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Effective Evolution Equations From Quantum Mechanics
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Book Synopsis Effective Evolution Equations from Quantum Dynamics by : Niels Benedikter
Download or read book Effective Evolution Equations from Quantum Dynamics written by Niels Benedikter and published by Springer. This book was released on 2015-11-04 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of the nonlinear Gross-Pitaevskii equation. Section 6 addresses fermionic systems (characterized by antisymmetric wave functions); here, the fermionic mean-field regime is naturally linked with a semiclassical regime, and it is proven that the evolution of approximate Slater determinants can be approximated using the nonlinear Hartree-Fock equation. In closing, Section 7 reexamines the same fermionic mean-field regime, but with a focus on mixed quasi-free initial data approximating thermal states at positive temperature.
Book Synopsis Evolution Equations by : David Ellwood
Download or read book Evolution Equations written by David Ellwood and published by American Mathematical Soc.. This book was released on 2013-06-26 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Book Synopsis C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics by : Jean-Bernard Bru
Download or read book C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics written by Jean-Bernard Bru and published by Springer Nature. This book was released on 2023-06-16 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive introduction to the mathematical foundations of quantum statistical physics. It presents a conceptually profound yet technically accessible path to the C*-algebraic approach to quantum statistical mechanics, demonstrating how key aspects of thermodynamic equilibrium can be derived as simple corollaries of classical results in convex analysis. Using C*-algebras as examples of ordered vector spaces, this book makes various aspects of C*-algebras and their applications to the mathematical foundations of quantum theory much clearer from both mathematical and physical perspectives. It begins with the simple case of Gibbs states on matrix algebras and gradually progresses to a more general setting that considers the thermodynamic equilibrium of infinitely extended quantum systems. The book also illustrates how first-order phase transitions and spontaneous symmetry breaking can occur, in contrast to the finite-dimensional situation. One of the unique features of this book is its thorough and clear treatment of the theory of equilibrium states of quantum mean-field models. This work is self-contained and requires only a modest background in analysis, topology, and functional analysis from the reader. It is suitable for both mathematicians and physicists with a specific interest in quantum statistical physics.
Book Synopsis XVIth International Congress on Mathematical Physics by : Pavel Exner
Download or read book XVIth International Congress on Mathematical Physics written by Pavel Exner and published by World Scientific. This book was released on 2010 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program. This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others.
Book Synopsis Macroscopic Limits of Quantum Systems by : Daniela Cadamuro
Download or read book Macroscopic Limits of Quantum Systems written by Daniela Cadamuro and published by Springer. This book was released on 2018-10-26 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the workshop of the same name, this proceedings volume presents selected research investigating the mathematics of collective phenomena emerging from quantum theory at observable scales. Featured contributions from leading scientists provide a thorough overview of current and active research. Methods from functional analysis, spectral theory, renormalization group theory, and variational calculus are used to prove rigorous results in quantum physics. Topics include superconductivity and mathematical aspects of the BCS theory, the Jellium model and Bose-Einstein condensation, among others. Presenting technical details in an accessible way, this book serves as an introduction to research for advanced graduate students and is suitable for specialists in mathematical physics. The workshop “Macroscopic Limits of Quantum Systems” was held over three days in the spring of 2017 at the Technical University of Munich. The conference celebrated the achievements of Herbert Spohn and his reception of the Max Planck Medal.
Book Synopsis Advances in Quantum Mechanics by : Alessandro Michelangeli
Download or read book Advances in Quantum Mechanics written by Alessandro Michelangeli and published by Springer. This book was released on 2017-08-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.
Book Synopsis XVIIth International Congress on Mathematical Physics by : Arne Jensen
Download or read book XVIIth International Congress on Mathematical Physics written by Arne Jensen and published by World Scientific. This book was released on 2014 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an in-depth study of not just about Tan Kah-kee, but also the making of a legend through his deeds, self-sacrifices, fortitude and foresight. This revised edition sheds new light on his political agonies in Mao's China over campaigns against capitalists and intellectuals.
