
A classical dynamical system is called isochronous if it features in its phase space an open, fully dimensional sector where all its solutions are periodic in all their degrees of freedom with the same, fixed period. Recently, a simple transformation has been introduced, featuring a real parameter ω and reducing to the identity for ω=0. This transformation is applicable to a quite large class of dynamical systems and it yields ωmodified autonomous systems which are isochronous, with period T = 2π/ω. This justifies the notion that isochronous systems are not rare. In this monograph—which covers work done over the last decade by its author and several collaborators—this technology to manufacture isochronous systems is reviewed. Many examples of such systems are provided, including manybody problems characterized by Newtonian equations of motion in spaces of one or more dimensions, Hamiltonian systems, and also nonlinear evolution equations (PDEs: Partial Differential Equations). This monograph shall be of interest to researchers working on dynamical systems, including integrable and nonintegrable models, with a finite or infinite number of degrees of freedom. It shall also appeal to experimenters and practitioners interested in isochronous phenomena. It might be used as basic or complementary textbook for an undergraduate or graduate course.

This book deals with an important class of manybody systems: those where the interaction potential decays slowly for large interparticle distance. In particular, systems where the decay is slower than the inverse interparticle distance raised to the dimension of the embedding space. Gravitational and Coulomb interactions are the most prominent examples. However, it has become clear that longrange interactions are more common than previously thought. This has stimulated a growing interest in the study of longrange interacting systems, which has led to a much better understanding of the many peculiarities in their behaviour. The seed of all particular features of these systems, both at equilibrium and outofequilibrium, is the lack of additivity. It is now well understood that this does not prevent a statistical mechanics treatment. However, it does require a more indepth study of the thermodynamic limit and of all related theoretical concepts. A satisfactory understanding of properties generally considered as oddities only a couple of decades ago has now been reached: ensemble inequivalence, negative specific heat, negative susceptibility, ergodicity breaking, outofequilibrium quasistationarystates, anomalous diffusion, etc. The first two parts describe the theoretical and computational instruments needed for addressing the study of both equilibrium and dynamical properties of systems subject to longrange forces. The third part of the book is devoted to discussing the applications of such techniques to the most relevant examples of longrange systems. The only prerequisite is a basic course in statistical mechanics.

Many scientists and engineers spend their lives designing, constructing, and running accelerators, yet few universities include a study of them in their curricula. This book is a straightforward introduction used by undergraduates and postgraduate students as well as by professional staff attending the summer schools run by the big accelerator laboratories. Research physicists should read it for important background. It covers the essentials of the subject for accelerator physicists and engineers, and is at the level of the introductory courses provided by the CERN and US Accelerator schools. Its style is to give enough information to understand the subject without an excess of mathematics or theory. The text includes exercises and answers to focus the attention of the reader on the calculations necessary to design a new machine. After a chapter on the history of the accelerators, four chapters cover the dynamics of particle beams as they are guided and focused by the magnets of a synchrotron or storage ring and as they are accelerated by rf cavities. Another two chapters cover linear and nonlinear effects from imperfect fields. There are chapters on synchrotron radiation, colliders, instabilities, and on future acceleration techniques. A chapter describes the applications of the ten thousand or more accelerators in the world ranging from the linear accelerators used for cancer therapy, through those used in industry and in other fields of research, to the giant ‘atom smashers’ at international particle physics laboratories. A final chapter is to stimulate new ideas for future acceleration techniques.

There are three parts to this book which addresses the analysis of musical sounds from the viewpoint of someone at the intersection between physicists, engineers, piano technicians, and musicians. The reader is introduced to a variety of waves and a variety of ways of presenting, visualizing, and analyzing them in the first part. A tutorial on the tools used throughout the book accompanies this introduction. The mathematics behind the tools is left to the appendices. Part 2 is a graphical survey of the classical areas of acoustics that pertain to musical instruments: vibrating strings, bars, membranes, and plates. Part 3 is devoted almost exclusively to the piano. Several two and threedimensional graphical tools are introduced to study the following characteristics of pianos: individual notes and interactions among them, the missing fundamental, inharmonicity, tuning visualization, the different distribution of harmonic power for the various zones of the piano keyboard, and potential uses for quality control. These techniques are also briefly applied to other musical instruments studied in earlier parts of the book. The book includes appendices to cover the mathematics lurking beneath the numerous graphs, and a brief introduction to Matlab® which was used to generate those graphs.

