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This book begins with the ancient parts of classical mechanics: the variational principle, Lagrangian and Hamiltonian formalisms, and Poisson brackets. The simple pendulum provides a glimpse of the beauty of elliptic curves, which will also appear later in rigid body mechanics. Geodesics in Riemannian geometry are presented as an example of a Hamiltonian system. Conversely, the path of a non-relativistic particle is a geodesic in a metric that depends on the potential. Orbits around a black hole are found. Hamilton-Jacobi theory is discussed, showing a path towards quantum mechanics and a connection to the eikonal of optics. The three body problem is studied in detail, including small orbits around the Lagrange points. The dynamics of a charged particle in a magnetic field, especially a magnetic monopole, is studied in the Hamiltonian formalism. Spin is shown to be a classical phenomenon. Symplectic integrators that allow numerical solutions of mechanical systems are derived. A simplified version of Feigenbaum's theory of period doubling introduces chaos. Following a classification of Mobius transformations, this book studies chaos on the complex plane: Julia sets, Fatou sets, and the Mandelblot are explained. Newton's method for solution of non-linear equations is viewed as a dynamical system, allowing a novel approach to the reduction of matrices to canonical form. This is used as a stepping stone to the KAM theory of maps of a circle to itself, unravelling a connection to the Diophantine problem of number theory. KAM theory of the solution of the Hamilton-Jacobi equation using Newton's iteration concludes the book.

The subject of this book is the Casimir effect, i.e., a manifestation of zero-point oscillations of the quantum vacuum in the form of forces acting between closely spaced bodies. It is a purely quantum effect. There is no force acting between neutral bodies in classical electrodynamics. The Casimir effect has become an interdisciplinary subject. It plays an important role in various fields of physics such as condensed matter physics, quantum field theory, atomic and molecular physics, gravitation and cosmology, and mathematical physics. Most recently, the Casimir effect has been applied to nanotechnology and for obtaining constraints on the predictions of unification theories beyond the Standard Model. The book assembles together the field-theoretical foundations of this phenomenon, the application of the general theory to real materials, and a comprehensive description of all recently performed measurements of the Casimir force, including the comparison between experiment and theory. There is increasing interest in forces of vacuum origin. Numerous new results have been obtained during the last few years which are not reflected in the literature, but are very promising for fundamental science and nanotechnology. The book provides a source of information which presents a critical assessment of all of the main results and approaches contained in published journal papers. It also proposes new ideas which are not yet universally accepted but are finding increasing support from experiment.

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. 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, 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 familiarise the student with similar techniques in quantum theory. Several of the current fundamental problems in theoretical physics, such as the development of quantum information technology and the problem of quantising the gravitational field, require a rethinking of the quantum-classical connection.

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics, and of the relation of classical mechanics to relativity and quantum theory. A distinguishing feature is its integration of special relativity into the 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. The definition of canonical transformation no longer excludes the Lorentz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum mechanics since 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 familiarise the student with similar techniques in quantum theory. Several of the current fundamental problems in theoretical physics require a rethinking of the quantum–classical connection.

Progress in modern radio astronomy led to the discovery of space masers in the microwave range, and it became a powerful tool for studies of interstellar star-forming molecular clouds. Progress in observational astronomy, particularly with ground-based huge telescopes and the space-based Hubble Space Telescope, has led to recent discoveries of space lasers in the optical range. These operate in gas condensations in the vicinity of the mysterious star Eta Carinae (one of the most luminous and massive stars of our Galaxy). Both maser and laser effects, first demonstrated under laboratory conditions, have now been discovered to occur under natural conditions in space too. This book describes consistently the elements of laser science, astrophysical plasmas, modern astronomical observation techniques, and the fundamentals and properties of astrophysical lasers.

This book gives an account of the progress that has been made in the fields of atomic physics and laser spectroscopy during the last fifty years. The first five chapters prepare the foundations of atomic physics, classical electro-magnetism, and quantum mechanics, which are necessary for an understanding of the interaction of electromagnetic radiation with free atoms. The application of these concepts to processes involving the spontaneous emission of radiation is then developed in Chapters 6, 7, and 8, while stimulated emission and the properties of gas and tunable dye lasers form the subject matter of Chapters 9 to 14. The last four chapters are concerned with the physics and applications of atomic resonance fluorescence, optical double-resonance, optical pumping, and atomic beam magnetic resonance.

