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Mathematical physics --- Physique mathématique --- Periodicals. --- Périodiques --- Mathematical physics. --- Physical mathematics --- Physics --- Mathematics --- Mathematical Physics. --- Applied Physics

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"This book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the deformation tensors of elasticity, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers, quarks, and the quark model for mesons. Before a discussion of abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should be of interest also to mathematics students. This book will be useful to graduate and advance undergraduate students of physics, engineering or mathematics. It can be used as a course text or for self-study. This third edition includes a new overview of Cartan's exterior differential forms. It previews many of the geometric concepts developed in the text and illustrates their applications to a single extended problem in engineering, namely the Cauchy stresses created by a small twist of an elastic cylindrical rod about its axis"--

Geometry, Differential --- Mathematical physics --- Géométrie différentielle --- Physique mathématique --- Geometry, Differential. --- Mathematical physics. --- Physical mathematics --- Physics --- Differential geometry --- Mathematics --- Topology. --- Géométrie différentielle --- Physique mathématique

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There have been many significant advances in time-dependent density functional theory over recent years, both in enlightening the fundamental theoretical basis of the theory, as well as in computational algorithms and applications. This book, as successor to the highly successful volume Time-Dependent Density Functional Theory (Lect. Notes Phys. 706, 2006) brings together for the first time all recent developments in a systematic and coherent way.  First, a thorough pedagogical presentation of the fundamental theory is given, clarifying aspects of the original proofs and theorems, as well as presenting fresh developments that extend the theory into new realms—such as alternative proofs of the original Runge-Gross theorem, open quantum systems, and dispersion forces to name but a few. Next, all of the basic concepts are introduced sequentially and building in complexity, eventually reaching the level of open problems of interest. Contemporary applications of the theory are discussed, from real-time coupled-electron-ion dynamics, to excited-state dynamics and molecular transport. Last but not least, the authors introduce and review recent advances in computational implementation, including massively parallel architectures and graphical processing units. Special care has been taken in editing this volume as a multi-author textbook, following a coherent line of thought, and making all the relevant connections between chapters and concepts consistent throughout. As such it will prove to be the text of reference in this field, both for beginners as well as expert researchers and lecturers teaching advanced quantum mechanical methods to model complex physical systems, from molecules to nanostructures, from biocomplexes to surfaces, solids and liquids. From the reviews of LNP 706: “This is a well structured text, with a common set of notations and a single comprehensive and up-to-date list of references, rather than just a compilation of research articles. Because of its clear organization, the book can be used by novices (basic knowledge of ground-state DFT is assumed) and experienced users of TD-DFT, as well as developers in the field.” (Anna I. Krylov, Journal of the American Chemical Society, Vol. 129 (21), 2007)  “This book is a treasure of knowledge and I highly recommend it. Although it is a compilation of chapters written by many different leading researchers involved in development and application of TDDFT, the contributors have taken great care to make sure the book is pedagogically sound and the chapters complement each other [...]. It is highly accessible to any graduate student of chemistry or physics with a solid grounding in many-particle quantum mechanics, wishing to understand both the fundamental theory as well as the exponentially growing number of applications. [...]  In any case, no matter what your background is, it is a must-read and an excellent reference to have on your shelf.” Amazon.com, October 15, 2008, David Tempel (Cambridge, MA).

Physics --- Chemistry --- Physical Sciences & Mathematics --- Physics - General --- Physical & Theoretical Chemistry --- Density functionals. --- Mathematical physics. --- Physical mathematics --- Density functional methods --- Density functional theory --- Functional methods, Density --- Functionals, Density --- Mathematics --- Physics. --- Chemistry, Physical and theoretical. --- Atomic structure. --- Molecular structure. --- Spectra. --- Condensed matter. --- Numerical and Computational Physics. --- Theoretical and Computational Chemistry. --- Condensed Matter Physics. --- Atomic/Molecular Structure and Spectra. --- Functional analysis --- Chemistry. --- Numerical and Computational Physics, Simulation. --- Physical sciences --- Atomic structure  . --- Molecular structure . --- Structure, Molecular --- Chemical structure --- Structural bioinformatics --- Structure, Atomic --- Atomic theory --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Natural philosophy --- Philosophy, Natural --- Dynamics --- Density functionals --- Mathematical physics --- Numerical and Computational Physics --- Fonctionnelles densité. --- Physique mathématique.