The book present essential theory and practice of the discrete communication systems design, based on the theory of discrete time stochastic processes, and their relation to the existing theory of digital communication systems. Using the notion of stochastic linear time invariant systems, in addition to the orhogonality principles, a general structure of the discrete communication system is constructed in terms of mathematical operators. Based on this structure, the MPSK, MFSK, QAM, OFDM and CDMA systems, using discrete modulation methods, are deduced as special cases. The signals are processed in the time and frequency domain, which requires precise derivatives of their amplitude spectral density functions, correlation functions and related energy and pover spectral densities. The book is selfsufficient, because it uses the unified notation both in the main ten chapters explaining communications systems theory and nine supplementary chapters dealing with the continuous and discrete time signal processing for both the deterministic and stochastic signals. In this context, the indexing of vital signals and finctions makes obvious distinction beteween them. Having in mind the controversial nature of the continuous time white Gaussian noise process, a separate chapter is dedicated to the noise discretisation by introducing notions of noise entropy and trauncated Gaussian density function to avoid limitations in applying the Nyquist criterion. The text of the book is acompained by the solutions of problems for all chapters and a set of deign projects with the defined projects’ topics and tasks and offered solutions.

Aperiodic crystals are crystalline materials with atomic structures that lack translational symmetry. This book gives a comprehensive account of the superspace theory for the description of the crystal structures, and symmetries of incommensurately modulated crystals and composite crystals. It also gives a brief introduction to quasicrystals, thus providing the necessary background for understanding the distinctive features of aperiodic crystals, and it provides the tools for the application of quantitative methods from the realms of crystallography, solid state chemistry, and solid state physics to aperiodic crystal structures. The second half of the book is devoted to crystallographic methods of structural analysis of incommensurate crystals. Thorough accounts are given of the diffraction by incommensurate crystals, the choice of parameters in structure refinements, and the use of superspace in analysing crystal structures. The presentation of methods of structure determination includes direct methods, Fourier methods, Patterson function methods, the maximum entropy method (MEM), and charge flipping. Socalled tplots are introduced as a versatile method for the crystal chemical analysis of incommensurately modulated structures and composite crystals.

This book tells the fascinating story of what truly makes the human body. The body that is with us all our lives is always changing. We are quite literally not who we were years, weeks, or even days ago: our cells die and are replaced by new ones at an astonishing pace. The entire body continually rebuilds itself, time and again, using the food and water that flow through us as fuel and as construction material. What persists over time is not fixed but merely a pattern in flux. We rebuild using elements captured from our surroundings, and are thereby connected to animals and plants around us, to the bacteria within us that help digest them, and to geological processes such as continental drift and volcanism here on the Earth. We are also intimately linked to the Sun’s nuclear furnace and to the solar wind, to collisions with asteroids, and to the cycles of the birth of stars and their deaths in cataclysmic supernovae. Ultimately, we are connected to the beginning of the universe. Our bodies are made of stardust, the burned out embers of stars that were released into the galaxy in massive explosions billions of years ago, mixed with atoms that formed only recently as ultrafast cosmic rays slammed into the Earth’s atmosphere. All of that is not just remote history but part of us now: our human body is inseparable from nature all around us, and is intertwined with the history of the universe.

The rapid development of microfabrication and assembly of nanostructures has opened up many opportunities to miniaturize structures that confine light, producing unusual and extremely interesting optical properties. This book addresses the large variety of optical phenomena taking place in confined solid state structures: microcavities. Microcavities represent a unique laboratory for quantum optics and photonics. They exhibit a number of beautiful effects, including lasing, superfluidity, superradiance, and entanglement. The book is written by four practitioners strongly involved in experiments and theories of microcavities. The introductory chapters present the semiclassical and quantum approaches to description of lightmatter coupling in various solid state systems, including planar cavities, pillars, and spheres; introduce excitonpolaritons, and discuss their statistics and optical properties. The weak and strong excitonlight coupling regimes are discussed further with emphasis on the Purcell effect, lasing, optical parametric oscillations, and BoseEinstein condensation of exciton polaritons. The last chapter discusses polarization and spin properties of cavity polaritons. The book also contains portraits of scientists who gave key contributions to classical electromagnetism, quantum optics, and exciton physics.

