In the past four decades, there has been growing interest in the exciting new topic of physics in low dimensions. Thousands of original ideas have been proposed in the literature, and some are confirmed experimentally, along with several Nobel prizes which have been awarded in this field. While there are several books available, almost all are technical and accessible only to expert researchers. This book provides an accessible introduction to the field, with less emphasis on technical details. Whilst this book does not provide a traditional history of nano-science, instead it uses simple explanations and case studies as vehicles to explain key discoveries and the importance of them, enabling readers without a background in the area to gain an understanding of some aspects of nanoscale physics. It will be of interest to researchers working in condensed matter physics, in addition to engineers and advanced students in those disciplines. It also remains accessible to 'physics enthusiasts' from other academic disciplines, as technical details are contained within boxes and footnotes which can be skipped for a general reading of the book. Features: - Provides an accessible introduction to a technical subject - Contains exciting developments from the cutting-edge science being conducted in the area - Authored by a recognised expert in the field

This is a practical introduction to the principal ideas in gauge theory and their applications to elementary particle physics. It explains technique and methodology with simple exposition backed up by many illustrative examples. Derivations, some of well known results, are presented in sufficient detail to make the text accessible to readers entering the field for the first time. The book focuses on the strong interaction theory of quantum chromodynamics and the electroweak interaction theory of Glashow, Weinberg, and Salam, as well as the grand unification theory, exemplified by the simplest SU(5) model. Not intended as an exhaustive survey, the book nevertheless provides the general background necessary for a serious student who wishes to specialize in the field of elementary particle theory. Physicists with an interest in general aspects of gauge theory will also find the book highly useful.

The core content of even the most intricate intellectual edifices is often a simple fact or idea. So is it with quantum mechanics; the entire mathematical fabric of the formal description of quantum mechanics stems essentially from the fact that quantum probabilities interfere (i.e., from the superposition principle). This book is dedicated to substantiating this claim. In the process, the book tries to demonstrate how the factual content of quantum mechanics can be transcribed in the formal language of vector spaces and linear transformations by disentangling the empirical content from the usual formal description. More importantly, it tries to bring out what this transcription achieves. The book uses a pedagogic strategy which reverse engineers the postulates of quantum mechanics to device a schematic outline of the empirical content of quantum mechanics from which the postulates are then reconstructed step by step. This strategy is adopted to avoid the disconcerting details of actual experiments (however simplified) to spare the beginner of issues that lurk in the fragile foundations of the subject. In the Copenhagen interpretation of quantum mechanics, the key idea is measurement. But "measurement" carries an entirely different meaning from the connotation that the term carries elsewhere in physics. This book strives to underline this as strongly as possible. The book is intended as an undergraduate text for a first course in quantum mechanics. Since the book is self contained, it may also be used by enthusiastic outsiders interested to get a glimpse of the core content of the subject. Features: Demonstrates why linear algebra is the appropriate mathematical language for quantum mechanics. Uses a reconstructive approach to motivate the postulates of quantum mechanics. Builds the vocabulary of quantum mechanics by showing how the entire body of its conceptual ingredients can be constructed from the single notion of quantum measurement.

This book presents new developments in the open quantum systems theory with emphasis on applications to the (frequent) measurement theory.In the first part of the book, the uniqueness theorems for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions are discussed. The major theme involves an intrinsic characterization of the simplest symmetric operator solutions to the Heisenberg uncertainty relations, the problem posed by Jorgensen and Muhly, followed by the proof of the uniqueness theorems for the simplest solutions to the restricted Weyl commutation relations. The detailed study of unitary invariants of the corresponding dissipative and symmetric operators opens up a look at the classical Stone-von Neumann uniqueness theorem from a new angle and provides an extended version of the uniqueness result relating various realizations of a differentiation operator on the corresponding metric graphs.The second part of the book is devoted to mathematical problems of the quantum measurements under continuous monitoring. Among the topics discussed are the complementarity of the Quantum Zeno effect and Exponential Decay scenario in frequent quantum measurements, and a rigorous treatment, within continuous monitoring paradigm, of the celebrated 'double-slit experiment' where the renowned exclusive and interference measurement alternatives approach in quantum theory is presented in a way that is accessible for mathematicians. One of the striking applications of the generalized (1-stable) central limit theorem is the mathematical evidence of exponential decay of unstable states of the quantum pendulum under continuous monitoring.

