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Author : Isabelle Catto
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (493 download)
Download or read book Analyse mathematique de modeles de la mecanique quantique written by Isabelle Catto and published by . This book was released on 1992 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Isabelle Catto
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (18 download)
Download or read book Analyse mathématique de modèles de la mécanique quantique written by Isabelle Catto and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cette thèse regroupe un ensemble de travaux relatifs à l'étude de problèmes de minimisation qui se posent dans la modélisation par la mécanique quantique des atomes et des molécules, en physique atomique, d'une part, et des noyaux, en physique nucléaire, d'autre part. Les deux parties de cette thèse traitent successivement de ces deux types de problèmes. Dans la première partie, nous nous intéressons à l'existence d'une géométrie optimale des noyaux, pour un ion ou une molécule donnés, dans le cadre des modèles de type Thomas-Fermi, de Hartree et de Hartree-Fock. La seconde partie est consacrée à l'étude de deux familles de modèles de la physique nucléaire : des modèles de type Hartree et un modèle de Hartree-Fock avec un potentiel simplifie de type Skyrme. Dans les deux cas, les questions posées se traduisent en termes de problèmes de minimisation dans l'espace à trois dimensions, invariants par translation, par le biais d'une fonctionnelle (d'énergie) dépendant d'une ou plusieurs fonctions soumises à diverses contraintes de normalisation. La perte de compacité des suites minimisantes, liée à l'invariance par translation, est analysée par la méthode de concentration-compacité
Author : Eric Cances
Publisher : Springer Science & Business Media
ISBN 13 : 3540376615
Total Pages : 420 pages
Book Rating : 4.5/5 (43 download)
Download or read book Méthodes mathématiques en chimie quantique. Une introduction written by Eric Cances and published by Springer Science & Business Media. This book was released on 2006-09-09 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ce cours est une introduction à la modélisation mathématique et à l'analyse numérique pour la chimie moléculaire quantique, un champ peu connu des mathématiciens et pourtant riche en sujets d'investigation. Le point de vue choisi est celui du mathématicien appliqué. Le cours est construit de manière auto-consistante.
Author : John Von Neumann
Publisher :
ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.:/5 (5 download)
Download or read book Les fondements mathématiques de la mécanique quantique written by John Von Neumann and published by . This book was released on 1947 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Brigitte Bidégaray-Fesquet
Publisher : Springer Science & Business Media
ISBN 13 : 3540377255
Total Pages : 180 pages
Book Rating : 4.5/5 (43 download)
Download or read book Hiérarchie de modèles en optique quantique written by Brigitte Bidégaray-Fesquet and published by Springer Science & Business Media. This book was released on 2006-08-31 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cet ouvrage présente les modèles d'interaction onde-matière faisant intervenir une description quantique de la matière (optique quantique), ainsi que des modèles classiques qui en sont dérivés. L'objectif est de décrypter pour des lecteurs mathématiciens ces modèles habituellement décrits dans des livres de physique et de donner les résultats mathématiques et les méthodes numériques existants.
Author : Boris Feigin
Publisher : World Scientific
ISBN 13 : 9814462926
Total Pages : 517 pages
Book Rating : 4.8/5 (144 download)
Download or read book New Trends In Quantum Integrable Systems - Proceedings Of The Infinite Analysis 09 written by Boris Feigin and published by World Scientific. This book was released on 2010-10-29 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project “Method of Algebraic Analysis in Integrable Systems” in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years.Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics.Through these topics, the reader can learn about the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.
Author : Boris Feigin
Publisher : World Scientific
ISBN 13 : 9814324361
Total Pages : 517 pages
Book Rating : 4.8/5 (143 download)
Download or read book New Trends in Quantum Integrable Systems written by Boris Feigin and published by World Scientific. This book was released on 2010-10-29 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems" in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years. Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics. Through these topics, the reader is exposed to the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.
Author : Matthias Ehrhardt
Publisher : Springer
ISBN 13 : 3319014277
Total Pages : 337 pages
Book Rating : 4.3/5 (19 download)
Download or read book Multi-Band Effective Mass Approximations written by Matthias Ehrhardt and published by Springer. This book was released on 2014-07-17 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses several mathematical models from the most relevant class of kp-Schrödinger systems. Both mathematical models and state-of-the-art numerical methods for adequately solving the arising systems of differential equations are presented. The operational principle of modern semiconductor nano structures, such as quantum wells, quantum wires or quantum dots, relies on quantum mechanical effects. The goal of numerical simulations using quantum mechanical models in the development of semiconductor nano structures is threefold: First they are needed for a deeper understanding of experimental data and of the operational principle. Secondly, they allow us to predict and optimize in advance the qualitative and quantitative properties of new devices in order to minimize the number of prototypes needed. Semiconductor nano structures are embedded as an active region in semiconductor devices. Thirdly and finally, the results of quantum mechanical simulations of semiconductor nano structures can be used with upscaling methods to deliver parameters needed in semi-classical models for semiconductor devices, such as quantum well lasers. This book covers in detail all these three aspects using a variety of illustrative examples. Readers will gain detailed insights into the status of the multiband effective mass method for semiconductor nano structures. Both users of the kp method as well as advanced researchers who want to advance the kp method further will find helpful information on how to best work with this method and use it as a tool for characterizing the physical properties of semiconductor nano structures. The book is primarily intended for graduate and Ph.D. students in applied mathematics, mathematical physics and theoretical physics, as well as all those working in quantum mechanical research or the semiconductor / opto-electronic industry who are interested in new mathematical aspects.