Atomic force microscopy (AFM) is an amazing technique that allies a versatile methodology (it allows the imaging of samples in liquid, vacuum or air) to imaging with unprecedented resolution. But it goes one step further than conventional microscopic techniques; it also allows us to make measurements of magnetic, electrical or mechanical properties of the widest possible range of samples, with nanometre resolution. This book will demystify AFM for the reader, making it easy to understand, and easy to use. Peter Eaton and Paul West share a common passion for atomic force microscopy. However, they have very different perspectives on the technique. Over the past 12 years Peter used AFMs as the focal point of his research in a variety of scientific projects from materials science to biology. Paul, on the other hand, is an instrument builder and has spent the past 25 years creating these microscopes for scientists and engineers. This insightful book covers the theory, practice and applications of atomic force microscopes and will serve as an introduction to AFM for scientists and engineers that want to learn about this powerful technique, and as a reference book for expert AFM users. Application examples from the physical, materials, and life sciences, nanotechnology and industry illustrate the many and varied capabilities of the technique.

Are the fundamental constants of Nature really constant? How can we build clocks that lose only a few seconds on the entire life of the Universe? This book answers these questions by illustrating the history and the most recent advances in atomic physics connected to the possibility of performing precise measurements and achieving the ultimate control of the atomic state. Written in an introductory style, this book is addressed to undergraduate and graduate students, as well as to more experienced researchers who need to stay up-to-date with the most recent advances. It is not a classical atomic physics textbook, in which the focus is on the theory of atomic structures and on light-matter interaction: it focuses on the experimental investigations, illustrating milestone experiments and key experimental techniques, as well as discussing the results and the challenges of contemporary research. Emphasis is given to the investigation of precision physics: from the determination of fundamental constants to tests of general relativity and quantum electrodynamics, from the realization of atomic clocks and interferometers to the precise simulation of condensed matter theories with ultracold gases. The book discusses these topics while tracing the evolution of experimental atomic physics from traditional laser spectroscopy to the revolution introduced by laser cooling, which allows the manipulation of atoms at a billionth of a degree above absolute zero, opening new frontiers in precision in atomic spectroscopy and revealing novel states of matter.

The purpose of this book is to provide a theoretical foundation and an understanding of atomistic spin-dynamics, and to give examples of where the atomistic Landau-Lifshitz-Gilbert equation can and should be used. The contents involve a description of density functional theory both from a fundamental viewpoint as well as a practical one, with several examples of how this theory can be used for the evaluation of ground state properties like spin and orbital moments, magnetic form-factors, magnetic anisotropy, Heisenberg exchange parameters, and the Gilbert damping parameter. This book also outlines how interatomic exchange interactions are relevant for the effective field used in the temporal evolution of atomistic spins. The equation of motion for atomistic spin-dynamics is derived starting from the quantum mechanical equation of motion of the spin-operator. It is shown that this lead to the atomistic Landau-Lifshitz-Gilbert equation, provided a Born-Oppenheimer-like approximation is made, where the motion of atomic spins is considered slower than that of the electrons. It is also described how finite temperature effects may enter the theory of atomistic spin-dynamics, via Langevin dynamics. Details of the practical implementation of the resulting stochastic differential equation are provided, and several examples illustrating the accuracy and importance of this method are given. Examples are given of how atomistic spin-dynamics reproduce experimental data of magnon dispersion of bulk and thin-film systems, the damping parameter, the formation of skyrmionic states, all-thermal switching motion, and ultrafast magnetization measurements.

One of the pillars of modern science, statistical mechanics, owes much to one man, the Austrian physicist Ludwig Boltzmann (1844–1906). As a result of his unusual working and writing styles, his enormous contribution remains little read and poorly understood. The purpose of this book is to make the Boltzmann corpus more accessible to physicists, philosophers, and historians, and so give it new life. The means are introductory biographical and historical materials, detailed and lucid summaries of every relevant publication, and a final chapter of critical synthesis. Special attention is given to Boltzmann’s theoretical tool-box and to his patient construction of lofty formal systems, even before their full conceptual import could be known. This constructive tendency largely accounts for his lengthy style, for the abundance of new constructions, for the relative vagueness of their object, and for the puzzlement of commentators. This book will help the reader cross the stylistic barrier and see how ingeniously Boltzmann combined atoms, mechanics, and probability to invent new bridges between the micro- and macro-worlds.

This book offers a grounding in the field of coherent X-ray optics, which in the closing years of the 20th century experienced something of a renaissance with the availability of third-generation synchrotron sources. It begins with a treatment of the fundamentals of X-ray diffraction for both coherent and partially coherent radiation, together with the interactions of X-rays with matter. X-ray sources, optical elements, and detectors are then discussed, with an emphasis on their role in coherent X-ray optics. Various aspects of coherent X-ray imaging are then considered, including holography, interferometry, self imaging, phase contrast, and phase retrieval. The foundations of the new field of singular X-ray optics are examined, focusing on the topic of X-ray phase vortices. Most topics in the book are developed from first principles using a chain of logic which ultimately derives from the Maxwell equations, with numerous references to the contemporary and historical research literature.

