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The Mean Field Limit Of Large Quantum Systems With Coulomb Interaction
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Book Synopsis Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity by : Adrian Muntean
Download or read book Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity written by Adrian Muntean and published by Springer. This book was released on 2016-01-28 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the offspring of a summer school school “Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity”, which was held in 2012 at the University of Twente, the Netherlands. The focus lies on mathematically rigorous methods for multiscale problems of physical origins. Each of the four book chapters is based on a set of lectures delivered at the school, yet all authors have expanded and refined their contributions. Francois Golse delivers a chapter on the dynamics of large particle systems in the mean field limit and surveys the most significant tools and methods to establish such limits with mathematical rigor. Golse discusses in depth a variety of examples, including Vlasov--Poisson and Vlasov--Maxwell systems. Lucia Scardia focuses on the rigorous derivation of macroscopic models using $\Gamma$-convergence, a more recent variational method, which has proved very powerful for problems in material science. Scardia illustrates this by various basic examples and a more advanced case study from dislocation theory. Alexander Mielke's contribution focuses on the multiscale modeling and rigorous analysis of generalized gradient systems through the new concept of evolutionary $\Gamma$-convergence. Numerous evocative examples are given, e.g., relating to periodic homogenization and the passage from viscous to dry friction. Martin Göll and Evgeny Verbitskiy conclude this volume, taking a dynamical systems and ergodic theory viewpoint. They review recent developments in the study of homoclinic points for certain discrete dynamical systems, relating to particle systems via ergodic properties of lattices configurations.
Book Synopsis Panorama of Contemporary Quantum Mechanics by : Trong Tuong Truong
Download or read book Panorama of Contemporary Quantum Mechanics written by Trong Tuong Truong and published by BoD – Books on Demand. This book was released on 2019-12-04 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to recent developments in quantum mechanics. After an Introductory chapter, Chapter 2 describes the cooperative spontaneous lasing mechanism in gas in three level systems and their possible quantum retardation effects. Chapter 3 is concerned with the evolution of states of large quantum particle systems via marginal correlation operators. Chapter 4 studies the effects of electronic transfer using ab initio quantum calculation methods to access biological macromolecular system behaviors. Chapter 5 concentrates on new features of supersymmetric quantum mechanics using the adjunction of boson-fermion symmetry. The book will be of interest to graduate and Ph.D students as well as scientists from various backgrounds who are concerned with quantum effects.
Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Boyan Sirakov
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Boyan Sirakov and published by World Scientific. This book was released on 2019-02-27 with total page 5393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
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 Optimal Transport on Quantum Structures by : Jan Maas
Download or read book Optimal Transport on Quantum Structures written by Jan Maas and published by Springer Nature. This book was released on with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Complex Quantum Systems by : Heinz Siedentop
Download or read book Complex Quantum Systems written by Heinz Siedentop and published by World Scientific Publishing Company. This book was released on 2013 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on lectures given during the program Complex Quantum Systems held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010. It guides the reader through two introductory expositions on large Coulomb systems to five of the most important developments in the field: derivation of mean field equations, derivation of effective Hamiltonians, alternative high precision methods in quantum chemistry, modern many body methods originating from quantum information, and - the most complex - semirelativistic quantum electrodynamics. These introductions are written by leaders in their fields; amongst them are Volker Bach, Rafael Benguria, Thomas Chen, and Jan Philip Solovej. Together, they fill a gap between current textbooks and the vast modern literature on complex quantum systems.
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 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 Many-Body Quantum Theory in Condensed Matter Physics by : Henrik Bruus
Download or read book Many-Body Quantum Theory in Condensed Matter Physics written by Henrik Bruus and published by Oxford University Press. This book was released on 2004-09-02 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.
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 Conductor Insulator Quantum Phase Transitions by : Vladimir Dobrosavljevic
Download or read book Conductor Insulator Quantum Phase Transitions written by Vladimir Dobrosavljevic and published by Oxford University Press. This book was released on 2012-06 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: When many particles come together how do they organize themselves? And what destroys this organization? Combining experiments and theory, this book describes intriguing quantum phases - metals, superconductors and insulators - and transitions between them. It captures the excitement and the controversies on topics at the forefront of research.
Book Synopsis Statistical Mechanics by : Giovanni Gallavotti
Download or read book Statistical Mechanics written by Giovanni Gallavotti and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This clear book presents a critical and modern analysis of the conceptual foundations of statistical mechanics as laid down in Boltzmann's works. The author emphasises the relation between microscopic reversibility and macroscopic irreversibility, explaining fundamental concepts in detail.
Book Synopsis Dynamics of Dissipation by : Piotr Garbaczewski
Download or read book Dynamics of Dissipation written by Piotr Garbaczewski and published by Springer Science & Business Media. This book was released on 2007-08-04 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of lectures treats the dynamics of open systems with a strong emphasis on dissipation phenomena related to dynamical chaos. This research area is very broad, covering topics such as nonequilibrium statistical mechanics, environment-system coupling (decoherence) and applications of Markov semi-groups to name but a few. The book addresses not only experienced researchers in the field but also nonspecialists from related areas of research, postgraduate students wishing to enter the field and lecturers searching for advanced textbook material.
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 Frontiers in Superconducting Materials by : Anant V. Narlikar
Download or read book Frontiers in Superconducting Materials written by Anant V. Narlikar and published by Springer Science & Business Media. This book was released on 2005-12-06 with total page 1122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Frontiers in Superconducting Materials gives a state-of-the-art report of the most important topics of the current research in superconductive materials and related phenomena. It comprises 30 chapters written by renowned international experts in the field. It is of central interest to researchers and specialists in Physics and Materials Science, both in academic and industrial research, as well as advanced students. It also addresses electronic and electrical engineers. Even non-specialists interested in superconductivity might find some useful answers.
Book Synopsis Active Particles, Volume 1 by : Nicola Bellomo
Download or read book Active Particles, Volume 1 written by Nicola Bellomo and published by Birkhäuser. This book was released on 2017-04-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects ten surveys on the modeling, simulation, and applications of active particles using methods ranging from mathematical kinetic theory to nonequilibrium statistical mechanics. The contributing authors are leading experts working in this challenging field, and each of their chapters provides a review of the most recent results in their areas and looks ahead to future research directions. The approaches to studying active matter are presented here from many different perspectives, such as individual-based models, evolutionary games, Brownian motion, and continuum theories, as well as various combinations of these. Applications covered include biological network formation and network theory; opinion formation and social systems; control theory of sparse systems; theory and applications of mean field games; population learning; dynamics of flocking systems; vehicular traffic flow; and stochastic particles and mean field approximation. Mathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.
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.
