This book explores the role of fractional calculus and associated partial differential equations in modeling multiscale phenomena and overlapping macroscopic & microscopic scales, offering an innovative and powerful tool for modeling complex systems. While integer order PDEs have a long-standing history, the novel setting of fractional PDEs opens up new possibilities for the simulation of multi-physics phenomena. The book examines a range of releavant examples that showcase the seamless transition from wave propagation to diffusion or from local to non-local dynamics in both continuum and discrete systems. These systems have been argued as being particularly relevant in contexts such as nonlinear optics, lattice nonlinear dynamical systems, and dispersive nonlinear wave phenomena, where the exploration of the potential fractionality has emerged as a highly active topic for current studies.

The subject of antenna design, primarily a discipline within electrical en- neering, is devoted to the manipulation of structural elements of and/or the electrical currents present on a physical object capable of supporting such a current. Almost as soon as one begins to look at the subject, it becomes clear that there are interesting mathematical problems which need to be addressed, in the ?rst instance, simply for the accurate modelling of the electromagnetic ?elds produced by an antenna. The description of the electromagnetic ?elds depends on the physical structure and the background environment in which thedeviceistooperate.

The concept of squeezing is intimately related to the idea of vacuum fluctu­ ations, once thought to place an absolute limit to the accuracy of measure­ ment. However, vacuum fluctuations are not unchangeable. By recognizing that these quantum fluctuations always occur in two complementary observ­ ables, physicists have been able to make an intriguing trade-off. Reduced fluctuations in one variable can be realized - at the expense of increased fluctuations in another, according to Heisenberg. This Heisenberg 'horse-trade' - originally predicted by theorists - was first accomplished experimentally by R. Slusher in 1985. Since then, the var­ ious techniques and applications of quantum squeezing have metamorphosed into a central tool in the wider field of quantum information. This book is a summary of the main ideas, methods and applications of quantum squeezing, written by those responsible for some of the chief developments in the field. The book is divided into three parts, to recognize that there are three areas in this research. These are the fundamental physics of quantum fluc­ tuations, the techniques of generating squeezed radiation, and the potential applications. Part I of the book, giving the fundamentals, is arranged as follows. • Chapter 1 introduces the basic ideas about what squeezing of quantum fluctuations is from the quantized free-field perspective. This chapter es­ tablishes the definitions and notations used throughout. • Chapter 2 explains how to quantize radiation in a dielectric, which is the basic technique that is used to make squeezed radiation.

Written in a clear pedagogic style, this book deals with the application of density matrix theory to atomic and molecular physics. The aim is to precisely characterize sates by a vector and to construct general formulas and proofs of general theorems. The basic concepts and quantum mechanical fundamentals (reduced density matrices, entanglement, quantum correlations) are discussed in a comprehensive way. The discussion leads up to applications like coherence and orientation effects in atoms and molecules, decoherence and relaxation processes. This third edition has been updated and extended throughout and contains a completely new chapter exploring nonseparability and entanglement in two-particle spin-1/2 systems. The text discusses recent studies in atomic and molecular reactions. A new chapter explores nonseparability and entanglement in two-particle spin-1/2 systems.

With its many beautiful colour pictures, this book gives fascinating insights into the unusual forms and behaviour of matter under extremely high pressures and temperatures. These extreme states are generated, among other things, by strong shock, detonation and electric explosion waves, dense laser beams, electron and ion beams, hypersonic entry of spacecraft into dense atmospheres of planets, and in many other situations characterized by extremely high pressures and temperatures.

This thesis covers the few-cycle laser-driven acceleration of electrons in a laser-generated plasma. This process, known as laser wakefield acceleration (LWFA), relies on strongly driven plasma waves for the generation of accelerating gradients in the vicinity of several 100 GV/m, a value four orders of magnitude larger than that attainable by conventional accelerators. This thesis demonstrates that laser pulses with an ultrashort duration of 8 fs and a peak power of 6 TW allow the production of electron energies up to 50 MeV via LWFA. The special properties of laser accelerated electron pulses, namely the ultrashort pulse duration, the high brilliance, and the high charge density, open up new possibilities in many applications of these electron beams.

The content of this book describes in detail the results of the present measurements of the partial and total doubly differential cross sections for the multiple-ionization of rare gas atoms by electron impact. These measurements show, beside other trends, the role of Auger transitions in the production of multiply ionized atoms in the region where the incident electron energy is sufficient to produce inner shell ionization. Other processes like Coster-Kronig transitions and shake off also contribute towards increasing the charge of the ions. The incident electron having energy of 6 keV, for example, in a collision with xenon atom can remove up to nine electrons! (*) X-ray-ion coincidence spectroscopy of the electron xenon atom collisions is also described.