This book deals with the structural crystallography of inorganic oxysalts in general. A special emphasis is placed upon structural topology and the methods of its description. The latter include graph theory, nets, 2D and 3D tilings, polyhedra, etc. The structures considered range from minerals to organically templated oxysalts, for all of which this book provides a unified approach to structure interpretation and classification. Most of the structures are analysed and it is shown that they possess the same topological genealogy and relationships, sometimes despite their obvious chemical differences. In order to expand the range of oxysalts considered, the book offers traditional schemes and also alternative approaches such as anion topologis, anioncentered polyhedra and cation arrays. It also looks into the amazingly complex and diverse world of inorganic oxysalts.

Geospace features highly dynamic populations of charged particles with a wide range of energies from thermal to ultrarelativistic. Influenced by magnetic and electric fields in the terrestrial magnetosphere driven by solar wind forcing, changes in the numbers and energies of these particles lead to a variety of space weather phenomena, some of which are detrimental to space infrastructure. This book includes investigations relevant to understanding and forecasting this space environment and the adverse impacts of space weather. Highenergy electrons and ions in the Van Allen radiation belts and the ring current are of particular interest and importance with regard to the operation of spacebased technological infrastructure upon which 21st century civilization increasingly relies. This book presents an overview of the latest discoveries, current scientific understanding, and the latest research on the sources, transport, acceleration and loss of these energetic particle populations, as well as their coupling during geospace magnetic storms.

The Shortt clock, made in the 1920s, is the most famous accurate clock pendulum ever known, having an accuracy of one second per year when kept at nearly constant temperature. Almost all of a pendulum clock's accuracy resides in its pendulum. If the pendulum is accurate, the clock will be accurate. This book describes many scientific aspects of pendulum design and operation in simple terms with experimental data, and little mathematics. It has been written, looking at all the different parts and aspects of the pendulum in great detail, chapter by chapter, reflecting the degree of attention necessary for making a pendulum run accurately. The topics covered include the dimensional stability of different pendulum materials, good and poor suspension spring designs, the design of mechanical joints and clamps, effect of quartz on accuracy, temperature compensation, air drag of different bob shapes and making a sinusoidal electromagnetic drive. One whole chapter is devoted to simple ways of improving the accuracy of ordinary lowcost pendulum clocks, which have a different construction compared to the more expensive designs of substantially wellmade ones. This book will prove invaluable to anyone who wants to know how to make a more accurate pendulum or pendulum clock.

This volume contains lectures delivered at the Les Houches Summer School ‘Integrability: from statistical systems to gauge theory’ held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics.

This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a selfcontained presentation, the text begins with a survey of classical probability theory and with an introduction to the foundations of quantum mechanics, with particular emphasis on its statistical interpretation and on the formulation of generalized measurement theory through quantum operations and effects. The fundamentals of density matrix theory, quantum Markov processes, and completely positive dynamical semigroups are developed. The most important master equations used in quantum optics and condensed matter theory are derived and applied to the study of many examples. Special attention is paid to the Markovian and nonMarkovian theory of environment induced decoherence, its role in the dynamical description of the measurement process, and to the experimental observation of decohering electromagnetic field states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics. The fundamentals of the treatment of nonMarkovian quantum processes in open systems are developed on the basis of various mathematical techniques, such as projection superoperator methods and influence functional techniques. In addition, the book expounds the relativistic theory of quantum measurements and the density matrix theory of relativistic quantum electrodynamics.

This book develops both spectroscopy and radiative transfer for planetary atmospheric composition in a rigorous and quantitative sense for students of atmospheric and/or planetary science. Spectroscopic field measurements including satellite remote sensing have advanced rapidly in recent years, and are being increasingly applied to provide information about planetary atmospheres. Examples include systematic observation of the atmospheric constituents that affect weather, climate, biogeochemical cycles, air quality on Earth, as well as the physics and evolution of planetary atmospheres in our solar system and beyond. Understanding atmospheric spectroscopy and radiative transfer is important throughout the disciplines of atmospheric science and planetary atmospheres to understand principles of remote sensing of atmospheric composition and the effects of atmospheric composition on climate. Atmospheric scientists need an understanding of the details, strength and weaknesses of the spectroscopic measurement sources. Those in remote sensing require an understanding of the information content of the measured spectra that are needed for the design of retrieval algorithms and for developing new instrumentation.

