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Dispersion Decay and Scattering Theory

Author : Alexander Komech

Publisher : John Wiley & Sons

Page : 236 pages

File Size : 29,26 MB

Release : 2014-08-21

Category : Mathematics

ISBN : 1118382889

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Book Description

A simplified, yet rigorous treatment of scattering theory methods and their applications Dispersion Decay and Scattering Theory provides thorough, easy-to-understand guidance on the application of scattering theory methods to modern problems in mathematics, quantum physics, and mathematical physics. Introducing spectral methods with applications to dispersion time-decay and scattering theory, this book presents, for the first time, the Agmon-Jensen-Kato spectral theory for the Schr?dinger equation, extending the theory to the Klein-Gordon equation. The dispersion decay plays a crucial role in the modern application to asymptotic stability of solitons of nonlinear Schr?dinger and Klein-Gordon equations. The authors clearly explain the fundamental concepts and formulas of the Schr?dinger operators, discuss the basic properties of the Schr?dinger equation, and offer in-depth coverage of Agmon-Jensen-Kato theory of the dispersion decay in the weighted Sobolev norms. The book also details the application of dispersion decay to scattering and spectral theories, the scattering cross section, and the weighted energy decay for 3D Klein-Gordon and wave equations. Complete streamlined proofs for key areas of the Agmon-Jensen-Kato approach, such as the high-energy decay of the resolvent and the limiting absorption principle are also included. Dispersion Decay and Scattering Theory is a suitable book for courses on scattering theory, partial differential equations, and functional analysis at the graduate level. The book also serves as an excellent resource for researchers, professionals, and academics in the fields of mathematics, mathematical physics, and quantum physics who would like to better understand scattering theory and partial differential equations and gain problem-solving skills in diverse areas, from high-energy physics to wave propagation and hydrodynamics.



Scattering Theory

Author : Alekseĭ Grigorʹevich Sitenko

Publisher : Springer

Page : 316 pages

File Size : 13,39 MB

Release : 1991-01-21

Category : Computers

ISBN :

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Book Description

This book is based on the course in theoretical nuclear physics that has been given by the author for some years at the T. G. Shevchenko Kiev State University. This version is supplemented and revised to include new results obtained after 1971 and 1975 when the first and second editions were published. This text is intended as an introduction to the nonrelativistic theory of po tential scattering. The analysis is based on the scattering matrix concept where the relationship between the scattering matrix and observable physical quantities is considered. The stationary formulation of the scattering problem is presented; particle wave functions in the external field are obtained. A formulation of the optical theorem is given as well as a discussion on time inversion and the reci procity theorem. Analytic properties of the scattering matrix, dispersion relations, and complex moments are analyzed. The dispersion relations for an arbitrary di rection scattering amplitude are proven, and analytic properties of the amplitude in the plane of the complex cosine of the scattering angle are studied in detail.



Lectures in Scattering Theory

Author : A. G. Sitenko

Publisher : Elsevier

Page : 280 pages

File Size : 26,79 MB

Release : 2013-10-22

Category : Science

ISBN : 1483186822

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Book Description

Lectures in Scattering Theory discusses problems in quantum mechanics and the principles of the non-relativistic theory of potential scattering. This book describes in detail the properties of the scattering matrix and its connection with physically observable quantities. This text presents a stationary formulation of the scattering problem and the wave functions of a particle found in an external field. This book also examines the analytic properties of the scattering matrix, dispersion relations, complex angular moments, as well as the separable representation of the scattering amplitude. The text also explains the method of factorizing the potential and the two-particle scattering amplitude, based on the Hilbert-Schmidt theorem for symmetric integral equations. In investigating the problem of scattering in a three-particle system, this book notes that the inapplicability of the Lippman-Schwinger equations can be fixed by appropriately re-arranging the equations. Faddeev equations are the new equations formed after such re-arrangements. This book also cites, as an example, the scattering of a spin-1/2 particle by a spinless particle (such as the scattering of a nucleon by a spinless nucleus). This text is suitable for students and professors dealing with quantum mechanics, theoretical nuclear physics, or other fields of advanced physics.



Three-particle Physics and Dispersion Relation Theory

Author : A. V. Anisovich

Publisher : World Scientific

Page : 342 pages

File Size : 23,71 MB

Release : 2013

Category : Science

ISBN : 9814478814

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Book Description

The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the framework of the dispersion technique. The relativistic dispersion description of amplitudes always takes into account processes connected with the investigated reaction by the unitarity condition or by virtual transitions; in the case of three-particle processes they are, as a rule, those where other many-particle states and resonances are produced. The description of these interconnected reactions and ways of handling them is the main subject of the book.



Collision Theory

Author : Marvin L. Goldberger

Publisher : Courier Corporation

Page : 930 pages

File Size : 20,48 MB

Release : 2004-01-01

Category : Science

ISBN : 0486435075

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Book Description

A systematic description of the basic principles of collision theory, this graduate-level text presents a detailed examination of scattering processes and formal scattering theory, the two-body problem with central forces, scattering by noncentral forces, lifetime and decay of virtual states, an introduction to dispersion theory, and more. 1964 edition.





Dispersion Relations for Hyperon Decay

Author : Edward Richard McCliment

Publisher :

Page : 186 pages

File Size : 43,47 MB

Release : 1962

Category : Dispersion

ISBN :

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Book Description

Conte t : Dispersion relations for yperon dec y The absorptive parts of the amplitude General considerations The rescatt ring t rm The b orn term The integral e uations Results Conclusions Relation with leptonic decays Application of time reversal invariance to decay amplitudes.



Nonlinear Dispersive Partial Differential Equations and Inverse Scattering

Author : Peter D. Miller

Publisher : Springer Nature

Page : 528 pages

File Size : 27,26 MB

Release : 2019-11-14

Category : Mathematics

ISBN : 1493998064

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Book Description

This volume contains lectures and invited papers from the Focus Program on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems and PDE with the goal of advancing the understanding of qualitative and long-time behavior in dispersive nonlinear equations. The program included Percy Deift’s Coxeter lectures, which appear in this volume together with tutorial lectures given during the first week of the focus program. The research papers collected here include new results on the focusing ​nonlinear Schrödinger (NLS) equation, the massive Thirring model, and the Benjamin-Bona-Mahoney equation as dispersive PDE in one space dimension, as well as the Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as dispersive PDE in two space dimensions. The Focus Program coincided with the fiftieth anniversary of the discovery by Gardner, Greene, Kruskal and Miura that the Korteweg-de Vries (KdV) equation could be integrated by exploiting a remarkable connection between KdV and the spectral theory of Schrodinger's equation in one space dimension. This led to the discovery of a number of completely integrable models of dispersive wave propagation, including the cubic NLS equation, and the derivative NLS equation in one space dimension and the Davey-Stewartson, Kadomtsev-Petviashvili and Novikov-Veselov equations in two space dimensions. These models have been extensively studied and, in some cases, the inverse scattering theory has been put on rigorous footing. It has been used as a powerful analytical tool to study global well-posedness and elucidate asymptotic behavior of the solutions, including dispersion, soliton resolution, and semiclassical limits.





Solitons and the Inverse Scattering Transform

Author : Mark J. Ablowitz

Publisher : SIAM

Page : 433 pages

File Size : 18,81 MB

Release : 2006-05-15

Category : Mathematics

ISBN : 089871477X

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Book Description

A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.