Based on the lectures given at TU Munich for third-year physics students, this book provides the basic concepts of relativistic quantum field theory, perturbation theory, Feynman graphs, Abelian and non-Abelian gauge theories, with application to QED, QCD, and the electroweak Standard Model. It also introduces quantum field theory and particle physics for beginning graduate students with an orientation towards particle physics and its theoretical foundations. Phenomenology of W and Z bosons, as well as Higgs bosons, is part of the electroweak chapter in addition to recent experimental results, precision tests and current status of the Standard Model.

This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quanti zation. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamil tonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as pro posed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direc tion vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit."

This introduction to quantum mechanics is intended for undergraduate students of physics, chemistry, and engineering with some previous exposure to quantum ideas. Following in Heisenberg's and Dirac's footsteps, this book is centered on the concept of the quantum state as an embodiment of all experimentally available information about a system, and its representation as a vector in an abstract Hilbert space. This conceptual framework and formalism are introduced immediately, and developed throughout the first four chapters, while the standard Schroedinger equation does not appear until Chapter 5. The book grew out of lecture notes developed by the author over fifteen years of teaching at the undergraduate level. In response to numerous requests by students, material is presented with an unprecedented level of detail in both derivation of technical results and discussion of their physical significance. The book is written for students to enjoy reading it, rather than to use only as a source of formulas and examples. The colloquial and personal writing style makes it easier for readers to connect with the material. Additionally, readers will find short, relatable snippets about the "founding fathers" of quantum theory, their difficult historical circumstances, personal failings and triumphs, and often tragic fate. This textbook, complete with extensive original end-of-chapter exercises, is recommended for use in one- or two-semester courses for upper level undergraduate and beginning graduate students in physics, chemistry, or engineering.

This book covers a range of new research on computational quantum chemistry, along with a special section devoted to exotic carbon allotropes and spiro quantum theory. The section on spiro quantum theory covers the technical presentation of the ideas surrounding the emergence of a synthetic, analytical, and theoretical spiro quantum chemistry edifice, as well as a chemical topology scheme that successfully describes molecules and patterns, including the hydrocarbons and allotropes of carbon. The second part of the book covers a range of new research on computational quantum chemistry.

This book focuses on recent topics of quantum science in both physics and chemistry. Until now, quantum science has not been fully discussed from the interdisciplinary vantage points of both physics and chemistry. This book, however, is written not only for theoretical physicists and chemists, but also for experimentalists in the fields of physical chemistry and condensed matter physics, as collaboration and interplay between construction of quantum theory, and experimentation has become more important. Tips for starting new types of research projects will be found in an understanding of cutting-edge quantum science. In Part I, quantum electronic structures are explained in cases of strongly correlated copper oxides and heavy elements. In Part II, quantum molecular dynamics is investigated by computational approaches and molecular beam experiments. In Part III, after lithium problem in big bang nucleosynthesis scenario is considered using supersymmetric standard model, quantum theories in atomic and molecular systems are reviewed. Finally, in Part IV, the development of quantum computational method is introduced.

During the last thirty years a great advancement in low energy physics, particularly interactions of atoms with the electromagnetic field, has been achieved and the development of electronics and laser techniques has allowed to implement a fine manipulation of atoms with photons. A wealth of important applications has sprung out from the ability of manipulating large samples of cold atoms. Among them, the improvement of atomic clocks and the creation of atomic gyroscopes and of atomic gravity meters, which is obviously of great interest for geodesists and geophysicists, particularly for potential applications in satellite geodesy. This book explains the fundamental concepts necessary to understand atom manipulation by photons, including the principles of quantum mechanics. It is conceived as a road that leads the reader from classical physics (mechanics and electromagnetism, considered as a common scientific background of geodesists and geophysicists), to the basics of quantum mechanics in order to understand the dynamics of atoms falling in the gravity field, while interacting with suitably resonant laser beams. There are different types of measurements of gravity based on the manipulation of ultra-cold atoms; the book presents the principles of the instruments based on stimulated Raman transition, which can be easily worked out analytically. However, the concepts explained in the text can provide a good starting point to understand also the applications based on the so-called Block oscillations or on the Bose-Einstein condensation.

