A Brief Introduction to Dispersion Relations
A Brief Introduction to Dispersion Relations

Author: José Antonio Oller

Publisher: Springer

Published: 2019-03-22

Total Pages: 142

ISBN-13: 3030135829

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This text offers a brief introduction to the dispersion relations as an approach to calculate S-matrix elements, a formalism that allows one to take advantage of the analytical structure of scattering amplitudes following the basic principles of unitarity and causality. First, the case of two-body scattering is considered and then its contribution to other processes through final-state interactions is discussed. For two-body scattering amplitudes, the general expression for a partial-wave amplitude is derived in the approximation where the crossed channel dynamics is neglected. This is taken as the starting point for many interesting nonperturbative applications, both in the light and heavy quark sector. Subsequently crossed channel dynamics is introduced within the equations for calculating the partial-wave amplitudes. Some applications based on methods that treat crossed-channel dynamics perturbatively are discussed too. The last part of this introductory treatment is dedicated to the further impact of scattering amplitudes on a variety of processes through final-state interactions. Several possible approaches are discussed such as the Muskhelishvili-Omnes dispersive integral equations and other closed formulae. These different formalisms are then applied in particular to the study of resonances presenting a number of challenging properties. The book ends with a chapter illustrating the use of dispersion relations in the nuclear medium for the evaluation of the energy density in nuclear matter.

Numerical Solution of the Dispersion Relations for a Hot Magnetoplasma with Collisions
Numerical Solution of the Dispersion Relations for a Hot Magnetoplasma with Collisions

Author: Robert J. Papa

Publisher:

Published: 1972

Total Pages: 48

ISBN-13:

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Detailed numerical studies have been made on the dispersion relations for electromagnetic waves propagating in partially ionized gases immersed in a dc magnetic field. Accurate values of the attenuation constant and phase shift are needed in the design of radio communications systems where waves must propagate through an ionized gas (such as in reentry communications systems), in the design of radar jamming devices used during missile reentry, and in the analytical study of ionospheric propagation phenomena. The numerical solution of the dispersion relations enable the effects of collisionless wave damping, velocity-dependent electron-neutral collisions, and Coulomb encounters to be studied. The attenuation and phase shift of waves propagating through a plasma are dependent upon the signal frequency, plasma temperature, plasma density, degree of ionization, and cross sections for electron scattering. Graphs are presented which enable attenuation constants and phase shifts to be readily evaluated for a very wide range of possible plasma conditions. (Author).

Dispersion Relations in Heavily-Doped Nanostructures
Dispersion Relations in Heavily-Doped Nanostructures

Author: Kamakhya Prasad Ghatak

Publisher: Springer

Published: 2015-10-26

Total Pages: 664

ISBN-13: 3319210009

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This book presents the dispersion relation in heavily doped nano-structures. The materials considered are III-V, II-VI, IV-VI, GaP, Ge, Platinum Antimonide, stressed, GaSb, Te, II-V, HgTe/CdTe superlattices and Bismuth Telluride semiconductors. The dispersion relation is discussed under magnetic quantization and on the basis of carrier energy spectra. The influences of magnetic field, magneto inversion, and magneto nipi structures on nano-structures is analyzed. The band structure of optoelectronic materials changes with photo-excitation in a fundamental way according to newly formulated electron dispersion laws. They control the quantum effect in optoelectronic devices in the presence of light. The measurement of band gaps in optoelectronic materials in the presence of external photo-excitation is displayed. The influences of magnetic quantization, crossed electric and quantizing fields, intense electric fields on the on the dispersion relation in heavily doped semiconductors and super-lattices are also discussed. This book contains 200 open research problems which form the integral part of the text and are useful for graduate students and researchers. The book is written for post graduate students, researchers and engineers.

Contemporary Art, Systems and the Aesthetics of Dispersion
Contemporary Art, Systems and the Aesthetics of Dispersion

Author: Francis Halsall

Publisher: Taylor & Francis

Published: 2023-05-16

Total Pages: 107

ISBN-13: 1000902730

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Using five case studies of contemporary art, this book uses ideas of systems and dispersion to understand identity and experience in late capitalism. This book considers five artists who exemplify contemporary art practice: Seth Price; Liam Gillick; Martin Creed; Hito Steyerl; and Theaster Gates. Given the diversity of materials used in art today, once-traditional artistic mediums and practices have become obsolete in describing what artists do today. Francis Halsall argues that, in the face of this obsolescence, the ideas of system and dispersion become very useful in understanding contemporary art. That is, practitioners now can be seen to be using whatever systems of distribution and display are available to them as their creative mediums. The two central arguments are first that any understanding of what art is will always be underwritten by a related view of what a human being is; and second that these both have a particular character in late capitalism or, as is named here, the Age of Dispersion. The book will be of interest to scholars and students working in art history, contemporary art, studio art, and theories of systems and networks.

Metallography of Dispersion Hardened Alloys and Its Relation to Creep Resistance
Metallography of Dispersion Hardened Alloys and Its Relation to Creep Resistance

Author: Ian Sydney Brammar

Publisher:

Published: 1963

Total Pages: 78

ISBN-13:

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Techniques are described for the preparation of thin foils of sintered alumina-aluminum alloys (S.A.P.) for study in the electron microscope. The morphology of the dispersed phase and its relation to the microstructure have been examined. The results are discussed with reference to the current theories of creep of S.A.P. (R).

Three-particle Physics and Dispersion Relation Theory
Three-particle Physics and Dispersion Relation Theory

Author: A. V. Anisovich

Publisher: World Scientific

Published: 2013

Total Pages: 342

ISBN-13: 9814478814

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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.

Dispersion, Complex Analysis and Optical Spectroscopy
Dispersion, Complex Analysis and Optical Spectroscopy

Author: Kai-Erik Peiponen

Publisher: Springer Science & Business Media

Published: 1998-11-30

Total Pages: 152

ISBN-13: 9783540645221

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This book is devoted to dispersion theory in linear and nonlinear optics. Dispersion relations and methods of analysis in optical spectroscopy are derived with the aid of complex analysis. The book introduces the mathematical basis and derivations of various dispersion relations that are used in optical spectroscopy. In addition, it presents the dispersion theory of the nonlinear optical processes which are essential in modern optical spectroscopy. The book includes new methods such as the maximum entropy model for wavelength-dependent spectra analysis.