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Scattering Theory For Transport Phenomena
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Book Synopsis Scattering Theory for Transport Phenomena by : Hassan Emamirad
Download or read book Scattering Theory for Transport Phenomena written by Hassan Emamirad and published by Springer Nature. This book was released on 2021-06-27 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Scattering Matrix Approach to Non-stationary Quantum Transport by : Michael V. Moskalets
Download or read book Scattering Matrix Approach to Non-stationary Quantum Transport written by Michael V. Moskalets and published by World Scientific. This book was released on 2012 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to introduce the basic elements of the scattering matrix approach to transport phenomena in dynamical quantum systems of non-interacting electrons. This approach permits a physically clear and transparent description of transport processes in dynamical mesoscopic systems, promising basic elements of solid-state devices for quantum information processing. One of the key effects, the quantum pump effect, is considered in detail. In addition, the theory for the recently implemented new dynamical source ? injecting electrons with time delay much larger than an electron coherence time ? is offered. This theory provides a simple description of quantum circuits with such a single-particle source and shows in an unambiguous way that the tunability inherent to the dynamical systems (in contrast to the stationary ones) leads to a number of unexpected but fundamental effects.
Book Synopsis Scattering Matrix Approach to Non-stationary Quantum Transport by : Michael V. Moskalets
Download or read book Scattering Matrix Approach to Non-stationary Quantum Transport written by Michael V. Moskalets and published by World Scientific. This book was released on 2012 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to introduce the basic elements of the scattering matrix approach to transport phenomena in dynamical quantum systems of non-interacting electrons. This approach admits a physically clear and transparent description of transport processes in dynamical mesoscopic systems promising basic elements of solid-state devices for quantum information processing. One of the key effects, the quantum pump effect, is considered in detail. In addition, the theory for a recently implemented new dynamical source OCo injecting electrons with time delay much larger than the electron coherence time OCo is offered. This theory provides a simple description of quantum circuits with such a single-particle source and shows in an unambiguous way that the tunability inherent to the dynamical systems leads to a number of unexpected but fundamental effects.
Book Synopsis Scattering Theory, Revised Edition by : Peter D. Lax
Download or read book Scattering Theory, Revised Edition written by Peter D. Lax and published by Academic Press. This book was released on 1990-02-22 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition of a classic book, which established scattering theory as an important and fruitful area of research, reflects the wealth of new results discovered in the intervening years. This new, revised edition should continue to inspire researchers to expand the application of the original ideas proposed by the authors.
Book Synopsis Electrons and Phonons by : J.M. Ziman
Download or read book Electrons and Phonons written by J.M. Ziman and published by Oxford University Press. This book was released on 2001-02 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a classic text of its time in condensed matter physics.
Book Synopsis Electron Transport Phenomena in Semiconductors by : B. M. Askerov
Download or read book Electron Transport Phenomena in Semiconductors written by B. M. Askerov and published by World Scientific. This book was released on 1994 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the first systematic and detailed exposition of the linear theory of the stationary electron transport phenomena in semiconductors. Arbitrary isotropic and anisotropic nonparabolic bands as well as p-Ge-type bands are considered. Phonon drag effect are taken account of in an arbitrary nonquantizing magnetic field. Scattering theory is discussed in detail with account taken of the Bloch wave functions effect. Transport phenomena in the quantizing magnetic field are studied as well as the size effects in thin films. Band structures of the semiconductors and semiconductor compounds of interest are also considered.The main part of the book deals with the three important problems: charge carrier statistics in a semiconductor, classical and quantum theory of the electron transport phenomena. All the theoretical results considered as well as the validity conditions are presented in the form which may be directly used to interpret experimental data.
Book Synopsis Principles of Scattering and Transport of Light by : Rémi Carminati
Download or read book Principles of Scattering and Transport of Light written by Rémi Carminati and published by Cambridge University Press. This book was released on 2021-07-29 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic and accessible treatment of light scattering and transport in disordered media from first principles.
