This book studies the widely used theoretical models for calculating properties of hot dense matter. Calculations are illustrated by plots and tables, and they are compared with experimental results. The purpose is to help understanding of atomic physics in hot plasma and to aid in developing efficient and robust computer codes for calculating opacity and equations of state for arbitrary material in a wide range of temperatures and densities.
This two-volume set can be naturally divided into two semester courses, and contains a full modern graduate course in quantum physics. The idea is to teach graduate students how to practically use quantum physics and theory, presenting the fundamental knowledge, and gradually moving on to applications, including atomic, nuclear and solid state physics, as well as modern subfields, such as quantum chaos and quantum entanglement. The book starts with basic quantum problems, which do not require full quantum formalism but allow the student to gain the necessary experience and elements of quantum thinking. Only then does the fundamental Schrodinger equation appear. The author has included topics that are not usually covered in standard textbooks and has written the book in such a way that every topic contains varying layers of difficulty, so that the instructor can decide where to stop. Although supplementary sources are not required, "Further reading" is given for each chapter, including references to scientific journals and publications, and a glossary is also provided. Problems and solutions are integrated throughout the text.
This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.
This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces. The applications of spinors in field theory and relativistic mechanics of continuous media are considered. The main mathematical part is connected with the study of invariant algebraic and geometric relations between spinors and tensors. The theory of spinors and the methods of the tensor representation of spinors and spinor equations are thoroughly expounded in four-dimensional and three-dimensional spaces. Very useful and important relations are derived that express the derivatives of the spinor fields in terms of the derivatives of various tensor fields. The problems associated with an invariant description of spinors as objects that do not depend on the choice of a coordinate system are addressed in detail. As an application, the author considers an invariant tensor formulation of certain classes of differential spinor equations containing, in particular, the most important spinor equations of field theory and quantum mechanics. Exact solutions of the Einstein–Dirac equations, nonlinear Heisenberg’s spinor equations, and equations for relativistic spin fluids are given. The book presents a large body of factual material and is suited for use as a handbook. It is intended for specialists in theoretical physics, as well as for students and post-graduate students of physical and mathematical specialties.
The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
Electronic structure and physical properties of strongly correlated materials containing elements with partially filled 3d, 4d, 4f and 5f electronic shells is analyzed by Dynamical Mean-Field Theory (DMFT). DMFT is the most universal and effective tool used for the theoretical investigation of electronic states with strong correlation effects. In the present book the basics of the method are given and its application to various material classes is shown. The book is aimed at a broad readership: theoretical physicists and experimentalists studying strongly correlated systems. It also serves as a handbook for students and all those who want to be acquainted with fast developing filed of condensed matter physics.
This book explains modern and interesting physics in heavy-fermion (HF) compounds to graduate students and researchers in condensed matter physics. It presents a theory of heavy-fermion (HF) compounds such as HF metals, quantum spin liquids, quasicrystals and two-dimensional Fermi systems. The basic low-temperature properties and the scaling behavior of the compounds are described within the framework of the theory of fermion condensation quantum phase transition (FCQPT). Upon reading the book, the reader finds that HF compounds with quite different microscopic nature exhibit the same non-Fermi liquid behavior, while the data collected on very different HF systems have a universal scaling behavior, and these compounds are unexpectedly uniform despite their diversity. For the reader's convenience, the analysis of compounds is carried out in the context of salient experimental results. The numerous calculations of the non-Fermi liquid behavior, thermodynamic, relaxation and transport properties, being in good agreement with experimental facts, offer the reader solid grounds to learn the theory's applications. Finally, the reader will learn that FCQPT develops unexpectedly simple, yet completely good description of HF compounds.
The aim of this book is the pedagogical exploration of the basic principles of quantum-statistical thermodynamics as applied to various states of matter – ranging from rare gases to astrophysical matter with high-energy density. The reader will learn in this work that thermodynamics and quantum statistics are still the concepts on which even the most advanced research is operating - despite of a flood of modern concepts, classical entities like temperature, pressure, energy and entropy are shown to remain fundamental. The physics of gases, plasmas and high-energy density matter is still a growing field and even though solids and liquids dominate our daily life, more than 99 percent of the visible Universe is in the state of gases and plasmas and the overwhelming part of matter exists at extreme conditions connected with very large energy densities, such as in the interior of stars. This text, combining material from lectures and advanced seminars given by the authors over many decades, is a must-have introduction and reference for both newcomers and seasoned researchers alike.
