Download or read book Quantum Inverse Scattering Method and Correlation Functions written by V. E. Korepin and published by Cambridge University Press. This book was released on 1997-03-06 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.
Download or read book Inverse Schr dinger Scattering in Three Dimensions written by Roger G. Newton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the laws of physics are expressed in the form of differential equations; that is our legacy from Isaac Newton. The customary separation of the laws of nature from contingent boundary or initial conditions, which has become part of our physical intuition, is both based on and expressed in the properties of solutions of differential equations. Within these equations we make a further distinction: that between what in mechanics are called the equations of motion on the one hand and the specific forces and shapes on the other. The latter enter as given functions into the former. In most observations and experiments the "equations of motion," i. e. , the structure of the differential equations, are taken for granted and it is the form and the details of the forces that are under investigation. The method by which we learn what the shapes of objects and the forces between them are when they are too small, too large, too remote, or too inaccessi ble for direct experimentation, is to observe their detectable effects. The question then is how to infer these properties from observational data. For the theoreti cal physicist, the calculation of observable consequences from given differential equations with known or assumed forces and shapes or boundary conditions is the standard task of solving a "direct problem. " Comparison of the results with experiments confronts the theoretical predictions with nature.
Download or read book Inverse Spectral and Scattering Theory written by Hiroshi Isozaki and published by Springer Nature. This book was released on 2020-09-26 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide basic knowledge of the inverse problems arising in various areas in mathematics, physics, engineering, and medical science. These practical problems boil down to the mathematical question in which one tries to recover the operator (coefficients) or the domain (manifolds) from spectral data. The characteristic properties of the operators in question are often reduced to those of Schrödinger operators. We start from the 1-dimensional theory to observe the main features of inverse spectral problems and then proceed to multi-dimensions. The first milestone is the Borg–Levinson theorem in the inverse Dirichlet problem in a bounded domain elucidating basic motivation of the inverse problem as well as the difference between 1-dimension and multi-dimension. The main theme is the inverse scattering, in which the spectral data is Heisenberg’s S-matrix defined through the observation of the asymptotic behavior at infinity of solutions. Significant progress has been made in the past 30 years by using the Faddeev–Green function or the complex geometrical optics solution by Sylvester and Uhlmann, which made it possible to reconstruct the potential from the S-matrix of one fixed energy. One can also prove the equivalence of the knowledge of S-matrix and that of the Dirichlet-to-Neumann map for boundary value problems in bounded domains. We apply this idea also to the Dirac equation, the Maxwell equation, and discrete Schrödinger operators on perturbed lattices. Our final topic is the boundary control method introduced by Belishev and Kurylev, which is for the moment the only systematic method for the reconstruction of the Riemannian metric from the boundary observation, which we apply to the inverse scattering on non-compact manifolds. We stress that this book focuses on the lucid exposition of these problems and mathematical backgrounds by explaining the basic knowledge of functional analysis and spectral theory, omitting the technical details in order to make the book accessible to graduate students as an introduction to partial differential equations (PDEs) and functional analysis.
Download or read book Conference on Inverse Scattering Theory and Application written by J. Bee Bednar and published by SIAM. This book was released on 1983-01-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Direct and Inverse Scattering for the Matrix Schr dinger Equation written by Tuncay Aktosun and published by Springer Nature. This book was released on 2020-05-19 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.
Download or read book Solitons Nonlinear Evolution Equations and Inverse Scattering written by Mark J. Ablowitz and published by Cambridge University Press. This book was released on 1991-12-12 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.