In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound, and Caratheodory's treatment of the second law of thermodynamics. All mathematical derivations are based on clear physical pictures which make even the most involved results — such as the Holevo bound — look comprehensible and transparent. Quantum information is a fascinating topic precisely because it shows that the laws of information processing are actually dependent on the laws of physics. However, it is also very interesting to see that information theory has something to teach us about physics. Both of these directions are discussed throughout the book. Other topics covered in the book are quantum mechanics, measures of quantum entanglement, general conditions of quantum error correction, pure state entanglement and Pauli matrices, pure states and Bell's inequalities, and computational complexity of quantum algorithms.

This book offers a grounding in the field of coherent Xray optics, which in the closing years of the 20th century experienced something of a renaissance with the availability of thirdgeneration synchrotron sources. It begins with a treatment of the fundamentals of Xray diffraction for both coherent and partially coherent radiation, together with the interactions of Xrays with matter. Xray sources, optical elements, and detectors are then discussed, with an emphasis on their role in coherent Xray optics. Various aspects of coherent Xray imaging are then considered, including holography, interferometry, self imaging, phase contrast, and phase retrieval. The foundations of the new field of singular Xray optics are examined, focusing on the topic of Xray 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.

Theoretical physics and foundations of physics have not made much progress in the last few decades. There is no consensus among researchers on how to approach unifying general relativity and quantum field theory (quantum gravity), explaining socalled dark energy and dark matter (cosmology), or the interpretation and implications of quantum mechanics and relativity. In addition, both fields are deeply puzzled about various facets of time including, above all, time as experienced. This book argues that this impasse is the result of the “dynamical universe paradigm,” the idea that reality fundamentally comprises physical entities that evolve in time from some initial state according to dynamical laws. Thus, in the dynamical universe, the initial conditions plus the dynamical laws explain everything else going exclusively forward in time. In cosmology, for example, the initial conditions reside in the Big Bang and the dynamical law is supplied by general relativity. Accordingly, the present state of the universe is explained exclusively by its past. A completely new paradigm (called Relational Blockworld) is offered here whereby the past, present, and future codetermine each other via “adynamical global constraints,” such as the least action principle. Accordingly, the future is just as important for explaining the present as the past is. Most of the book is devoted to showing how Relational Blockworld resolves many of the current conundrums of both theoretical physics and foundations of physics, including the mystery of time as experienced and how that experience relates to the block universe.

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 uptodate 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 lightmatter 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.

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 condensedmatter and highenergy physics. The book comprises twelve chapters corresponding to lectures delivered at the school.

In 1969, Princeton physicist Gerard O'Neill began looking outward to space colonies as the new frontier for humanity's expansion. A decade later, Eric Drexler turned his attention to the molecular world as the place where society's future needs could be met using selfreplicating nanoscale machines. These modern utopians predicted that their technologies could transform society as humans mastered the ability to create new worlds, undertook atomicscale engineering, and, if truly successful, overcame their own biological limits. This book tells the story of how these scientists and the communities they fostered imagined, designed, and popularized speculative technologies such as space colonies and nanotechnologies. The book traces how these visioneers blended countercultural ideals with hard science, entrepreneurship, libertarianism, and unbridled optimism about the future. It shows how they built networks that communicated their ideas to writers, politicians, and corporate leaders. But the visioneers were not immune to failure. O'Neill and Drexler faced difficulty funding their work and overcoming colleagues' skepticism, and saw their ideas coopted and transformed. Ultimately, both men struggled to overcome stigma and ostracism as they tried to unshackle their visioneering from pejorative labels like “fringe” and “pseudoscience”? This book provides a balanced look at the successes and pitfalls they encountered. It exposes the dangers of promotion that can plague exploratory science. But above all, it highlights the importance of radical new ideas that inspire us to support cuttingedge research into tomorrow's technologies.