With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies
The purpose of this book is to describe the theory of Hankel operators, one of the most important classes of operators on spaces of analytic func tions. Hankel operators can be defined as operators having infinite Hankel matrices (i. e. , matrices with entries depending only on the sum of the co ordinates) with respect to some orthonormal basis. Finite matrices with this property were introduced by Hankel, who found interesting algebraic properties of their determinants. One of the first results on infinite Han kel matrices was obtained by Kronecker, who characterized Hankel matri ces of finite rank as those whose entries are Taylor coefficients of rational functions. Since then Hankel operators (or matrices) have found numerous applications in classical problems of analysis, such as moment problems, orthogonal polynomials, etc. Hankel operators admit various useful realizations, such as operators on spaces of analytic functions, integral operators on function spaces on (0,00), operators on sequence spaces. In 1957 Nehari described the bounded Hankel operators on the sequence space £2. This description turned out to be very important and started the contemporary period of the study of Hankel operators. We begin the book with introductory Chapter 1, which defines Hankel operators and presents their basic properties. We consider different realiza tions of Hankel operators and important connections of Hankel operators with the spaces BMa and V MO, Sz. -Nagy-Foais functional model, re producing kernels of the Hardy class H2, moment problems, and Carleson imbedding operators.
Chemistry is the science of substances (today we would say molecules) and their transformations. Central to this science is the complexity of shape and function of its typical representatives. There lies, no longer dependent on its vitalistic antecedents, the rich realm of molecular possibility called organic chemistry. In this century we have learned how to determine the three-dimensional structure of molecules. Now chemistry as whole, and organic chemistry in particular, is poised to move to the exploration of its dynamic dimension, the busy business of transformations or reactions. Oh, it has been done all along, for what else is synthesis? What I mean is that the theoretical framework accom panying organic chemistry, long and fruitfully laboring on a quantum chemical understanding of structure, is now making the first tentative motions toward building an organic theory of reactivity. The Minkin, Simkin, Minyaev book takes us in that direction. It incorporates the lessons of frontier orbital theory and of Hartree-Fock SCF calculations; what chemical physicists have learned about trajectory calculations of selected reactions, and a simplified treatment of all-important solvent effects. It is written by professional, accomplished organic chemists for other organic chemists; it is consistently even-toned in its presentation of contending approaches. And very much up to date. That this contemporary work should emerge from a regional university in a country in which science has been highly centralized and organic chemistry not very modern, invites reflection.
With its many beautiful colour pictures, this book gives fascinating insights into the unusual forms and behaviour of matter under extremely high pressures and temperatures. These extreme states are generated, among other things, by strong shock, detonation and electric explosion waves, dense laser beams, electron and ion beams, hypersonic entry of spacecraft into dense atmospheres of planets and in many other situations characterized by extremely high pressures and temperatures. Written by one of the world's foremost experts on the topic, this book will inform and fascinate all scientists dealing with materials properties and physics and also serve as an excellent introduction to plasma-, shock-wave and high-energy-density physics for students and newcomers seeking an overview. This second edition is thoroughly revised and expanded, in particular with new material on high energy-density physics, nuclear explosions and other nuclear transformation processes.
This advanced textbook presents an extensive and diverse study of low-energy nuclear physics considering the nucleus as a quantum system of strongly interacting constituents. The contents guide students from the basic facts and ideas to more modern topics including important developments over the last 20 years, resulting in a comprehensive collection of major modern-day nuclear models otherwise unavailable in the current literature. The book emphasizes the common features of the nucleus and other many-body mesoscopic systems currently in the center of interest in physics. The authors have also included full problem sets that can be selected by lecturers and adjusted to specific interests for more advanced students, with many chapters containing links to freely available computer code. As a result, readers are equipped for scientific work in mesoscopic physics.
