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Author: Jean-Paul Blaizot
Publisher: Mit Press
ISBN: 9780262022149
Category : Science
Languages : en
Pages : 657
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Book Description
This book provides a comprehensive and pedagogical account of the various methods used in the quantum theory of finite systems, including molecular, atomic, nuclear, and particle phenomena. Covering both background material and advanced topics and including nearly 200 problems, Quantum Theory of Finite Systems has been designed to serve primarily as a text and will also prove useful as a reference in research. The first of the book's four parts introduces the basic mathematical apparatus: second quantization, canonical transformations, Wick theorems and the resulting diagram expansions, and oscillator models. The second part presents mean field approximations and the recently developed path integral methods for the quantization of collective modes. Part three develops perturbation theory in terms of both time-dependent Feynman diagrams and time-independent Goldstone diagrams. A fourth part discusses variational methods based on correlated wavefunctions, including spin correlations. The approximation schemes are formulated for fermions and bosons at eigher zero or non-zero temperature. Although the formalism developed applies to both finite and infinite systems, the book stresses those aspects of the theory that are specific to the description of finite systems. Thus special attention is given to mean field approximations, the ensuing broken symmetries, and the associated collective motions such as rotations. Conversely, some specific features of systems with infinite numbers of degrees of freedom (such as the thermodynamic limit, critical phenomena, and the elimination of ultraviolet divergencies) are deliberately omitted. Jean-Paul Blaizot and Georges Ripka are associated with the Centre d'Etudes Nucleaires de Saclay.
Author: Jean-Paul Blaizot
Publisher: Mit Press
ISBN: 9780262022149
Category : Science
Languages : en
Pages : 657
Get Book Here
Book Description
This book provides a comprehensive and pedagogical account of the various methods used in the quantum theory of finite systems, including molecular, atomic, nuclear, and particle phenomena. Covering both background material and advanced topics and including nearly 200 problems, Quantum Theory of Finite Systems has been designed to serve primarily as a text and will also prove useful as a reference in research. The first of the book's four parts introduces the basic mathematical apparatus: second quantization, canonical transformations, Wick theorems and the resulting diagram expansions, and oscillator models. The second part presents mean field approximations and the recently developed path integral methods for the quantization of collective modes. Part three develops perturbation theory in terms of both time-dependent Feynman diagrams and time-independent Goldstone diagrams. A fourth part discusses variational methods based on correlated wavefunctions, including spin correlations. The approximation schemes are formulated for fermions and bosons at eigher zero or non-zero temperature. Although the formalism developed applies to both finite and infinite systems, the book stresses those aspects of the theory that are specific to the description of finite systems. Thus special attention is given to mean field approximations, the ensuing broken symmetries, and the associated collective motions such as rotations. Conversely, some specific features of systems with infinite numbers of degrees of freedom (such as the thermodynamic limit, critical phenomena, and the elimination of ultraviolet divergencies) are deliberately omitted. Jean-Paul Blaizot and Georges Ripka are associated with the Centre d'Etudes Nucleaires de Saclay.
Author: Jordan G Brankov
Publisher: World Scientific
ISBN: 9814494569
Category : Science
Languages : en
Pages : 459
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Book Description
The aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) reveals the intimate mechanism of how the critical singularities build up in the thermodynamic limit; and (4) can be fruitfully used to explain the low-temperature behaviour of quantum critical systems.The exposition is given in a self-contained form which presumes the reader's knowledge only in the framework of standard courses on the theory of phase transitions and critical phenomena. The instructive role of simple models, both classical and quantum, is demonstrated by putting the accent on the derivation of rigorous and exact analytical results.
Author: Joshua Jortner
Publisher: Springer Science & Business Media
ISBN: 9400940017
Category : Science
Languages : en
Pages : 391
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Book Description
The Twentieth Jerusalem Symposium reflected the high standards of these distinguished scientific meetings which convene once a year at the Israel Academy of Sciences and Humanities in Jerusalem to discuss a specific topic in the broad area of quantum chemistry and biochemistry. The Twentieth Jerusalem Symposium marked an auspicious occasion. commemorating two decades of this scientific endeavour. The topic at this year's Jerusalem Symposium was Large Finite Systems which constitutes a truly interdisciplinary subject of central interest in the broad areas of chemistry. physics. astrophysics and biophysics. The main theme of the Symposium was built around bridging the gap between molecular. surface and condensed matter chemical physics. Emphasis was placed on the interrelationship between the properties of large molecules. van der Waals complexes and clusters. focusing on the structure. dynamics of nuclear motion. quantum and thermodynamics size effects. the nature of electronic states and excited-state energetics and dynamics of large finite systems. The interdisciplinary nature of these research areas was deliberated by intensive and extensive interactions between scientists from different disciplines and between theory and experiment. This volume provides a record of the invited lectures at the Symposium.