Download or read book Forward and Inverse Scattering for Discrete One dimensional Lossy and Discretized Two dimensional Lossless Media written by Jeffrey Lee Frolik and published by . This book was released on 1995 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Computations on One dimensional Inverse Scattering Problems written by Mark H. Dunn and published by . This book was released on 1983 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Scattering and Applications written by David H. Sattinger and published by American Mathematical Soc.. This book was released on 1991 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents papers given at a Conference on Inverse Scattering on the Line, held in June 1990 at the University of Massachusetts, Amherst. A wide variety of topics in inverse problems were covered: inverse scattering problems on the line; inverse problems in higher dimensions; inverse conductivity problems; and numerical methods. In addition, problems from statistical physics were covered, including monodromy problems, quantum inverse scattering, and the Bethe ansatz. One of the aims of the conference was to bring together researchers in a variety of areas of inverse problems which have seen intensive activity in recent years. scattering
Download or read book Inverse Problems in Scattering written by G.M.L. Gladwell and published by Springer Science & Business Media. This book was released on 1993-10-31 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Problems in Scattering exposes some of the mathematics which has been developed in attempts to solve the one-dimensional inverse scattering problem. Layered media are treated in Chapters 1--6 and quantum mechanical models in Chapters 7--10. Thus, Chapters 2 and 6 show the connections between matrix theory, Schur's lemma in complex analysis, the Levinson--Durbin algorithm, filter theory, moment problems and orthogonal polynomials. The chapters devoted to the simplest inverse scattering problems in quantum mechanics show how the Gel'fand--Levitan and Marchenko equations arose. The introduction to this problem is an excursion through the inverse problem related to a finite difference version of Schrödinger's equation. One of the basic problems in inverse quantum scattering is to determine what conditions must be imposed on the scattering data to ensure that they correspond to a regular potential, which involves Lebesque integrable functions, which are introduced in Chapter 9.
Download or read book Inverse Problems in Scattering and Imaging written by Bertero and published by CRC Press. This book was released on 1992-02-27 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Problems in Scattering and Imaging is a collection of lectures from a NATO Advanced Research Workshop that integrates the expertise of physicists and mathematicians in different areas with a common interest in inverse problems. Covering a range of subjects from new developments on the applied mathematics/mathematical physics side to many areas of application, the book achieves a blend of research, review, and tutorial contributions. It is of interest to researchers in the areas of applied mathematics and mathematical physics as well as those working in areas where inverse problems can be applied.
Download or read book Inverse Problems and Inverse Scattering of Plane Waves written by D.N. Roy and published by Academic Press. This book was released on 2001-10-04 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this text is to present the theory and mathematics of inverse scattering, in a simple way, to the many researchers and professionals who use it in their everyday research. While applications range across a broad spectrum of disciplines, examples in this text will focus primarly, but not exclusively, on acoustics. The text will be especially valuable for those applied workers who would like to delve more deeply into the fundamentally mathematical character of the subject matter.Practitioners in this field comprise applied physicists, engineers, and technologists, whereas the theory is almost entirely in the domain of abstract mathematics. This gulf between the two, if bridged, can only lead to improvement in the level of scholarship in this highly important discipline. This is the book's primary focus.
Download or read book Multiresolution Fast Algorithms for One dimensional Inverse Scattering and Linear Least squares Estimation written by Rajashri R. Joshi and published by . This book was released on 1997 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scattering Two Volume Set written by E. R. Pike and published by Elsevier. This book was released on 2001-10-09 with total page 1831 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering is the collision of two objects that results in a change of trajectory and energy. For example, in particle physics, such as electrons, photons, or neutrons are "scattered off" of a target specimen, resulting in a different energy and direction. In the field of electromagnetism, scattering is the random diffusion of electromagnetic radiation from air masses is an aid in the long-range sending of radio signals over geographic obstacles such as mountains. This type of scattering, applied to the field of acoustics, is the spreading of sound in many directions due to irregularities in the transmission medium. Volume I of Scattering will be devoted to basic theoretical ideas, approximation methods, numerical techniques and mathematical modeling. Volume II will be concerned with basic experimental techniques, technological practices, and comparisons with relevant theoretical work including seismology, medical applications, meteorological phenomena and astronomy. This reference will be used by researchers and graduate students in