presents recent developments in magnetic coupling phenomena of ferrimagnetic rare-earth transition-metal Tb-Fe alloys and coupled systems consisting of ferri-/ferromagnetic heterostructures. Taking advantage of the tunability of the exchange coupling between ferrimagnetic and ferromagnetic layers by means of stoichiometry of the Tb-Fe layer, the variable number of repetitions in the Co/Pt multilayer as well as the thickness of an interlayer spacer, it is demonstrated that large perpendicular unidirectional anisotropy can be induced at room temperature. This robust perpendicular exchange bias at room temperature opens up a path towards applications in spintronics.

This PhD thesis documents two of the highest-profile searches for supersymmetry performed at the ATLAS experiment using up to 80/fb of proton-proton collision data at a center-of-mass energy of 13 TeV delivered by the Large Hadron Collider (LHC) during its Run 2 (2015-2018). The signals of interest feature a high multiplicity of jets originating from the hadronisation of b-quarks and large missing transverse momentum, which constitutes one of the most promising final state signatures for discovery of new phenomena at the LHC. The first search is focused on the strong production of a pair of gluinos, with each gluino decaying into a neutralino and a top-antitop-quark pair or a bottom-antibottom-quark pair. The second search targets the pair production of higgsinos, with each higgsino decaying into a gravitino and a Higgs boson, which in turn is required to decay into a bottom-antibottom-quark pair. Both searches employ state-of-the-art experimental techniques and analysis strategies at the LHC, resulting in some of the most restrictive bounds available to date on the masses of the gluino,neutralino, and higgsino in the context of the models explored.

This book presents the theoretical and experimental investigations on antiferromagnetically coupled ferrimagnets and reveals new aspects of ferrimagnetic dynamics in terms of the role of angular momentum. The purpose of this book is to show readers that antiferromagnets/ferrimagnets are useful in spintronic devices in that (1) The non adiabatic spin transfer torque in antiferromagnets acts as a staggered magnetic field, which can drive the magnetic domain walls, and (2) The Gilbert damping parameter , the energy dissipation rate associated with the magnetic dynamics of ferrimagnets, is insensitive to temperature in contrast to the conventional understanding that the effective of ferrimagnets diverges at the angular momentum compensation temperature. This book provides readers with a scientific platform of ferrimagnetic dynamics, which serves as a useful basis for realizing the next generation of spintronic devices.

This book is a tribute to the scientific legacy of GianCarlo Ghirardi, who was one of the most influential scientists in the field of modern foundations of quantum theory. In this appraisal, contributions from friends, collaborators and colleagues reflect the influence of his world of thoughts on theory, experiments and philosophy, while also offering prospects for future research in the foundations of quantum physics. The themes of the contributions revolve around the physical reality of the wave function and its notorious collapse, randomness, relativity and experiments.

As an introductory account of the theory of phase transitions and critical phenomena, Elements of Phase Transitions and Critical Phenomena reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japanese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the text useful for self-teaching, as well as for classroom learning.

Covers the State of the Art in Superfluidity and Superconductivity Superfluid States of Matter addresses the phenomenon of superfluidity/superconductivity through an emergent, topologically protected constant of motion and covers topics developed over the past 20 years. The approach is based on the idea of separating universal classical-field superfluid properties of matter from the underlying system's "quanta." The text begins by deriving the general physical principles behind superfluidity/superconductivity within the classical-field framework and provides a deep understanding of all key aspects in terms of the dynamics and statistics of a classical-field system. It proceeds by explaining how this framework emerges in realistic quantum systems, with examples that include liquid helium, high-temperature superconductors, ultra-cold atomic bosons and fermions, and nuclear matter. The book also offers several powerful modern approaches to the subject, such as functional and path integrals. Comprised of 15 chapters, this text: Establishes the fundamental macroscopic properties of superfluids and superconductors within the paradigm of the classical matter field Deals with a single-component neutral matter field Considers fundamentals and properties of superconductors Describes new physics of superfluidity and superconductivity that arises in multicomponent systems Presents the quantum-field perspective on the conditions under which classical-field description is relevant in bosonic and fermionic systems Introduces the path integral formalism Shows how Feynman path integrals can be efficiently simulated with the worm algorithm Explains why nonsuperfluid (insulating) ground states of regular and disordered bosons occur under appropriate conditions Explores superfluid solids (supersolids) Discusses the rich dynamics of vortices and various aspects of superfluid turbulence at T 0 Provides account of BCS theory for the weakly interacting Fermi gas Highlights and analyzes the most crucial developments that has led to the current understanding of superfluidity and superconductivity Reviews the variety of superfluid and superconducting systems available today in nature and the laboratory, as well as the states that experimental realization is currently actively pursuing