This book covers the entire span of quantum mechanics whose developments have taken place during the early part of the twentieth century up till the present day. We start with the Rutherford-Bohr model of the atom followed by Schrodinger's wave mechanics with its application to the solution of calculating the energy spectrum of a particle in a box, the harmonic oscillator and finally the hydrogen atom. Heisenberg's matrix mechanics and its duality with Schrodinger's wave mechanics, quantum mechanics in the interaction picture. Dirac's relativistic theory of the electron exhibiting the spin of the electron as a relativistic effect when it interacts with an external electromagnetic field. Feynman's path integral approach to non-relativistic quantum mechanics with is a marvellous intuitive interpretation as a sum over paths and how classical mechanics is obtained from its limit as Planck' constant tends to zero, methods for computing the spectra of the Dirac Hamiltonian in a radial potential, quantum field theory as developed by Feynman, Schwinger, Tomonaga and Dyson for describing the interaction between electrons, positrons, and photons via propagators using both the operator theoretic expansions and Feynman's path integral. We also introduce time independent and time dependent perturbation theory in quantum mechanics with applications to quantum gate design for quantum computers forming a major part of the research conducted by the author's research group, Quantum noise introduced into the Schrodinger and Dirac's equation based on the Hudson-Parthasarathy quantum stochastic calculus in Boson Fock space, scattering theory and wave operators with applications to quantum gate design, some aspects of second quantization like the interpretation of Boson Fock space in terms of harmonic oscillator algebras and the BCS theory of superconductivity, Wigner-Mackey-Frobenius theory of induced representations of a group with applications to Wigner's theory of particle classification, Dirac's equation in a gravitational field and Yang-Mills non-Abelian gauge theories with application to the construction of unified quantum field theories and finally, the more recent theory of super-symmetry which is a Boson-Fermion unification theory. We have discussed the statistics of Boson's, Fermions and Maxwell-Boltzmann based on entropy maximization. The book is written in problem-solution format and it would be of use to physicists and engineers interested respectively in developing unified field theories and in the design of quantum gates. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

Many technological applications exploit a variety of magnetic structures, or magnetic phases, to produce and optimise solid-state functionality. However, most research advances are restricted to a reduced number of phases owing to computational and resource constraints. This thesis presents an ab-initio theory to efficiently describe complex magnetic phases and their temperature-dependent properties. The central assumption is that magnetic phases evolve slowly compared with the underlying electronic structure from which they emerge. By describing how the electronic structure adapts to the type and extent of magnetic order, a theory able to describe multi-spin correlations and their effect on the magnetism at finite temperature is obtained. It is shown that multi-spin correlations are behind the temperature and magnetic field dependence of the diverse magnetism in the heavy rare earth elements. Magnetically frustrated Mn-based materials and the effect of strain are also investigated. These studies demonstrate that the performance of solid-state refrigeration can be enhanced by multi-spin effects.

In the last several decades, the quantum Hall effect has provided a remarkable platform for manipulating one-dimensional electronic modes and investigating fundamental physical phenomena. However, certain limitations make it difficult for various kinds of interesting modes structures to be formed using this platform. One example is the so called helical mode structure, in which two one-dimensional, counter propagating modes have opposite spins and thus spin and momentum are locked. Such helical modes have lately attracted significant interest, since, when coupled to a conventional superconductor, they are expected to manifest topological superconductivity and host Majorana zero modes. Even more interesting are fractional helical modes, which open the way for realizing generalized parafermionic zero modes. Possessing non-abelian exchange statistics, these quasiparticles may serve as building blocks in topological quantum computing. Here we present a new platform for manipulating integer and fractional quantum Hall edge modes, which allows the formation of robust one-dimensional helical as well as fractional helical modes. The platform is based on a carefully designed double-quantum-well structure in a GaAs based system hosting two electronic sub-bands in the quantum Hall effect regime. By electrostatic gating of different areas of the structure, counter-propagating integer, as well as fractional, edge modes with opposite spins are formed and their spin protection is verified. Beyond the formation of helical modes, the new platform can serve as a rich playground for new research. Some new possibilities include the artificial induction of compounded fractional edge modes and the construction of new edge mode-based interferometers.