This volume gathers the lectures notes of Session CVII of the Les Houches summer school of Physics, entitled “Current trends in Atomic Physics”. The school took place in July 2016 and had the goal to give the participants a broad overview of Atomic Physics as a whole, and in particular its connections to other areas of physics, such as condensed-matter and high-energy physics. The book comprises twelve chapters corresponding to lectures delivered at the school.

This book contains spectra of the doubly charged positive ions (dications) of some 75 molecules, including the major constituents of terrestrial and planetary atmospheres and prototypes of major chemical groups. It is intended to be a new resource for research in all areas of molecular spectroscopy involving high energy environments, both terrestrial and extra-terrestrial. All the spectra have been produced by photoionisation using laboratory lamps or synchrotron radiation and have been measured using the magnetic bottle time-of-flight technique by coincidence detection of correlated electron pairs. Full references to published work on the same species are given, though for several molecules these are the first published spectra. Double ionisation energies are listed and discussed in relation to the molecular electronic structure of the molecules. A full introduction to the field of molecular double ionisation is included and the mechanisms by which double photoionisation can occur are examined in detail. A preliminary chapter covers double photoionisation of an atom in order to explain the basic principles of the technique, then five chapters present spectra of molecules of increasing size. A seventh chapter on the new fields of core–core and core–valence double ionisations, with selected examples, completes the main body of the book. Appendices explain the detailed mechanisms of double photoionisation, the calibration of the electron spectrometers, and give a brief summary of the methods by which double ionisation energies are calculated theoretically.

X-ray diffraction is a major tool for the study of crystal structures and the characterization of crystal perfection. Since the discovery of X-ray diffraction by von Laue, Friedrich, and Knipping in 1912 two basic theories have been used to describe this diffraction. One is the approximate geometrical, or kinematical theory, applicable to small or highly imperfect crystals; it is used for the determination of crystal structures and the study of powders and polycrystalline materials. The other one is the rigorous dynamical theory, applicable to perfect or nearly perfect crystals and, for that reason, is the one used for the assessment of the structural properties of high technology materials. It has witnessed exciting developments since the advent of synchrotron radiation. This book provides an account of the dynamical theory of diffraction and of its applications. The first part serves as an introduction to the subject, presenting early developments, Ewald's theory of dispersion and the basic results of Laue's dynamical theory. This is followed in the second part by a detailed development of the diffraction and propagation properties of X-rays in perfect crystals, including the study of anomalous absorption, Pendellösung, grazing incidence diffraction (GID) and n-beam or multiple-beam diffraction. The third part constitutes an extension of the theory to the case of slightly and highly deformed crystals. The last part gives three applications of the theory: X-ray optics for synchrotron radiation, location of atoms at surfaces and interfaces and X-ray diffraction topography.

A classic text in the field providing a readable and accessible guide for students of electrical and electronic engineering. Fundamentals of electric properties of materials are illustrated and put into context with contemporary applications in engineering. Mathematical content is kept to a minimum allowing the reader to focus on the subject. The starting point is the behaviour of the electron, which is explored both in the classical and in the quantum-mechanical context. Then comes the study of bonds, the free electron model, band structure, and the theory of semiconductors, followed by a chapter on semiconductor devices. Further chapters are concerned with the fundamentals of dielectrics, magnetic materials, lasers, optoelectronics, and superconductivity. The last chapter is on metamaterials, which has been a quite popular subject in the past decade. The book includes problems, the worked solutions are available in a separate publication: Solutions manual for electrical properties of materials. There is an appendix giving a list of Nobel Prize winners whose work was crucial for describing the electric properties of materials, and there are further appendices giving descriptions of phenomena which did not fit easily within the main text. In particular there is a quite detailed appendix that summarizes the properties of memory elements. The book is ideal for undergraduates, and is also an invaluable reference for graduate students and others wishing to explore this rapidly changing field.

Electromagnetic Radiation is a graduate level book on classical electrodynamics with a strong emphasis on radiation. This book is meant to quickly and efficiently introduce students to the electromagnetic radiation science essential to a practicing physicist. While a major focus is on light and its interactions, topics in radio frequency radiation, x-rays, and beyond are also treated. Special emphasis is placed on applications, with many exercises and homework problems. The format of the book is designed to convey the basic concepts of a topic in the main central text in the book in a mathematically rigorous manner, but with detailed derivations routinely relegated to the accompanying side notes or end of chapter “Discussions.” The book is composed of four parts: Part I is a review of basic E&M, and assumes the reader has a had a good upper division undergraduate course, and while it offers a concise review of topics covered in such a course, it does not treat any given topic in detail; specifically electro- and magnetostatics. Part II addresses the origins of radiation in terms of time variations of charge and current densities within the source, and presents Jefimenko’s field equations as derived from retarded potentials. Part III introduces special relativity and its deep connection to Maxwell’s equations, together with an introduction to relativistic field theory, as well as the relativistic treatment of radiation from an arbitrarily accelerating charge. A highlight of this part is a chapter on the still partially unresolved problem of radiation reaction on an accelerating charge. Part IV treats the practical problems of electromagnetic radiation interacting with matter, with chapters on energy transport, scattering, diffraction and finally an illuminating, application-oriented treatment of fields in confined environments.