In recent years, there has been much synergy between the exciting areas of quantum information science and ultracold atoms. This volume, as part of the proceedings for the XCI session of Les Houches School of Physics (held for the first time outside Europe in Singapore) brings together experts in both fields. The theme of the school focused on two principal topics: quantum information science and ultracold atomic physics. The topics range from Bose Einstein Condensates to Degenerate Fermi Gases to fundamental concepts in Quantum Information Sciences, including some special topics on Quantum Hall Effects, Quantum Phase Transition, Interactions in Quantum Fluids, Disorder and Interference Phenomenoma, Trapped Ions and Atoms, and Quantum Optical Devices.

This is the first book on secure quantum network coding, which integrates quantum cryptography into quantum communication. It summarizes the main research findings on quantum network coding, while also systematically introducing readers to secure quantum network coding schemes. With regard to coding methods, coding models and coding security, the book subsequently provides a series of quantum network coding schemes based on the integration of quantum cryptography into quantum communication. Furthermore, it describes the general security analysis method for quantum cryptographic protocols. Accordingly, the book equips readers with effective tools for researching and applying quantum network coding.

This book highlights the overview of Spintronics, including What is Spintronics ?; Why Do We Need Spintronics ?; Comparative merit-demerit of Spintronics and Electronics ; Research Efforts put on Spintronics ; Quantum Mechanics of Spin; Dynamics of magnetic moments : Landau-Lifshitz-Gilbert Equation; Spin-Dependent Band Gap in Ferromagnetic Materials; Functionality of 'Spin' in Spintronics; Different Branches of Spintronics etc. Some important notions on basic elements of Spintronics are discussed here, such as - Spin Polarization, Spin Filter Effect, Spin Generation and Injection, Spin Accumulation, Different kinds of Spin Relaxation Phenomena, Spin Valve, Spin Extraction, Spin Hall Effect, Spin Seebeck Effect, Spin Current Measurement Mechanism, Magnetoresistance and its different kinds etc. Concept of Giant Magnetoresistance (GMR), different types of GMR, qualitative and quantitative explanation of GMR employing Resistor Network Theory are presented here. Tunnelling Magnetoresistance (TMR), Magnetic Junctions, Effect of various parameters on TMR, Measurement of spin relaxation length and time in the spacer layer are covered here. This book highlights the concept of Spin Transfer Torque (STT), STT in Ferromagnetic Layer Structures, STT driven Magnetization Dynamics, STT in Magnetic Multilayer Nanopillar etc. This book also sheds light on Magnetic Domain Wall (MDW) Motion, Ratchet Effect in MDW motion, MDW motion velocity measurements, Current-driven MDW motion, etc. The book deals with the emerging field of spintronics, i.e., Opto-spintronics. Special emphasis is given on ultrafast optical controlling of magnetic states of antiferromagnet, Spin-photon interaction, Faraday Effect, Inverse Faraday Effect and outline of different all-optical spintronic switching. One more promising branch i.e., Terahertz Spintronics is also covered. Principle of operation of spintronic terahertz emitter, choice of materials, terahertz writing of an antiferromagnetic magnetic memory device is discussed. Brief introduction of Semiconductor spintronics is presented that includes dilute magnetic semiconductor, feromagnetic semiconductor, spin polarized semiconductor devices, three terminal spintronic devices, Spin transistor, Spin-LED, and Spin-Laser. This book also emphasizes on several modern spintronics devices that includes GMR Read Head of Modern Hard Disk Drive, MRAM, Position Sensor, Biosensor, Magnetic Field sensor, Three Terminal Magnetic Memory Devices, Spin FET, Race Track Memory and Quantum Computing.

Trace and determinant functionals on operator algebras provide a means of constructing invariants in analysis, topology, differential geometry, analytic number theory, and quantum field theory. The consequent developments around such invariants have led to significant advances both in pure mathematics and theoretical physics. As the fundamental tools of trace theory have become well understood and clear general structures have emerged, so the need for specialist texts which explain the basic theoretical principles and computational techniques has become increasingly urgent. Providing a broad account of the theory of traces and determinants on algebras of differential and pseudodifferential operators over compact manifolds, this text is the first to deal with trace theory in general, encompassing a number of the principle applications and backed up by specific computations which set out in detail the nuts-and-bolts of the basic theory. Both the microanalytic approach to traces and determinants via pseudodifferential operator theory and the more computational approach directed by applications in geometric analysis, are developed in a general framework that will be of interest to mathematicians and physicists in a number of different fields.

