Series: Cambridge Monographs on Mathematical Physics
Hardback (ISBN-13: 9780521641685)
Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts and methodology are applied to current research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. Divided into five parts, with each part addressing a particular stage in the conceptual and technical development of the subject, this self-contained book is a valuable reference for graduate students and researchers in particle physics, gravitation, cosmology, atomic-optical and condensed matter physics.
? The self-supporting nature of the book enables students to get started and removes the need to buy additional texts ? Material is divided into sections that address the different stages in the conceptual and technical development of the subject at graded levels of difficulty ? Novel presentation of the intersection of nonequilibrium statistical mechanics and quantum field theory cannot be found in much of the existing literature
Contents
Part I. Fundamentals of Nonequilibrium Statistical Mechanics: 1. Basic issues in nonequilibrium statistical mechanics; 2. Relaxation, dissipation, noise and fluctuations; 3. Quantum open systems; Part II. Basics of Nonequilibrium Quantum Field Theory: 4. Quantum fields on time-dependent backgrounds: particle creation; 5. Open systems of interacting quantum fields; 6. Functional methods in nonequilibrium QFT; Part III. Gauge Invariance, Dissipation, Entropy, Noise and Decoherence: 7. Closed time path effective action for gauge theories; 8. Dissipation and noise in mean field dynamics; 9. Entropy generation and decoherence of quantum fields; Part IV. Thermal, Kinetic and Hydrodynamic Regimes: 10. Thermal field and linear response theory; 11. Quantum kinetic field theory; 12. Hydrodynamics and thermalization; 13. Nonequilibrium Bose-Einstein condensates; 14. Nonequilibrium issues in RHICs and DCCs; 15. Nonequilibrium quantum processes in the early universe; References; Index.
Series: Encyclopedia of Mathematics and its Applications (No. 66)
Paperback (ISBN-13: 9780521057189)
77 line diagrams 4 tables
Size: 234 x 156 mm
Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research.
? First book to cover star partitions ? Draws together a wide range of research ? Authors are leading figures in graph theory
Contents
1. A background in graph spectra; 2. Eigenvectors of graphs; 3. Eigenvectors of techniques; 4. Graph angles; 5. Angle techniques; 6. Graph perturbations; 7. Star partitions; 8. Canonical star bases; 9. Miscellaneous results.
Review
‘Specialists in graph theory and mathematical chemistry will welcome this treatment of important new research.’ European Mathematical Society
Series: Cambridge Studies in Advanced Mathematics (No. 64)
Paperback (ISBN-13: 9780521057127)
This textbook on the calculus of variations leads the reader from the basics to modern aspects of the theory. One-dimensional problems and the classical issues like Euler-Lagrange equations are treated, as are Noether’s theorem, Hamilton-Jacobi theory, and in particular geodesic lines, thereby developing some important geometric and topological aspects. The basic ideas of optimal control theory are also given. The second part of the book deals with multiple integrals. After a review of Lebesgue integration, Banach and Hilbert space theory and Sobolev spaces (with complete and detailed proofs), there is a treatment of the direct methods and the fundamental lower semicontinuity theorems. Subsequent chapters introduce the basic concepts of the modern calculus of variations, namely relaxation, Gamma convergence, bifurcation theory and minimax methods based on the Palais?Smale condition. The only prerequisites are basic results from calculus of one and several variables. After having studied this book, the reader will be well-equipped to read research papers in the calculus of variations.
* Plenty of new material, much of it basic * Relevant for many applications
in physics and engineering * Many key examples treated in detail
Contents
Part I. One-Dimensional Variational Problems: 1. The classical theory; 2. Geodesic curves; 3. Saddle point constructions; 4. The theory of Hamilton and Jacobi; 5. Dynamic optimization; Part II. Multiple Integrals in the Calculus of Variations: 6. Lebesgue integration theory; 7. Banach spaces; 8. Lp and Sobolev spaces; 9. The direct methods; 10. Nonconvex functionals: relaxation; 11. G-convergence; 12. BV-functionals and G-convergence: the example of Modica and Mortola; Appendix A. The coarea formula; Appendix B. The distance function from smooth hypersurfaces; 13. Bifurcation theory; 14. The Palais?Smale condition and unstable critical points of variational problems.