This book describes recent theoretical and experimental developments in the study of static and dynamic properties of atomic nuclei, many-body systems of strongly interacting neutrons and protons. The theoretical approach is based on the concept of the mean field, describing the motion of a nucleon in terms of a self-consistent single-particle potential well which approximates the interactions of a nucleon with all the other nucleons. The theoretical approaches also go beyond the mean-field approximation by including the effects of two-body collisions.The self-consistent mean-field approximation is derived using the effective nucleon-nucleon Skyrme-type interaction. The many-body problem is described next in terms of the Wigner phase space of the one-body density, which provides a basis for semi-classical approximations and leads to kinetic equations. Results of static properties of nuclei and properties associated with small amplitude dynamics are also presented. Relaxation processes, due to nucleon-nucleon collisions, are discussed next, followed by instability and large amplitude motion of excited nuclei. Lastly, the book ends with the dynamics of hot nuclei. The concepts and methods developed in this book can be used for describing properties of other many-body systems.
The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.
This book presents an account of the exact solution of the Hubbard model in one dimension. The early chapters develop a self-contained introduction to Bethe's ansatz and its application to the one-dimensional Hubbard model. The later chapters address more advanced topics.
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.
The book is devoted to the description of the fundamentals in the area of magnetic resonance. The book covers two domains: radiospectroscopy and quantum radioelectronics. Radiospectroscopy comprises nuclear magnetic resonance , electron paramagnetic resonance, nuclear quadrupolar resonance, and some other phenomena. The radiospectroscopic methods are widely used for obtaining the information on internal (nano, micro and macro) structure of objects. Quantum radioelectronics, which was developed on the basis of radiospectroscopic methods, deals with processes in quantum amplifiers, generators and magnetometers. We do not know analogues of the book presented. The book implies a few levels of the general consideration of phenomena, that can be useful for different groups of readers (students, PhD students, scientists from other scientific branches: physics, chemistry, physical chemistry, biochemistry, biology and medicine).
Multiphoton ionization of atoms in intense laser-light fields is gaining ground as a spectroscopic diagnostic tool. In this volume, Delone and Krainov present their and others' theoretical description of the process occurring in atoms under conditions of multi-photon impacts, in particular, the shift, broadening, and mixing of electronic states which complicate the interpretation of spectra. The topics of individual chapters include tunneling ionization, above-threshold ionization, ionization of multiply charged ions, resonance-enhenced ionization, super-intense radiation fields, and properties of Rydberg states in strong fields.
This thesis reports results of precision mass spectrometry of exotic nuclides as a means of elucidating their structure. The work was performed with the ISOLTRAP spectrometer at CERN’s ISOLDE facility. The author furthermore offers an overview of existing techniques used in Penning-trap mass spectrometry and also reports on recent promising developments regarding ISOLTRAP. This eloquently written treatment covers both theory and experiment, and includes a general phenomenological introduction to the nuclear-structure intuition contained in the trends of nuclear binding energies.
Despite the rapidly expanding ambit of physical research and the continual appearance of new branches of physics, the main thrust in its development was and is the attempt at a theoretical synthesis of the entire body of physical knowledge. The main triumphs in physical science were, as a rule, associ ated with the various phases of this synthesis. The most radical expression of this tendency is the program of construction of a unified physical theory. After Maxwellian electrodynamics had unified the phenomena of electricity, magnetism, and optics in a single theoretical scheme on the basis of the con cept of the electromagnetic field, the hope arose that the field concept would become the precise foundation of a new unified theory of the physical world. The limitations of an electromagnetic-field conception of physics, however, already had become clear in the first decade of the 20th century. The concept of a classical field was developed significantly in the general theory of relativity, which arose in the elaboration of a relativistic theory of gravitation. It was found that the gravitational field possesses, in addition to the properties inherent in the electromagnetic field, the important feature that it expresses the metric structure of the space-time continuum. This resulted in the following generalization of the program of a field synthesis of physics: The unified field representing gravitation and electromagnetism must also describe the geometry of space-time.
With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This fourth volume covers AdS/CFT, Virasoro and affine (super-)algebras.
This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.