The structure of quantum theory permits interference of indistinguishable paths. At the same time, however, it also limits such interference to certain orders and any higher-order interference is prohibited. This thesis develops and studies concepts to test quantum theory with higher-order interference using many-particle correlations, the latter being generally richer and typically more subtle than single-particle correlations. It is demonstrated that quantum theory in general allows for interference up to order 2M in M-particle correlations. Depending on the mutual coherence of the particles, however, the related interference hierarchy can terminate earlier. In this thesis, we show that mutually coherent particles can exhibit interference of the highest orders allowed. We further demonstrate that interference of mutually incoherent particles truncates already at order M+1, although interference of the latter is principally more multifaceted than their coherent counterpart. We introduce two families of many-particle Sorkin parameters, whose members are expected to be all zero when quantum mechanics holds. As proof of concept, we demonstrate the disparate vanishing of such higher-order interference terms as a function of coherence in experiments with mutually coherent and incoherent sources. Finally, we investigate the influence of exotic kinked or looped quantum paths, which are permitted by Feynman's path integral approach, in such setups.

The last decade witnessed an increasing interest of mathematicians in prob lems originated in mathematical physics. As a result of this effort, the scope of traditional mathematical physics changed considerably. New problems es pecially those connected with quantum physics make use of new ideas and methods. Together with classical and functional analysis, methods from dif ferential geometry and Lie algebras, the theory of group representation, and even topology and algebraic geometry became efficient tools of mathematical physics. On the other hand, the problems tackled in mathematical physics helped to formulate new, purely mathematical, theorems. This important development must obviously influence the contemporary mathematical literature, especially the review articles and monographs. A considerable number of books and articles appeared, reflecting to some extend this trend. In our view, however, an adequate language and appropriate methodology has not been developed yet. Nowadays, the current literature includes either mathematical monographs occasionally using physical terms, or books on theoretical physics focused on the mathematical apparatus. We hold the opinion that the traditional mathematical language of lem mas and theorems is not appropriate for the contemporary writing on mathe matical physics. In such literature, in contrast to the standard approaches of theoretical physics, the mathematical ideology must be utmost emphasized and the reference to physical ideas must be supported by appropriate mathe matical statements. Of special importance are the results and methods that have been developed in this way for the first time."

This thesis presents a revolutionary technique for modelling the dynamics of a quantum system that is strongly coupled to its immediate environment. This is a challenging but timely problem. In particular it is relevant for modelling decoherence in devices such as quantum information processors, and how quantum information moves between spatially separated parts of a quantum system. The key feature of this work is a novel way to represent the dynamics of general open quantum systems as tensor networks, a result which has connections with the Feynman operator calculus and process tensor approaches to quantum mechanics. The tensor network methodology developed here has proven to be extremely powerful: For many situations it may be the most efficient way of calculating open quantum dynamics. This work is abounds with new ideas and invention, and is likely to have a very significant impact on future generations of physicists.

The second edition of this successful textbook provides an up-to-date account of the optical physics of solid state materials. The basic principles of absorption, reflection, luminescence, and light scattering are covered for a wide range of materials, including insulators, semiconductors and metals. The text starts with a review of classical optics, and then moves on to the treatment of optical transition rates by quantum theory. In addition to the traditional discussion of crystalline materials, glasses and molecular solids are also covered.
The first edition included a number of subjects that are not normally covered in standard texts, notably semiconductor quantum wells, molecular materials, vibronic solid state lasers, and nonlinear optics. The basic structure of the second edition is unchanged, but all of the chapters have been updated and improved. Futhermore, a number of important new topics have been added, including:
DT Optical control of spin
DT Quantum dots
DT Plasmonics
DT Negative refraction
DT Carbon nanostructures (graphene, nanotubes and fullerenes)
DT NV centres in diamond
The text is aimed at final year undergraduates, masters students and researchers. It is mainly written for physicists, but might also be useful for electrical engineers, materials scientists and physical chemists. The topics are written in a clear tutorial style with worked examples, chapter summaries and exercises.
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This research monograph offers an introduction to advanced quantum field theoretical techniques for many-particle systems beyond perturbation theory. Several schemes for resummation of the Feynman diagrams are described. The resulting approximations are especially well suited for strongly correlated fermion and boson systems. Also considered is the crossover from BCS superconductivity to Bose--Einstein condensation in fermion systems with strong attractive interaction. In particular, a field theoretic formulation of "bosonization" is presented; it is published here for the first time. This method is applied to the fractional quantum Hall effect, to the Coulomb plasma, and to several exactly solvable models.