Download or read book Scattering Theory written by Peter D. Lax and published by Elsevier. This book was released on 2016-06-03 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering Theory describes classical scattering theory in contrast to quantum mechanical scattering theory. The book discusses the formulation of the scattering theory in terms of the representation theory. The text also explains the relation between the behavior of the solution of the perturbed problem at small distances for large positive times and the analytic continuation of the scattering matrix. To prove the representation theorem, the text cites the methods used by Masani and Robertson in their work dealing with stationary stochastic processes. The book also applies the translation representation theory to a wave equation to obtain a comparison of the asymptotic properties of the free space solution with those of the solution in an exterior domain. The text discusses the solution of the wave equation in an exterior domain by fitting this problem into the abstract framework to get a verification of the hypotheses in some other theorems. The general theory of scattering can be applied to symmetric hyperbolic systems in which all sound speeds are different from zero, as well as to the acoustic equation which has a potential that can cause an energy form to become indefinite. The book is suitable for proponents of analytical mathematics, particle physics, and quantum physics.
Book Synopsis Transport Phenomena by : Henrik Smith
Download or read book Transport Phenomena written by Henrik Smith and published by Oxford University Press, USA. This book was released on 1989 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the concepts used to understand transport phenomena, which pervade all of physics. The focus is on the application of the statistical principles of kinetic theory to non-equilibrium situations, not only in the gas phase but also regarding plasmas, liquids, and solids. These powerful techniques are applied within the framework of the Boltzmann equation to a range of systems. The text is aimed at postgraduates and theoreticians, and assumes familiarity with the basic concepts of statistical mechanics and condensed matter physics. Beginning with the dilute classical gas, the authors then consider electron conduction in normal metals, insulators, superconductors and quantum liquids, and Bose liquids.
Book Synopsis III: Scattering Theory by : Michael Reed
Download or read book III: Scattering Theory written by Michael Reed and published by Elsevier. This book was released on 1979-05-29 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.
Book Synopsis Transport Phenomena in Materials Processing and Manufacturing by :
Download or read book Transport Phenomena in Materials Processing and Manufacturing written by and published by . This book was released on 1994 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Transport Phenomena by : R. Byron Bird
Download or read book Transport Phenomena written by R. Byron Bird and published by John Wiley & Sons. This book was released on 2006-12-11 with total page 935 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transport Phenomena has been revised to include deeper and more extensive coverage of heat transfer, enlarged discussion of dimensional analysis, a new chapter on flow of polymers, systematic discussions of convective momentum,and energy. Topics also include mass transport, momentum transport and energy transport, which are presented at three different scales: molecular, microscopic and macroscopic. If this is your first look at Transport Phenomena you'll quickly learn that its balanced introduction to the subject of transport phenomena is the foundation of its long-standing success.
Book Synopsis Preformed Pair Theory of Quasiparticle Scattering and Transport in the Superconducting and Pseudogap States by : Daniel Steven Wulin
Download or read book Preformed Pair Theory of Quasiparticle Scattering and Transport in the Superconducting and Pseudogap States written by Daniel Steven Wulin and published by . This book was released on 2012 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Central to the field of high temperature superconductivity is understanding the pseudogap phase. This phase is associated with an anomalous normal state excitation gap. In BCS theory which describes classical superconductors, an excitation gap is only found at and below the transition temperature Tc. A central debate in the field is whether this normal state excitation gap in the cuprates is related to superconductivity or whether it reflects a new order parameter. The work in this thesis subscribes to the first of these alternatives, but proceeds in a general way to look at the implications of a small number of assumptions. The challenge is to elucidate the origin of the pseudogap by (i) addressing a large variety of different experiments (including both transport and scattering) and (ii) by studying the interrelated behavior above and below Tc. The challenges that are associated with understanding the pseudogap phase of high-Tc cuprates become particularly evident in the context of transport experiments. Constraints such as gauge invariance and related sum rules must be enforced and these can be seen to aid in the construction of a minimalistic theory, albeit adding in some ways to the complexity. This thesis starts from the point of view that only a small number of physical assumptions are needed in order to construct a theory of scattering and transport in the pseudogap phase and that its implications are of a general nature. Later chapters of the thesis show that the minimalistic theory belongs to a class of preformed pair theories and is, effectively, equivalent to the BCS-BEC crossover theory. Such a theory is constructed and applied to a wide range of scattering and transport phenomena, both in the context of cuprates and cold Fermi gases. The experiments that are analyzed are chosen based on the importance of their results to either elucidating the pseudogap state or raising crucial questions or challenges to theories of the pseudogap phase. A number of key themes emerge regarding the interplay of superconductivity and the pseudogap and how the related energy scales manifest themselves in experiments.
