Effective Evolution Equations From Many Body Quantum Mechanics PDF Download
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Author | : Niels Benedikter |
Publisher | : Springer |
Total Pages | : 97 |
Release | : 2015-11-04 |
Genre | : Science |
ISBN | : 3319248987 |
Download Effective Evolution Equations from Quantum Dynamics Book in PDF, ePub and Kindle
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.
Author | : Niels Benedikter |
Publisher | : |
Total Pages | : 154 |
Release | : 2014 |
Genre | : |
ISBN | : |
Download Effective evolution equations from many-body quantum mechanics Book in PDF, ePub and Kindle
Author | : David Ellwood |
Publisher | : American Mathematical Soc. |
Total Pages | : 587 |
Release | : 2013-06-26 |
Genre | : Mathematics |
ISBN | : 0821868616 |
Download Evolution Equations Book in PDF, ePub and Kindle
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).
Author | : Nikolai Leopold |
Publisher | : |
Total Pages | : |
Release | : 2018 |
Genre | : |
ISBN | : |
Download Effective Evolution Equations from Quantum Mechanics Book in PDF, ePub and Kindle
Author | : Henrik Bruus |
Publisher | : Oxford University Press |
Total Pages | : 458 |
Release | : 2004-09-02 |
Genre | : Science |
ISBN | : 0198566336 |
Download Many-Body Quantum Theory in Condensed Matter Physics Book in PDF, ePub and Kindle
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.
Author | : Pavel Exner |
Publisher | : World Scientific |
Total Pages | : 709 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 9814304638 |
Download XVIth International Congress on Mathematical Physics Book in PDF, ePub and Kindle
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.
Author | : Arne Jensen |
Publisher | : World Scientific |
Total Pages | : 743 |
Release | : 2014 |
Genre | : Science |
ISBN | : 9814449245 |
Download XVIIth International Congress on Mathematical Physics Book in PDF, ePub and Kindle
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.
Author | : Alessandro Michelangeli |
Publisher | : Springer |
Total Pages | : 292 |
Release | : 2017-08-01 |
Genre | : Mathematics |
ISBN | : 3319589040 |
Download Advances in Quantum Mechanics Book in PDF, ePub and Kindle
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.
Author | : Berthold-georg Englert |
Publisher | : World Scientific |
Total Pages | : 397 |
Release | : 2023-02-10 |
Genre | : Science |
ISBN | : 9811272166 |
Download Density Functionals For Many-particle Systems: Mathematical Theory And Physical Applications Of Effective Equations Book in PDF, ePub and Kindle
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.
Author | : Daniela Cadamuro |
Publisher | : Springer |
Total Pages | : 257 |
Release | : 2018-10-26 |
Genre | : Science |
ISBN | : 3030016021 |
Download Macroscopic Limits of Quantum Systems Book in PDF, ePub and Kindle
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.