Multiple Scattering in Solids


Book Description

A description of general techniques for solving linear partial differential equations by dividing space into regions to which the equations are independently applied and then assembling a global solution from the partial ones. Intended for researchers and graduates involved in calculations of the electronic structure of materials, this will also be of interest to workers in quantum chemistry, electron microscopy, acoustics, optics, and other fields. The book begins with an intuitive approach to scattering theory and then turns to partial waves and a formal development of multiple scattering theory, with applications to the solid state. The authors then present a variational derivation of the formalism and an augmented version of the theory, concluding with a discussion of the relativistic formalism and a discussion of the Poisson equation. Appendices discuss Green's functions, spherical functions, Moller operators and the Lippmann-Schwinger equation, irregular solutions, and singularities in Green's functions.




Multiple Scattering Theory


Book Description

In 1947, it was discovered that multiple scattering theory (MST) can be used to solve the Schröedinger equation for the stationary states of electrons in a solid. Written by experts in the field, J S Faulkner, G Malcolm Stocks and Yang Wang, this book collates the results of numerous studies in the field of MST and provides a comprehensive, systematic approach to it. For many scientists, students and engineers working with multiple scattering programmes, this will be a useful guide to help expand the existing knowledge of MST as well as understanding its future implications.




Multiple Scattering


Book Description

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Fundamentals and Applications of Acoustic Metamaterials


Book Description

In the last few decades, metamaterials have revolutionized the ways in which waves are controlled, and applied in physics and practical situations. The extraordinary properties of metamaterials, such as their locally resonant structure with deep subwavelength band gaps and their ranges of frequency where propagation is impossible, have opened the way to a host of applications that were previously unavailable. Acoustic metamaterials have been able to replace traditional treatments in several sectors, due to their better performance in targeted and tunable frequency ranges with strongly reduced dimensions. This is a training book composed of nine chapters written by experts in the field, giving a broad overview of acoustic metamaterials and their uses. The book is divided into three parts, covering the state-of-the-art, the fundamentals and the real-life applications of acoustic metamaterials.




Multiple Scattering of Light by Particles


Book Description

This monograph on multiple scattering of light by small particles is an ideal resource for science professionals, engineers, and graduate students.




Multiple Light Scattering


Book Description

Multiple Light Scattering: Tables, Formulas, and Applications, Volume 1 serves to give concise and handy information related to multiple scattering theory in such a way that the reader would not have to rely on extensive literature on the subject. The book is divided into two parts. Part I: General Theory covers the basic concepts, terms, and notations related to multiple scattering theory; exponential integrals and related functions; reciprocity and detailed balance; different related methods; and homogenous atmospheres with arbitrary phase function and single-scattering albedo. Part II: Isotropic Scattering discusses related concepts such as solutions using the Milne operator; semi-infinite atmospheres; the H-functions; and finite slabs. The text is recommended for practitioners in optics, atmospheric physics, astronomy, and other fields that need a reference book in the subject of multiple light scattering.




Integral Equation Methods in Scattering Theory


Book Description

This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.




Electron Scattering in Solid Matter


Book Description

Addressing graduate students and researchers, this book gives a very detailed theoretical and computational description of multiple scattering in solid matter. Particular emphasis is placed on solids with reduced dimensions, on full potential approaches and on relativistic treatments. For the first time approaches such as the screened Korringa-Kohn-Rostoker method are reviewed, considering all formal steps such as single-site scattering, structure constants and screening transformations, and also the numerical point of view. Furthermore, a very general approach is presented for solving the Poisson equation, needed within density functional theory in order to achieve self-consistency. Special chapters are devoted to the Coherent Potential Approximation and to the Embedded Cluster Method, used, for example, for describing nanostructured matter in real space. In a final chapter, physical properties related to the (single-particle) Green's function, such as magnetic anisotropies, interlayer exchange coupling, electric and magneto-optical transport and spin-waves, serve to illustrate the usefulness of the methods described.




Variational Methods in Electron-Atom Scattering Theory


Book Description

The investigation of scattering phenomena is a major theme of modern physics. A scattered particle provides a dynamical probe of the target system. The practical problem of interest here is the scattering of a low energy electron by an N-electron atom. It has been difficult in this area of study to achieve theoretical results that are even qualitatively correct, yet quantitative accuracy is often needed as an adjunct to experiment. The present book describes a quantitative theoretical method, or class of methods, that has been applied effectively to this problem. Quantum mechanical theory relevant to the scattering of an electron by an N-electron atom, which may gain or lose energy in the process, is summarized in Chapter 1. The variational theory itself is presented in Chapter 2, both as currently used and in forms that may facilitate future applications. The theory of multichannel resonance and threshold effects, which provide a rich structure to observed electron-atom scattering data, is presented in Chapter 3. Practical details of the computational implementation of the variational theory are given in Chapter 4. Chapters 5 and 6 summarize recent appli cations of the variational theory to problems of experimental interest, with many examples of the successful interpretation of complex structural fea tures observed in scattering experiments, and of the quantitative prediction of details of electron-atom scattering phenomena.




The Mie Theory


Book Description

This book presents in a concise way the Mie theory and its current applications. It begins with an overview of current theories, computational methods, experimental techniques, and applications of optics of small particles. There is also some biographic information on Gustav Mie, who published his famous paper on the colour of Gold colloids in 1908. The Mie solution for the light scattering of small spherical particles set the basis for more advanced scattering theories and today there are many methods to calculate light scattering and absorption for practically any shape and composition of particles. The optics of small particles is of interest in industrial, atmospheric, astronomic and other research. The book covers the latest developments in divers fields in scattering theory such as plasmon resonance, multiple scattering and optical force.