physics, applied physics, biophysics, chemical physics, medical physics, acoustics, geosciences, optics, mathematics, and engineering. This is the first encyclopedic-range work on the topic of scattering theory in quantum mechanics, elastodynamics, acoustics, and electromagnetics. It serves as a comprehensive interdisciplinary presentation of scattering and inverse scattering theory and applications in a wide range of scientific fields, with an emphasis, and details, up-to-date developments. Scattering also places an emphasis on the problems that are still in active current research. The first interdisciplinary reference source on scattering to gather all world expertise in this technique Covers the major aspects of scattering in a common language, helping to widening the knowledge of researchers across disciplines The list of editors, associate editors and contributors reads like an international Who's Who in the interdisciplinary field of scattering
Download or read book Forward and Inverse Scattering Algorithms Based on Contrast Source Integral Equations written by Peter M. van den Berg and published by John Wiley & Sons. This book was released on 2021-02-15 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to wave-field computational methods based on contrast source type of integral equations Forward and Inverse Scattering Algorithms Based on Contrast Source Integral Equations presents a text that examines wave-field computational methods based on contrast source type of integral equations and the computational implementation in wave-field based imaging methods. Written by a noted expert on the topic, the book provides a guide to efficient methods for calculating wave fields in a known inhomogeneous medium. The author provides a link between the fundamental scattering theory and its discrete counterpart and discusses the forward scattering problem based on the contrast-source integral equations. The book fully describes the calculation of wave fields inside and outside a scattering object with general shape and material property and reviews the inverse scattering problem, in which material properties are resolved from wave-field measurements outside the scattering object. The theoretical approach is the inverse of the forward scattering problem that determines how radiation is scattered, based on the scattering object. This important book: Provides a guide to the effects of scalar waves, acoustic waves and electromagnetic waves Describes computer modeling in 1D, 2D and 3D models Includes an online site for computer codes with adjustable configurations Written for students, researchers, and professionals, Forward and Inverse Scattering Algorithms Based on Contrast Source Integral Equations offers a guide to wave-field computational methods based on contrast source type of integral equations and the computational implementation in wave-field based imaging methods.
Download or read book An Introduction to Electromagnetic Inverse Scattering written by K.I. Hopcraft and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the advent of the comparatively new disciplines of remote sensing and non-destructive evaluation of materials, the topic of inverse scattering has broadened from its origins in elementary particle physics to encompass a diversity of applications. One such area which is of increasing importance in inverse scattering within the context of electromagnetism and this text aims to serve as an introduction to that particular speciality. The subject's development has progressed at the hands of engineers, mathematicians and physicists alike, with an inevitable disparity of emphasis and notation. One of the main objectives of this text is to distill the essence of the subject and to present it in the form of a graduated and coherent development of ideas and techniques. The text provides a physical approach to inverse scattering solutions, emphasizing the applied aspects rather than the mathematical rigour. The authors' teaching and research backgrounds in physics, electrical engineering and applied mathematics enable them to explore and stress the cross disciplinary nature of the subject. This treatment will be of use to anyone embarking on a theoretical or practical study of inverse electromagnetic scattering.
Download or read book Inverse Problems in Quantum Scattering Theory written by Khosrow Chadan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: The normal business of physicists may be schematically thought of as predic ting the motions of particles on the basis of known forces, or the propagation of radiation on the basis of a known constitution of matter. The inverse problem is to conclude what the forces or constitutions are on the basis of the observed motion. A large part of our sensory contact with the world around us depends on an intuitive solution of such an inverse problem: We infer the shape, size, and surface texture of external objects from their scattering and absorption of light as detected by our eyes. When we use scattering experiments to learn the size or shape of particles, or the forces they exert upon each other, the nature of the problem is similar, if more refined. The kinematics, the equations of motion, are usually assumed to be known. It is the forces that are sought, and how they vary from point to point. As with so many other physical ideas, the first one we know of to have touched upon the kind of inverse problem discussed in this book was Lord Rayleigh (1877). In the course of describing the vibrations of strings of variable density he briefly discusses the possibility of inferring the density distribution from the frequencies of vibration. This passage may be regarded as a precursor of the mathematical study of the inverse spectral problem some seventy years later.