Author: Michael I. Gil'
Publisher: Springer Science & Business Media
ISBN: 9780792382218
Category : Mathematics
Languages : en
Pages : 386
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Book Description
The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations. Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint. This book contains solutions to the problems connected with the Aizerman and generalized Aizerman conjectures and presents fundamental results by A. Yu. Levin for the stability of nonautonomous systems having variable real characteristic roots. Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first-year graduate-level course in analysis.
Author: Roger W. Brockett
Publisher: SIAM
ISBN: 1611973872
Category : Mathematics
Languages : en
Pages : 260
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Book Description
Originally published in 1970, Finite Dimensional Linear Systems is a classic textbook that provides a solid foundation for learning about dynamical systems and encourages students to develop a reliable intuition for problem solving. The theory of linear systems has been the bedrock of control theory for 50 years and has served as the springboard for many significant developments, all the while remaining impervious to change. Since linearity lies at the heart of much of the mathematical analysis used in applications, a firm grounding in its central ideas is essential. This book touches upon many of the standard topics in applied mathematics, develops the theory of linear systems in a systematic way, making as much use as possible of vector ideas, and contains a number of nontrivial examples and many exercises.
Author: ?ordan Brankov
Publisher: World Scientific
ISBN: 9789810239251
Category : Science
Languages : en
Pages : 468
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Book Description
The aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) reveals the intimate mechanism of how the critical singularities build up in the thermodynamic limit; and (4) can be fruitfully used to explain the low-temperature behaviour of quantum critical systems. The exposition is given in a self-contained form which presumes the reader's knowledge only in the framework of standard courses on the theory of phase transitions and critical phenomena. The instructive role of simple models, both classical and quantum, is demonstrated by putting the accent on the derivation of rigorous and exact analytical results.
Author: Ricardo Americo Broglia
Publisher: World Scientific
ISBN: 9814412503
Category : Science
Languages : en
Pages : 693
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Book Description
This unique volume reviews more than fifty years of theoretical and experimental developments of the concept that properties of atomic nuclei up to a great extent are defined by the pair correlations of nuclear constituents — protons and neutrons. Such correlations in condensed matter are responsible for quantum phenomena on a macroscopic level — superfluidity and superconductivity. After introducing Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity of metals, it became clear that atomic nuclei have properties of superfluid drops, and practically all features of nuclei strongly depend on the pair correlations. Presenting a comprehensive overview of the progress of nuclear science, the contributions from leading physicists around the world, cover the whole spectrum of studies in nuclear physics and physics of other small systems. With the most updated information written in an accessible way, the volume will serve as an irreplaceable source of references covering many years of development and insight into several new problems at the frontiers of science. It will be useful not only for physicists working in nuclear and condensed matter physics, astrophysicists, chemists and historians of science, but will also help students understand the current status and perspectives for the future.
Author: Daniel Gerbner
Publisher: CRC Press
ISBN: 0429804113
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Extremal Finite Set Theory surveys old and new results in the area of extremal set system theory. It presents an overview of the main techniques and tools (shifting, the cycle method, profile polytopes, incidence matrices, flag algebras, etc.) used in the different subtopics. The book focuses on the cardinality of a family of sets satisfying certain combinatorial properties. It covers recent progress in the subject of set systems and extremal combinatorics. Intended for graduate students, instructors teaching extremal combinatorics and researchers, this book serves as a sound introduction to the theory of extremal set systems. In each of the topics covered, the text introduces the basic tools used in the literature. Every chapter provides detailed proofs of the most important results and some of the most recent ones, while the proofs of some other theorems are posted as exercises with hints. Features: Presents the most basic theorems on extremal set systems Includes many proof techniques Contains recent developments The book’s contents are well suited to form the syllabus for an introductory course About the Authors: Dániel Gerbner is a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences in Budapest, Hungary. He holds a Ph.D. from Eötvös Loránd University, Hungary and has contributed to numerous publications. His research interests are in extremal combinatorics and search theory. Balázs Patkós is also a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences. He holds a Ph.D. from Central European University, Budapest and has authored several research papers. His research interests are in extremal and probabilistic combinatorics.
Author: Eduardo D. Sontag
Publisher: Springer Science & Business Media
ISBN: 1461205778
Category : Mathematics
Languages : en
Pages : 543
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Book Description
Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.
Author: Ferdinand Wagner
Publisher: CRC Press
ISBN: 1420013645
Category : Computers
Languages : en
Pages : 391
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Book Description
Modeling Software with Finite State Machines: A Practical Approach explains how to apply finite state machines to software development. It provides a critical analysis of using finite state machines as a foundation for executable specifications to reduce software development effort and improve quality. It discusses the design of a state machine and of a system of state machines. It also presents a detailed analysis of development issues relating to behavior modeling with design examples and design rules for using finite state machines. This text demonstrates the implementation of these concepts using StateWORKS software and introduces the basic components of this software.
