Scattering theory for transport phenomena / Hassan Emamirad.
Emamirad, Hassan, author.
2021
QC794.6.S3 E43 2021
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Title Scattering theory for transport phenomena / Hassan Emamirad.
Author Emamirad, Hassan, author.
ISBN 9789811623738 (electronic bk.)
9811623732 (electronic bk.)
9789811623721
9811623724
DOI https://doi.org/10.1007/978-981-16-2373-8
Published Singapore : Springer, [2021]
Copyright ©2021
Language English
Description 1 online resource (xxi, 179 pages) : illustrations.
Item Number 10.1007/978-981-16-2373-8 doi
Call Number QC794.6.S3 E43 2021
Dewey Decimal Classification 539.7/58
Summary "The scattering theory for transport phenomena was initiated by P. Lax and R. Phillips in 1967. Since then, great progress has been made in the field and the work has been ongoing for more than half a century. This book shows part of that progress. The book is divided into 7 chapters, the first of which deals with preliminaries of the theory of semigroups and C*-algebra, different types of semigroups, Schatten-von Neuman classes of operators, and facts about ultraweak operator topology, with examples using wavelet theory. Chapter 2 goes into abstract scattering theory in a general Banach space. The wave and scattering operators and their basic properties are defined. Some abstract methods such as smooth perturbation and the limiting absorption principle are also presented. Chapter 3 is devoted to the transport or linearized Boltzmann equation, and in Chapter 4 the Lax and Phillips formalism is introduced in scattering theory for the transport equation. In their seminal book, Lax and Phillips introduced the incoming and outgoing subspaces, which verify their representation theorem for a dissipative hyperbolic system initially and also matches for the transport problem. By means of these subspaces, the Lax and Phillips semigroup is defined and it is proved that this semigroup is eventually compact, hence hyperbolic. Balanced equations give rise to two transport equations, one of which can satisfy an advection equation and one of which will be nonautonomous. For generating, the Howland semigroup and Howland's formalism must be used, as shown in Chapter 5. Chapter 6 is the highlight of the book, in which it is explained how the scattering operator for the transport problem by using the albedo operator can lead to recovery of the functionality of computerized tomography in medical science. The final chapter introduces the Wigner function, which connects the Schrödinger equation to statistical physics and the Husimi distribution function. Here, the relationship between the Wigner function and the quantum dynamical semigroup (QDS) can be seen"--Print version, page 4 of cover.
Bibliography, etc. Note Includes bibliographical references (pages 171-175) and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed July 1, 2021).
Series Mathematical physics studies. 0921-3767
Available in Other Form Scattering theory for transport phenomena.
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All Resources
Semigroups of linear operators
Wave and scattering operators
Existence of the wave operators for the transport equation
The Lax and Phillips formalism for the transport problems
Scattering theory for a charged particle transport problem
Relationship between the Albedo and scattering operators
Scattering theory for quantum transport equation.

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