Book Synopsis Mathematical Problems in Quantum Physics by : Federico Bonetto
Download or read book Mathematical Problems in Quantum Physics written by Federico Bonetto and published by American Mathematical Soc.. This book was released on 2018-10-24 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the QMATH13: Mathematical Results in Quantum Physics conference, held from October 8–11, 2016, at the Georgia Institute of Technology, Atlanta, Georgia. In recent years, a number of new frontiers have opened in mathematical physics, such as many-body localization and Schrödinger operators on graphs. There has been progress in developing mathematical techniques as well, notably in renormalization group methods and the use of Lieb–Robinson bounds in various quantum models. The aim of this volume is to provide an overview of some of these developments. Topics include random Schrödinger operators, many-body fermionic systems, atomic systems, effective equations, and applications to quantum field theory. A number of articles are devoted to the very active area of Schrödinger operators on graphs and general spectral theory of Schrödinger operators. Some of the articles are expository and can be read by an advanced graduate student.
Book Synopsis The Physics of Quantum Mechanics by : James Binney
Download or read book The Physics of Quantum Mechanics written by James Binney and published by Oxford University Press, USA. This book was released on 2013-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title gives students a good understanding of how quantum mechanics describes the material world. The text stresses the continuity between the quantum world and the classical world, which is merely an approximation to the quantum world.
Book Synopsis Density Functionals For Many-particle Systems: Mathematical Theory And Physical Applications Of Effective Equations by : Berthold-georg Englert
Download or read book Density Functionals For Many-particle Systems: Mathematical Theory And Physical Applications Of Effective Equations written by Berthold-georg Englert and published by World Scientific. This book was released on 2023-02-10 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density Functional Theory (DFT) first established it's theoretical footing in the 1960s from the framework of Hohenberg-Kohn theorems. DFT has since seen much development in evaluation techniques as well as application in solving problems in Physics, Mathematics and Chemistry.This review volume, part of the IMS Lecture Notes Series, is a collection of contributions from the September 2019 Workshop on the topic, held in the Institute for Mathematical Sciences, National University of Singapore.With contributions from prominent Mathematicians, Physicists, and Chemists, the volume is a blend of comprehensive review articles on the Mathematical and the Physicochemical aspects of DFT and shorter contributions on particular themes, including numerical implementations.The book will be a useful reference for advanced undergraduate and postgraduate students as well as researchers.
Book Synopsis Ideas of Quantum Chemistry by : Lucjan Piela
Download or read book Ideas of Quantum Chemistry written by Lucjan Piela and published by Elsevier. This book was released on 2006-11-28 with total page 1122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideas of Quantum Chemistry shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field.Ideas of Quantum Chemistry has both textbook and reference work aspects. Like a textbook, the material is organized into digestable sections with each chapter following the same structure. It answers frequently asked questions and highlights the most important conclusions and the essential mathematical formulae in the text. In its reference aspects, it has a broader range than traditional quantum chemistry books and reviews virtually all of the pertinent literature. It is useful both for beginners as well as specialists in advanced topics of quantum chemistry. The book is supplemented by an appendix on the Internet.* Presents the widest range of quantum chemical problems covered in one book * Unique structure allows material to be tailored to the specific needs of the reader * Informal language facilitates the understanding of difficult topics
Book Synopsis Regular Black Holes by : Cosimo Bambi
Download or read book Regular Black Holes written by Cosimo Bambi and published by Springer Nature. This book was released on 2023-07-06 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Black holes are one of the most fascinating predictions of general relativity. They are the natural product of the complete gravitational collapse of matter and today we have a body of observational evidence supporting the existence of black holes in the Universe. However, general relativity predicts that at the center of black holes there are spacetime singularities, where predictability is lost and standard physics breaks down. It is widely believed that spacetime singularities are a symptom of the limitations of general relativity and must be solved within a theory of quantum gravity. Since we do not have yet any mature and reliable candidate for a quantum gravity theory, researchers have studied toy-models of singularity-free black holes and of singularity-free gravitational collapses in order to explore possible implications of the yet unknown theory of quantum gravity. This book reviews all main models of regular black holes and non-singular gravitational collapses proposed in the literature, and discuss the theoretical and observational implications of these scenarios.
