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Symbol Correspondences for Spin Systems

2014-10-10 Mathematics
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Release : 2014-10-10
Genre : Mathematics
Kind : eBook
Book Rating : 985/5 ( reviews)

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Book Synopsis Symbol Correspondences for Spin Systems by : Pedro de M. Rios

Download or read book Symbol Correspondences for Spin Systems written by Pedro de M. Rios. This book was released on 2014-10-10. Available in PDF, EPUB and Kindle. Book excerpt: In mathematical physics, the correspondence between quantum and classical mechanics is a central topic, which this book explores in more detail in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems. A detailed presentation of quantum spin-j systems, with emphasis on the SO(3)-invariant decomposition of their operator algebras, is first followed by an introduction to the Poisson algebra of the classical spin system and then by a similarly detailed examination of its SO(3)-invariant decomposition. The book next proceeds with a detailed and systematic study of general quantum-classical symbol correspondences for spin-j systems and their induced twisted products of functions on the 2-sphere. This original systematic presentation culminates with the study of twisted products in the asymptotic limit of high spin numbers. In the context of spin systems it shows how classical mechanics may or may not emerge as an asymptotic limit of quantum mechanics. The book will be a valuable guide for researchers in this field and its self-contained approach also makes it a helpful resource for graduate students in mathematics and physics.

Real Spinorial Groups

2018-11-22 Mathematics
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Release : 2018-11-22
Genre : Mathematics
Kind : eBook
Book Rating : 04X/5 ( reviews)

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Book Synopsis Real Spinorial Groups by : Sebastià Xambó-Descamps

Download or read book Real Spinorial Groups written by Sebastià Xambó-Descamps. This book was released on 2018-11-22. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.

Fundamentals of Natural Computing

2006-06-02 Computers
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Release : 2006-06-02
Genre : Computers
Kind : eBook
Book Rating : 448/5 ( reviews)

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Book Synopsis Fundamentals of Natural Computing by : Leandro Nunes de Castro

Download or read book Fundamentals of Natural Computing written by Leandro Nunes de Castro. This book was released on 2006-06-02. Available in PDF, EPUB and Kindle. Book excerpt: Natural computing brings together nature and computing to develop new computational tools for problem solving; to synthesize natural patterns and behaviors in computers; and to potentially design novel types of computers. Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications presents a wide-ranging survey of novel techniqu

Analysis of NMR Spectra

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 050/5 ( reviews)

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Book Synopsis Analysis of NMR Spectra by : R. A. Hoffman

Download or read book Analysis of NMR Spectra written by R. A. Hoffman. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Nuclear magnetic resonance spectroscopy, which has evolved only within the last 20 years, has become one of the very important tools in chemistry and physics. The literature on its theory and application has grown immensely and a comprehensive and adequate treatment of all branches by one author, or even by several, becomes increasingly difficult. This series is planned to present articles written by experts working in various fields of nuclear magnetic resonance spectroscopy, and will contain review articles as well as progress reports and original work. Its main aim, however, is to fill a gap, existing in literature, by publishing articles written by specialists, which take the reader from the introductory stage to the latest development in the field. The editors are grateful to the authors for the time and effort spent in writing the articles, and for their invaluable cooperation. The Editors Analysis of NMR Spectra A Guide for Chemists R. A. HOFFMAN t S. FORSEN Division of Physical Chemistry, Chemical Center, Lund Institute of Technology, Lund, Sweden B. GESTBLOM Institute of Physics, University of Uppsala, Sweden Contents I. Principles of NMR Spectroscopy 4 1. 1. The Magnetic Resonance Phenomenon 4 a) Nuclear Moments. . . . . . . . 4 b) Magnetic Spin States and Energy Levels 5 c) The Magnetic Resonance Condition. 7 d) The Larmor Precession. . 7 e) Experimental Aspects . . . . 8 1. 2. Chemical Shifts . . . . . . . . 9 a) The Screening Constant 11. . . 9 b) Chemical Shift Scales (11 and r) 10 1. 3. Spin Coupling Constants 12 1. 4. Intensities. . . . . . . .

Frustrated Spin Systems (Third Edition)

2020-06-19 Science
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Release : 2020-06-19
Genre : Science
Kind : eBook
Book Rating : 158/5 ( reviews)

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Book Synopsis Frustrated Spin Systems (Third Edition) by : Hung-the Diep

Download or read book Frustrated Spin Systems (Third Edition) written by Hung-the Diep. This book was released on 2020-06-19. Available in PDF, EPUB and Kindle. Book excerpt: Frustrated spin systems have been first investigated five decades ago. Well-known examples include the Ising model on the antiferromagnetic triangular lattice studied by G H Wannier in 1950 and the Heisenberg helical structure discovered independently by A Yoshimori, J Villainn and T A Kaplan in 1959. However, extensive investigations on frustrated spin systems have really started with the concept of frustration introduced at the same time by G Toulouse and by J Villain in 1977 in the context of spin glasses. The frustration is generated by the competition of different kinds of interaction and/or by the lattice geometry. As a result, in the ground state all bonds are not fully satisfied. In frustrated Ising spin systems, a number of spins behave as free spins. In frustrated vector spin systems, the ground-state configuration is usually non-collinear. The ground state of frustrated spin systems is therefore highly degenerate and new induced symmetries give rise to unexpected behaviors at finite temperatures. Many properties of frustrated systems are still not well understood at present. Theoretically, recent studies shown in this book reveal that established theories, numerical simulations as well as experimental techniques have encountered many difficulties in dealing with frustrated systems. In some sense, frustrated systems provide an excellent testing ground for approximations and theories. Experimentally, more and more frustrated materials are discovered with interesting properties for applications.

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