The study of electrons and holes confined to two, one, and even zero dimensions has uncovered a rich variety of new physics and applications. This book describes the interaction between these confined carriers and the optic and acoustic phonons within and around the confined regions. Phonons provide the principal channel of energy transfer between the carriers and their surroundings and also the main restriction to their room temperature mobility. However, they also have many other roles; they contribute, for example, an essential feature to the operation of the quantum cascade laser. Since their momenta at relevant energies are well matched to those of electrons, they can also be used to probe electronic properties such as the confinement width of two-dimensional (2-D) electron gases and the dispersion curve of quasiparticles in the fractional quantum Hall effect. The book describes both the physics of the electron-phonon interaction in the different confined systems and the experimental and theoretical techniques that have been used in its investigation. The experimental methods include optical and transport techniques as well as techniques in which phonons are used as the experimental probe. This book provides an up-to-date review of the physics and its significance in device performance.

The book treats in a unified way electronic properties of molecules (magnetic, electrical, photophysical), culminating with the mastering of electrons, i.e. molecular electronics and spintronics and molecular machines. Chapter 1 recalls basic concepts. Chapter 2 describes the magnetic properties due to localized electrons. This includes phenomena such as spin cross-over, exchange interaction from dihydrogen to extended molecular magnetic systems, and magnetic anisotropy with single-molecule magnets. Chapter 3 is devoted to the electrical properties due to moving electrons. One considers first electron transfer in discrete molecular systems, in particular in mixed valence compounds. Then, extended molecular solids, in particular molecular conductors, are described by band theory. Special attention is paid to structural distortions (Peierls instability) and interelectronic repulsions in narrow-band systems. Chapter 4 treats photophysical properties, mainly electron transfer in the excited state and its applications to photodiodes, organic light emitting diodes, photovoltaic cells and water photolysis. Energy transfer is also treated. Photomagnetism (how a photonic excitation modifies magnetic properties) is introduced. Finally, Chapter 5 combines the previous knowledge for three advanced subjects: first molecular electronics in its hybrid form (molecules connected to electrodes acting as wires, diodes, memory elements, field-effect transistors) or in the quantum computation approach. Then, molecular spintronics, using, besides the charge, the spin of the electron. Finally the theme of molecular machines is presented, with the problem of the directionality control of their motion.

This book treats in a unified way electronic properties of molecules (magnetic, electrical, photophysical), culminating with the mastering of electrons: molecular electronics. Chapter 1 reviews basic concepts. Chapter 2 describes the magnetic properties due to localized electrons. This includes phenomena such as spin crossover, exchange interaction from dihydrogen to extended molecular magnetic systems, and magnetic anisotropy with single-molecule magnets. Chapter 3 is devoted to electrical properties due to moving electrons, first considering electron transfer in discrete molecular systems — in particular, in mixed valence compounds — and then, extended molecular solids described by band theory. Special attention is paid to structural distortions (Peierls instability) and interelectronic repulsions in narrow-band systems. Chapter 4 examines the properties of excited electrons responsible for photophysical properties, and dicusses electron transfer in the excited state and its application to photodiodes, organic light-emitting diodes, photovoltaic devices, and water photolysis. Energy transfer is treated in a similar way. Photomagnetism (how a photonic excitation modifies magnetic properties) is also introduced. In Chapter 5, most of the previous knowledge is combined in molecular electronics. The concept of hybrid molecular electronics (molecules connected to metal electrodes) is developed, fed by examples such as molecular wires, diodes, memory elements, field-effect transistors, and the use of magnetic properties for molecular spintronics. The extension to quantum computing is discussed.

This book details the studies of the properties of electronic and vibrational excitations in organic solids. It brings together most of the theory in this field together with many illustrations of experiments. There is a detailed treatment of many topics in uniform style, and the book also contains discussions of new phenomena. In different chapters, the theory of the Frenkel excitons, charge transfer excitons and polaritons, and their contribution to the optical properties of organic solids (bulk, superlattices, surfaces, nanostructures) will be found. The surface electronic excitations, optical biphonons, and Fermiresonance by polaritons are also discussed. The book presents the theory of hybrid Frenkel-Wannier-Mott excitons in nanostructures, the theory of polaritons in organic microcavities including hybrid microcavities, the new concept for LED, the effects of mixing of Frenkel and charge-transfer excitons, and the theory of excitons, and polaritons in one- and two-dimensional crystals. There are plenty of references to current research and to important historical work.