Book Synopsis An Introduction to Non-Perturbative Foundations of Quantum Field Theory by : Franco Strocchi
Download or read book An Introduction to Non-Perturbative Foundations of Quantum Field Theory written by Franco Strocchi and published by Oxford University Press, USA. This book was released on 2013-02-14 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses fundamental aspects of Quantum Field Theory and of Gauge theories, with attention to mathematical consistency. Basic issues of the standard model of elementary particles (Higgs mechanism and chiral symmetry breaking in quantum Chromodynamics) are treated without relying on the perturbative expansion and on instanton calculus.
Book Synopsis Semiclassical and Stochastic Gravity by : Bei-Lok B. Hu
Download or read book Semiclassical and Stochastic Gravity written by Bei-Lok B. Hu and published by Cambridge University Press. This book was released on 2020-03-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two pillars of modern physics are general relativity and quantum field theory, the former describes the large scale structure and dynamics of space-time, the latter, the microscopic constituents of matter. Combining the two yields quantum field theory in curved space-time, which is needed to understand quantum field processes in the early universe and black holes, such as the well-known Hawking effect. This book examines the effects of quantum field processes back-reacting on the background space-time which become important near the Planck time (10-43 sec). It explores the self-consistent description of both space-time and matter via the semiclassical Einstein equation of semiclassical gravity theory, exemplified by the inflationary cosmology, and fluctuations of quantum fields which underpin stochastic gravity, necessary for the description of metric fluctuations (space-time foams). Covering over four decades of thematic development, this book is a valuable resource for researchers interested in quantum field theory, gravitation and cosmology.
Book Synopsis Finite Difference Methods for Nonlinear Evolution Equations by : Zhi-Zhong Sun
Download or read book Finite Difference Methods for Nonlinear Evolution Equations written by Zhi-Zhong Sun and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-05-08 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear evolution equations are widely used to describe nonlinear phenomena in natural and social sciences. However, they are usually quite difficult to solve in most instances. This book introduces the finite difference methods for solving nonlinear evolution equations. The main numerical analysis tool is the energy method. This book covers the difference methods for the initial-boundary value problems of twelve nonlinear partial differential equations. They are Fisher equation, Burgers' equation, regularized long-wave equation, Korteweg-de Vries equation, Camassa-Holm equation, Schrödinger equation, Kuramoto-Tsuzuki equation, Zakharov equation, Ginzburg-Landau equation, Cahn-Hilliard equation, epitaxial growth model and phase field crystal model. This book is a monograph for the graduate students and science researchers majoring in computational mathematics and applied mathematics. It will be also useful to all researchers in related disciplines.
Book Synopsis Quantum Mathematics II by : Michele Correggi
Download or read book Quantum Mathematics II written by Michele Correggi and published by Springer Nature. This book was released on 2024-01-09 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second volume that provides an unique overview of the most recent and relevant contributions in the field of mathematical physics with a focus on the mathematical features of quantum mechanics. It is a collection of review papers together with brand new works related to the activities of the INdAM Intensive Period "INdAM Quantum Meetings (IQM22)", which took place at the Politecnico di Milano in Spring 2022 at Politecnico di Milano. The range of topics covered by the book is wide, going ranging from many-body quantum mechanics to quantum field theory and open quantum systems.
Book Synopsis The Meaning of the Wave Function by : Shan Gao
Download or read book The Meaning of the Wave Function written by Shan Gao and published by Cambridge University Press. This book was released on 2017-03-16 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering much of the recent debate, this ambitious text provides new, decisive proof of the reality of the wave function.