Book Synopsis Scattering Theory in Mathematical Physics by : J.A. Lavita
Download or read book Scattering Theory in Mathematical Physics written by J.A. Lavita and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain lectures given at the N.A.T.O. Advanced Study Institute entitled "Scattering Theory in Mathematics and Physics" held in Denver, Colorado, June 11-29, 1973. We have assembled the main series of lectures and some presented by other participants that seemed naturally to complement them. Unfortunately the size of this volume does not allow for a full account of all the contributions made at the Conference; however, all present were pleased by the number and breadth of those topics covered in the informal afternoon sessions. The purpose of the meeting, as reflected in its title, was to examine the single topic of scattering theory in as many of its manifestations as possible, i.e. as a hub of concepts and techniques from both mathematics and physics. The format of all the topics presented here is mathematical. The physical content embraces classical and quantum mechanical scattering, N-body systems and quantum field theoretical models. Left out are such subjects as the so-called analytic S-matrix theory and phenomeno logical models for high energy scattering. We would like to thank the main lecturers for their excellent presentations and written summaries. They provided a focus for the exceptionally strong interaction among the participants and we hope that some of the coherence achieved is reflected in these published notes. We have made no attempt to unify notation.
Book Synopsis Semiconductor Optics and Transport Phenomena by : Wilfried Schäfer
Download or read book Semiconductor Optics and Transport Phenomena written by Wilfried Schäfer and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well-balanced and up-to-date introduction to the field of semiconductor optics, including transport phenomena in semiconductors. Starting with the theoretical fundamentals of this field the book develops, assuming a basic knowledge of solid-state physics. The application areas of the theory covered include semiconductor lasers, detectors, electro-optic modulators, single-electron transistors, microcavities and double-barrier resonant tunneling diodes. One hundred problems with hints for solution help the readers to deepen their knowledge.
Book Synopsis Principles of Scattering and Transport of Light by : Rémi Carminati
Download or read book Principles of Scattering and Transport of Light written by Rémi Carminati and published by Cambridge University Press. This book was released on 2021-07-29 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Light scattering is one of the most well-studied phenomena in nature. It occupies a central place in optical physics, and plays a key role in multiple fields of science and engineering. This volume presents a comprehensive introduction to the subject. For the first time, the authors bring together in a self-contained and systematic manner, the physical concepts and mathematical tools that are used in the modern theory of light scattering and transport, presenting them in a clear, accessible style. The power of these tools is demonstrated by a framework that links various aspects of the subject: scattering theory to radiative transport, radiative transport to diffusion, and field correlations to the statistics of speckle patterns. For graduate students and researchers in optical physics and optical engineering, this book is an invaluable resource on the interaction of light with complex media and the theory of light scattering in disordered and complex systems.
Book Synopsis A Modern Course in Transport Phenomena by : David C. Venerus
Download or read book A Modern Course in Transport Phenomena written by David C. Venerus and published by Cambridge University Press. This book was released on 2018-03-15 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrating nonequilibrium thermodynamics and kinetic theory, this unique text presents a novel approach to the subject of transport phenomena.