Magnetic and spintronic materials are ubiquitous in modern technological applications, e.g. in electric motors, power generators, sensors and actuators, not to mention information storage and processing. Medical technology has also greatly benefited from magnetic materials - especially magnetic nanoparticles - for therapy and diagnostics methods. All of the above-mentioned applications rely on the properties of the materials used. These properties in turn depend on intrinsic and extrinsic material parameters. The former are related to the actual elements used and their properties, e.g. atomic magnetic moment and exchange interaction between atoms; the latter are related to the structural and microstructural properties of the materials used, e.g. their crystal structure, grain size, and grain boundary phases. Focusing on state-of-the-art magnetic and spintronic materials, this book will introduce readers to a range of related topics in Physics and Materials Science. Phenomena and processes at the nanoscale are of particular importance in this context; accordingly, much of the book addresses such topics.

Based on the analytical methods and the computer programs presented in this book, all that may be needed to perform MRI tissue diagnosis is the availability of relaxometric data and simple computer program proficiency. These programs are easy to use, highly interactive and the data processing is fast and unambiguous. Laboratories (with or without sophisticated facilities) can perform computational magnetic resonance diagnosis with only T1 and T2 relaxation data. The results have motivated the use of data to produce data-driven predictions required for machine learning, artificial intelligence (AI) and deep learning for multidisciplinary and interdisciplinary research. Consequently, this book is intended to be very useful for students, scientists, engineers, the medical personnel and researchers who are interested in developing new concepts for deeper appreciation of computational magnetic resonance imaging for medical diagnosis, prognosis, therapy and management of tissue diseases.

In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. Nonrelativistic quantum mechanics as well as classical relativistic mechanics appear as special cases. They are the sources of familiar names such as "orbital angular momentum," "spin-orbit coupling" and "magnetic moment" for operators of the relativistic quantum formalism. The theory of binaries, in terms of differential equations, is treated for the first time in this book. These have the mathematical structure of the corresponding one-body equations (Klein-Gordon for two spinless particles, Dirac for two spinor particles) with a relativistically reduced mass. They allow the calculation of radiative corrections via the vector potential operator. This second edition of the successful textbook adds various new sections on relativistic quantum chemistry and on the relativistic treatment of the proton in hydrogen. Others chapters have been expanded, e.g. on hyperfinite interactions, or carefully revisited.

This is the first book to discuss the search for new physics in charged leptons, neutrons, and quarks in one coherent volume. The area of indirect searches for new physics is highly topical; though no new physics particles have yet been observed directly at the Large Hadron Collider at CERN, the methods described in this book will provide researchers with the necessary tools to keep searching for new physics. It describes the lines of research that attempt to identify quantum effects of new physics particles in low-energy experiments, in addition to detailing the mathematical basis and theoretical and phenomenological methods involved in the searches, whilst making a clear distinction between model-dependent and model-independent methods employed to make predictions. This book will be a valuable guide for graduate students and early-career researchers in particle and high energy physics who wish to learn about the techniques used in modern predictions of new physics effects at low energies, whilst also serving as a reference for researchers at other levels. Key features: * Takes an accessible, pedagogical approach suitable for graduate students and those seeking an overview of this new and fast-growing field * Illustrates common theoretical trends seen in different subfields of particle physics * Valuable both for researchers in the phenomenology of elementary particles and for experimentalists

Quantum mechanics is one of mankind's most remarkable intellectual achievements. Stunningly successful and elegant, it challenges our deepest intuitions about the world. In this book, seventeen physicists and philosophers, all deeply concerned with understanding quantum mechanics, reply to Schlosshauer's penetrating questions about the central issues. They grant us an intimate look at their radically different ways of making sense of the theory's strangeness. What is quantum mechanics about? What is it telling us about nature? Can quantum information or new experiments help lift the fog? And where are we headed next? Everyone interested in the contemporary but often longstanding conundrums of quantum theory, whether lay reader or expert, will find much food for thought in these pages. A wealth of personal reflections and anecdotes guarantee an engaging read. Participants: Guido Bacciagaluppi, Caslav Brukner, Jeffrey Bub, Arthur Fine, Christopher Fuchs, GianCarlo Ghirardi, Shelly Goldstein, Daniel Greenberger, Lucien Hardy, Anthony Leggett, Tim Maudlin, David Mermin, Lee Smolin, Antony Valentini, David Wallace, Anton Zeilinger, and Wojciech Zurek.