Series: Cambridge Tracts in Mathematics (No. 104)
Paperback (ISBN-13: 9780521056861)
Sporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern mathematics. The classification demonstrates that each finite simple group is either a finite analogue of a simple Lie group or one of 26 pathological sporadic groups. Sporadic Groups provides for the first time a self-contained treatment of the foundations of the theory of sporadic groups accessible to mathematicians with a basic background in finite groups such as in the author’s text Finite Group Theory. Introductory material useful for studying the sporadics, such as a discussion of large extraspecial 2-subgroups and Tits’ coset geometries, opens the book. A construction of the Mathieu groups as the automorphism groups of Steiner systems follows. The Golay and Todd modules, and the 2-local geometry for M24 are discussed. This is followed by the standard construction of Conway of the Leech lattice and the Conway group. The Monster is constructed as the automorphism group of the Griess algebra using some of the best features of the approaches of Griess, Conway, and Tits, plus a few new wrinkles. Researchers in finite group theory will find this text invaluable. The subjects treated will interest combinatorists, number theorists, and conformal field theorists.
* An excellent companion to Aschbacher’s Finite Group Theory, just published
in PB
Contents
Preface; 1. Preliminary results; 2. 2-Structure in finite groups; 3. Algebras, codes and forms; 4. Symplectic 2-loops; 5. The discovery, existence, and uniqueness of the sporadics; 6. The Mathieu groups, their Steiner systems, and the Golay code; 7. The geometry and structure of M24; 8. The Conway groups and the Leech lattice; 9. Subgroups of .0; 10. The Griess algebra and the Monster; 11. Subgroups of groups of Monster type; 12. Coverings of graphs and simplicial complexes; 13. The geometry of amalgams; 14. The uniqueness of groups of type M24, He, and L5(2); 15. The groups U4(3); 16. Groups of Conway, Suzuki, and Hall-Janko type; 17. Subgroups of prime order in five sporadic groups; Tables; References; Index.
December 2007. 24 x 17 cm. XIV, 438 pages. Hardcover.
ISBN 978-3-11-019666-5
Series: Inverse and III-Posed Problems Series
Languages: English
Type of Publication: Monograph
Keywords
Evolution equation, ordinary differential equation, inverse problem, parameter estimation, partial differential equation
Prices subject to change. *Prices include VAT, shipping costs will be added. sFr-prices are recommended retail prices.
Grobner Bases in Symbolic Analysis
Ed. by Rosenkranz, Markus / Wang, Dongming
Contents
Series: de Gruyter Series in Nonlinear Analysis and Applications 12
24 x 17 cm. Approx. 248 pages. Hardcover.
ISBN 978-3-11-020222-9
Languages: English
Type of Publication: Monograph
to be published March 2008
About this Title
The authors present functional analytical methods for solving a class of partial differential equations. The results have important applications to the numerical treatment of rheology (specific examples are the behaviour of blood or print colours) and to other applications in fluid mechanics.
A class of methods for solving problems in hydrodynamics is presented.
Subjects
Mathematics > Analysis
Mathematics > Numerical Mathematics
Keywords
Hydrodynamics, Nonlinear Analysis
Readership
Researchers, Graduate Students of Mathematics; Academic Libraries
24 x 17 cm. Approx. 450 pages. Hardcover.
ISBN 978-3-11-020147-5
Languages: English
Type of Publication: Monograph
to be published April 2008
About this Title
A thorough, self-contained and easily accessible treatment of the theory on the polynomial best approximation of functions with respect to maximum norms. The topics include Chebychev theory, Weierstras theorems, smoothness of functions, and continuation of functions.
Subjects
Mathematics > Analysis
Keywords
Uniform Approximation; Polynomial; Alternation Set; Best Approximation
Readership
Students of Mathematics, Engineering, and Natural Sciences; Researchers; Academic Libraries
Series: de Gruyter Expositions in Mathematics 43
January 2008. 24 x 17 cm. Approx. IX, 357 pages. Hardcover
ISBN 978-3-11-020053-9
Languages: English
Type of Publication: MonographAbout
This book provides the first systematic treatment of modules over discrete valuation domains which plays an important role in various areas of algebra, especially in commutative algebra. Many important results representing the state of the art are presented in the text which is supplemented by exercises and interesting open problems.
An important contribution to commutative algebra.
Subjects
Mathematics > Algebra, Number theory
Keywords
Algebra: Ring; Module Theory; Discrete Valuation Domain
Readership
Lecturers, Graduate Students; Academic Libraries
Contents