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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.
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.
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.
This is a classic text of its time in condensed matter physics.
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.
A systematic and accessible treatment of light scattering and transport in disordered media from first principles.
This book provides the basic theoretical background for X-ray and neutron scattering experiments. Since these techniques are increasingly being used by biologists and chemists, as well as physicists, the book is intended to be accessible to a broad spectrum of scientists.
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.
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.
Advances in nanotechnology have allowed physicists and engineers to miniaturize electronic structures to the limit where finite-size related phenomena start to impact their properties. This book discusses such phenomena and models made for their description. The book starts from the semiclassical description of nonequilibrium effects, details the scattering theory used for quantum transport calculations, and explains the main interference effects. It also describes how to treat fluctuations and correlations, how interactions affect transport through small islands, and how superconductivity modifies these effects. The last two chapters describe new emerging fields related with graphene and nanoelectromechanics. The focus of the book is on the phenomena rather than formalism, but the book still explains in detail the main models constructed for these phenomena. It also introduces a number of electronic devices, including the single-electron transistor, the superconducting tunnel junction refrigerator, and the superconducting quantum bit.