Astrophysical observations implying the existence of Dark Matter and Dark Energy, which are not described by the Standard Model (SM) of particle physics, have led to extensions of the SM predicting new particles that could be directly produced at the Large Hadron Collider (LHC) at CERN. Based on 2015 and 2016 ATLAS proton-proton collision data, this thesis presents searches for the supersymmetric partner of the top quark, for Dark Matter, and for DarkEnergy, in signatures with jets and missing transverse energy. Muon detection is key to some of the most important LHC physics results, including the discovery of the Higgs boson and the measurement of its properties. The efficiency with which muons can be detected with the ATLAS detector is measured using Z boson decays. The performance of high-precision Monitored Drift Tube muon chambers under background rates similar to the ones expected for the High Luminosity-LHC is studied.

This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems. The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measure theory with potential applications in life sciences, are opened.

Peter Byrne tells the story of Hugh Everett III (1930-1982), whose "many worlds" theory of multiple universes has had a profound impact on physics and philosophy. Using Everett's unpublished papers (recently discovered in his son's basement) and dozens of interviews with his friends, colleagues, and surviving family members, Byrne paints, for the general reader, a detailed portrait of the genius who invented an astonishing way of describing our complex universe from the inside. Everett's mathematical model (called the "universal wave function") treats all possible events as "equally real," and concludes that countless copies of every person and thing exist in all possible configurations spread over an infinity of universes: many worlds.
Afflicted by depression and addictions, Everett strove to bring rational order to the professional realms in which he played historically significant roles. In addition to his famous interpretation of quantum mechanics, Everett wrote a classic paper in game theory; created computer algorithms that revolutionized military operations research; and performed pioneering work in artificial intelligence for top secret government projects. He wrote the original software for targeting cities in a nuclear hot war; and he was one of the first scientists to recognize the danger of nuclear winter. As a Cold Warrior, he designed logical systems that modeled "rational" human and machine behaviors, and yet he was largely oblivious to the emotional damage his irrational personal behavior inflicted upon his family, lovers, and business partners.
He died young, but left behind a fascinating record of his life, including correspondence with such philosophically inclined physicists as Niels Bohr, Norbert Wiener, and John Wheeler. These remarkable letters illuminate the long and often bitter struggle to explain the paradox of measurement at the heart of quantum physics. In recent years, Everett's solution to this mysterious problem-the existence of a universe of universes-has gained considerable traction in scientific circles, not as science fiction, but as an explanation of physical reality.

A thorough introduction to modern classical and quantum optics, appropriate for advanced undergraduates or beginning graduates. The emphasis is on building an understanding in straightforward steps. Digital cameras, LCD screens, laser welding, and the optical fibre-based internet illustrate the penetration of optics in twenty-first century life: many such modern applications are presented from first principles.
Self-contained themes covered in the book include:
- Paraxial ray optics for devices including matrix methods and aberrations.
- Interference, coherence and interferometry.
- Diffraction, spectrometry and Gaussian optics.
- Fourier optics, holography and information processing.
- Astronomical telescopes, adaptive optics and aperture synthesis.
- Maxwell's theory; scattering, absorption and dispersion in bulk materials; multilayer filters.
- Quantum phenomena, wave-particle duality and the uncertainty principle.
- Schroedinger's analysis of spectra, photon properties.
- Laser principles; He: Ne to MQW lasers and applications.
- Detectors: photodiodes, CCDs, PMs and image intensifiers; response, noise and linearity.
- Fibre optics: single mode fibre analysis; the modern data highway; fibre sensors.
- Photon-atom interactions, optical cooling and optical clocks.
- Second quantization, photon correlations, SPDC, entanglement.
This thoroughly revised and updated edition includes new coverage of photonic crystals and Bloch waves, as well as quantum dots and microcavities.

This thesis reports the calculation of neutrino production for the T2K experiment; the most precise a priori estimate of neutrino production that has been achieved for any accelerator-based neutrino oscillation experiment to date. The production of intense neutrino beams at accelerator facilities requires exceptional understanding of chains of particle interactions initiated within extended targets. In this thesis, the calculation of neutrino production for T2K has been improved by using measurements of particle production from a T2K replica target, taken by the NA61/SHINE experiment. This enabled the reduction of the neutrino production uncertainty to the level of 5%, which will have a significant impact on neutrino oscillation and interaction measurements by T2K in the coming years. In addition to presenting the revised flux calculation methodology in an accessible format, this thesis also reports a joint T2K measurement of muon neutrino and antineutrino disappearance, and the accompanying electron neutrino and antineutrino appearance, with the updated beam constraint.