The PUILS series delivers up-to-date reviews of progress in Ultrafast Intense Laser Science, a newly emerging interdisciplinary research field spanning atomic and molecular physics, molecular science, and optical science, which has been stimulated by the recent developments in ultrafast laser technologies. Each volume compiles peer-reviewed articles authored by researchers at the forefront of each their own subfields of UILS. Every chapter opens with an overview of the topics to be discussed, so that researchers unfamiliar to the subfield, as well as graduate students, can grasp the importance and attractions of the research topic at hand; these are followed by reports of cutting-edge discoveries. This sixth volume covers a broad range of topics from this interdisciplinary research field, focusing on responses of molecules to ultrashort intense laser pulses, generation and characterization of attosecond pulses and high-order harmonics, and filamentation and laser-plasma interaction.

This book intended as a guide for scientists and students who have just discovered the field as a new and attractive area of research, and for scientists who have worked in another field and want to join now the subject of laser plasmas. In the first chapter the plasma dynamics is described phenomenologically by a two fluid model and similarity relations from dimensional analysis. Chapter 2 is devoted to plasma optics and collisional absorption in the dielectric and ballistic model. Linear resonance absorption at the plasma frequency and its mild nonlinearities as well as the self-quenching of high amplitude electron plasma waves by wave breaking are discussed in Chapter 3. With increasing laser intensity the plasma dynamics is dominated by radiation pressure, at resonance producing all kinds of parametric instabilities and out of resonance leading to density steps, self-focusing and filamentation, described in Chapters 4 and 5. A self-contained treatment of field ionization of atoms and related phenomena are found in Chapter 6. The extension of laser interaction to the relativistic electron acceleration as well as the physics of collisionless absorption are the subject of Chapter 7. Throughout the book the main emphasis is on the various basic phenomena and on their underlying physics.

Simulation of materials at the atomistic level is an important tool in studying microscopic structures and processes. The atomic interactions necessary for the simulations are correctly described by Quantum Mechanics, but the size of systems and the length of processes that can be modelled are still limited. The framework of Gaussian Approximation Potentials that is developed in this thesis allows us to generate interatomic potentials automatically, based on quantum mechanical data. The resulting potentials offer several orders of magnitude faster computations, while maintaining quantum mechanical accuracy. The method has already been successfully applied for semiconductors and metals.

This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries.

Magnetohydrodynamics, or MHD, is a theoretical way of describing the statics and dynamics of electrically conducting uids. The most important of these uids occurring in both nature and the laboratory are ionized gases, called plasmas. These have the simultaneous properties of conducting electricity and being electrically charge neutral on almost all length scales. The study of these gases is called plasma physics. MHD is the poor cousin of plasma physics. It is the simplest theory of plasma dynamics. In most introductory courses, it is usually afforded a short chapter or lecture at most: Alfven ´ waves, the kink mode, and that is it. (Now, on to Landau damping!) In advanced plasma courses, such as those dealing with waves or kinetic theory, it is given an even more cursory treatment, a brief mention on the way to things more profound and interesting. (It is just MHD! Besides, real plasma phy- cists do kinetic theory!) Nonetheless, MHD is an indispensable tool in all applications of plasma physics.

This book results from recent studies aimed at answering questions raised by astrophycists who use values of transport coefficients that are old and often unsatisfactory. The few books dealing with the rigorous kinetic theory of a ionized plasma are based on the so called Landau (Fokker-Planck) equation and they seldom relate the microscopic results with their macroscopic counterpart provided by classical non-equilibrium thermodynamics. In this book both issues are thoroughly covered. Starting from the full Boltzmann equation for inert dilute plasmas and using the Hilbert-Chapman-Enskog method to solve the first two approximations in Knudsen´s parameter, we construct all the transport properties of the system within the framework of linear irreversible thermodynamics. This includes a systematic study of all possible cross effects (which, except for a few cases, were never treated in the literature) as well as the famous H-theorem. The equations of magneto-hydrodynamics for dilute plasmas, including the rather surprising results obtained for the viscomagnetic effects, may be now fully assessed. This book will be of immediate interest to the plasma physics community, as well as to astrophysicists. It is also likely to make an impact in the field of cold plasmas, involving laser cooled Rydberg atoms.

Intended for nonspecialists with some knowledge of physics or engineering, The Quantum Beat covers a wide range of salient topics relevant to atomic clocks, treated in a broad intuitive manner with a minimum of mathematical formalism. Detailed descriptions are given of the design principles of the rubidium, cesium, hydrogen maser, and mercury ion standards; the revolutionary changes that the advent of the laser has made possible, such as laser cooling, optical pumping, the formation of "optical molasses," and the cesium "fountain" standard; and the time-based global navigation systems, Loran-C and the Global Positioning System. Also included are topics that bear on the precision and absolute accuracy of standards, such as noise, resonance line shape, the relativistic Doppler effect as well as more general relativistic notions of time relevant to synchronization of remote clocks, and time reversal symmetry.

Electron magnetic resonance in the time domain has been greatly facilitated by the introduction of novel resonance structures and better computational tools, such as the increasingly widespread use of density-matrix formalism. This second v- ume in our series, devoted both to instrumentation and computation, addresses - plications and advances in the analysis of spin relaxation time measurements. Chapters 1 deals with the important problem of measuring spin relaxation times over a broad temporal range.