Organosilicon Compounds: Experiment (Physico-Chemical Studies) and Applications, volume 2, also contains two parts. In its first part, Experiment (Physico-Chemical Studies), the application of modern instrumental tools (such as X-ray crystallography, 29Si NMR spectroscopy, UV-Photoelectron Spectroscopy, and other methods) for assessing the structures of organosilicon compounds is described. The second part, Applications, reviews the current research in the field of material science, specifically the use of organosilicon compounds in synthetic chemistry directed towards the creation of new materials. Organosilicon Compounds: From Theory to Synthesis to Applications provides a comprehensive overview of this important area of organic and organometallic chemistry, dealing with compounds containing carbon–silicon bonds. This field, which includes compounds that are widely encountered in commercial products such as in the fabrication of sealants, adhesives, and coatings, has seen many milestone discoveries reported during the last two decades. Beginning with the theoretical aspects of organosilicon compounds' structure and bonding, the book then explores their synthetic aspects, including main group element organosilicon compounds, transition metal complexes, silicon cages and clusters, low-coordinate organosilicon derivatives (cations, radicals, anions, multiple bonds to silicon, silaaromatics), and more. Next, readers will find valuable sections that explore physical and chemical properties of organosilicon compounds by means of X-ray crystallography, 29Si NMR spectroscopy, photoelectron spectroscopy, and other methods. Finally, the work delves into applications for industrial uses and in many related fields, such as polymers, material science, nanotechnology, bioorganics, and medicinal silicon chemistry. - Features valuable contributions from prominent experts cover both fundamental (theoretical, synthetic, physico-chemical) and applied (material science, applications) aspects of modern organosilicon chemistry - Covers important breakthroughs in the field as well as with the historically significant achievements of the past - Includes applied information for a wide range of specialists from junior and senior researchers (from both academia and industry), working in organometallic, organosilicon, main group element, transition metal, and industrial silicon chemistry, as well as those from interdisciplinary fields such as polymer, material science, nanotechnology
Multiphoton Processes in Atoms in intense laser-light fields is gaining ground as a spectroscopic diagnostic tool. The authors present descriptions of processes occurring in atoms under the action of strong electromagnetic radiation, in particular, the shift, broadening, and mixing of atomic states. The topics include tunneling ionization, above-threshold ionization, ionization of multiply charged ions, resonance-enhanced ionization, super-intense radiation fields, and properties of Rydberg states strongly perturbed by laser radiation.
The quantum theory of magnetism is a well-developed part of contemporary solid-state physics. The basic concepts of this theory can be used to describe such important effects as ferromagnetic ordering oflocalized magnetic moments in crystals and ferromagnetism of metals produced by essentially delocalized electrons, as well as various types of mutual orientation of atomic magnetic moments in solids possessing different crystal lattices and compositions. In recent years,the spin-fluctuational approach has been developed, which can overcome some contradictions between "localized" and "itinerant" models in the quantum mechanics of magnetic crystals. These are only some of the principal achievements of quantum magnetic theory. Almost all of the known magnetic properties of solids can be qualitat ively explained on the basis of its concepts. Further developments should open up the possibility of reliable quantitative description of magnetic properties of solids. Unfortunately, such calculations based on model concepts appear to be very complicated and, quite often, not definite enough. The rather small number of parameters of qualitative models are usually not able to take into account the very different types of magnetic interactions that appear in crystals. Further development of magnetic theory requires quantitative information on electronic wave function in the crystal considered. This can be proved by electronic band structure and cluster calculations. In many cases the latter can be a starting point for quantitative calculations of parameters used in magnetic theory.
This is a unique 21st-century monograph that reveals a basic, yet deep understanding of the universe, as well as the human mind and body OCo all from the perspective of quantum mechanics and quantum field theory.This book starts with both non-mathematical and mathematical preliminaries. It presents the basics of both non-relativistic and relativistic quantum mechanics, and introduces Feynman path integrals and their application to quantum fields and string theory, as well as some non-quantum applications. It then describes the quantum universe in the form of loop quantum gravity and quantum cosmology. Lastly, the book turns to the human body and mind, applying quantum theory to electro-muscular stimulation and consciousness.It can be used as a graduate (or advanced undergraduate) textbook for a two-semester course in quantum physics and its modern applications. Some parts of the book can also be used by engineers, biologists, psychologists and computer scientists, as well as applied mathematicians, both in industry and academia.
Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers. The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations, as well as numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations. Included for nearly every method are: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition.
This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator — “Human Biodynamics Engine”, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools — this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.
Proceedings of SPIE present the original research papers presented at SPIE conferences and other high-quality conferences in the broad-ranging fields of optics and photonics. These books provide prompt access to the latest innovations in research and technology in their respective fields. Proceedings of SPIE are among the most cited references in patent literature.
SPIE-International Society for Optical Engineering
Published Date
ISBN 10
0819453994
ISBN 13
9780819453990
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