Author : Huzihiro Araki
Publisher : Springer Science & Business Media
ISBN 13 : 9401728232
Total Pages : 452 pages
Book Rating : 4.4/5 (17 download)
Download or read book Quantum and Non-Commutative Analysis written by Huzihiro Araki and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.
Author : Asao Arai
Publisher : World Scientific
ISBN 13 : 9813207132
Total Pages : 893 pages
Book Rating : 4.8/5 (132 download)
Download or read book Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields: An Introduction To Mathematical Analysis Of Quantum Fields written by Asao Arai and published by World Scientific. This book was released on 2017-12-20 with total page 893 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation relations and canonical anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and a short description to each model is given.To graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory, this book is a good introductory text. It is also well suited for self-study and will provide readers a firm foundation of knowledge and mathematical techniques for reading more advanced books and current research articles in the field of mathematical analysis on quantum fields. Also, numerous problems are added to aid readers to develop a deeper understanding of the field.
Author : P.E.T. Jorgensen
Publisher : Elsevier
ISBN 13 : 0080872581
Total Pages : 347 pages
Book Rating : 4.0/5 (88 download)
Download or read book Operators and Representation Theory written by P.E.T. Jorgensen and published by Elsevier. This book was released on 1987-12-01 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly elegant manner by the use of Lie algebras, extensions, and projective representations. In several cases, this Lie algebraic approach to questions in mathematical physics and C*-algebra theory is new; for example, the Lie algebraic treatment of the spectral theory of curved magnetic field Hamiltonians, the treatment of irrational rotation type algebras, and the Virasoro algebra.Also examined are C*-algebraic methods used (in non-traditional ways) in the study of representations of infinite-dimensional Lie algebras and their extensions, and the methods developed by A. Connes and M.A. Rieffel for the study of the Yang-Mills problem.Cutting across traditional separations between fields of specialization, the book addresses a broad audience of graduate students and researchers.
Author : Mathieu Lewin
Publisher : Springer
ISBN 13 : 9783030934354
Total Pages : 330 pages
Book Rating : 4.9/5 (343 download)
Download or read book Théorie spectrale et mécanique quantique written by Mathieu Lewin and published by Springer. This book was released on 2022-04-08 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ce livre présente la théorie spectrale des opérateurs auto-adjoints en dimension infinie ainsi que son application à la mécanique quantique. Le concept d'auto-adjonction, découvert par John von Neumann dans les années 1930, est bien plus subtil dans ce cadre que pour les matrices hermitiennes en dimension finie. Cet ouvrage peut aussi servir d’introduction mathématique à la mécanique quantique. De multiples exemples physiques servent ainsi à illustrer et motiver les théorèmes plus abstraits. Les deux derniers chapitres présentent des résultats plus récents concernant l'équation de Schrödinger pour les atomes, les molécules et les solides. Aucune connaissance physique n'est cependant requise pour lire ces pages. Premier livre en français sur le sujet destiné aux étudiants de Master, ce livre pourra accompagner un cours à ce niveau. Il devrait aussi être utile aux lecteurs plus avancés désirant en savoir plus sur cette théorie. *** This book presents the spectral theory of self-adjoint operators on Hilbert space, with applications to quantum mechanics. The concept of self-adjointness in infinite dimension was discovered by John von Neumann in the 1930s and it is much more involved than in the case of Hermitian matrices in finite dimension. The book also provides an introduction to quantum mechanics, suitable for students with a mathematics background. The presentation provides numerous physical examples illustrating the abstract theory. The last two chapters present recent results on Schrödinger’s equation for systems of particles. No previous knowledge of physics is required for the book. Based on the author’s teaching and intended for graduate courses, this French language textbook can also serve as a useful introduction to the topic for more advanced readers.
Author : C.B. Wang
Publisher : Springer Science & Business Media
ISBN 13 : 3642385656
Total Pages : 222 pages
Book Rating : 4.6/5 (423 download)
Download or read book Application of Integrable Systems to Phase Transitions written by C.B. Wang and published by Springer Science & Business Media. This book was released on 2013-07-20 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The eigenvalue densities in various matrix models in quantum chromodynamics (QCD) are ultimately unified in this book by a unified model derived from the integrable systems. Many new density models and free energy functions are consequently solved and presented. The phase transition models including critical phenomena with fractional power-law for the discontinuities of the free energies in the matrix models are systematically classified by means of a clear and rigorous mathematical demonstration. The methods here will stimulate new research directions such as the important Seiberg-Witten differential in Seiberg-Witten theory for solving the mass gap problem in quantum Yang-Mills theory. The formulations and results will benefit researchers and students in the fields of phase transitions, integrable systems, matrix models and Seiberg-Witten theory.
Author : Sébastien Poinat
Publisher : Hermann
ISBN 13 : 9782705688639
Total Pages : 506 pages
Book Rating : 4.6/5 (886 download)
Download or read book Mécanique quantique written by Sébastien Poinat and published by Hermann. This book was released on 2014 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cet ouvrage est une contribution a la question: comment faut-il comprendre la mecanique quantique ? La reponse que defend l'auteur est qu'il ne faut pas chercher a l'interpreter mais qu'il faut au contraire prendre au serieux ce qu'elle dit explicitement, sans intermediaire ni reformulation. Cette perspective est defendue a partir de l'analyse d'un argument qui mobilise la mecanique quantique en faveur de la these emergentiste contre le reductionnisme. Sans chercher a arbitrer cette querelle de facon generale, l'auteur s'attache a montrer que cet argument est d'emblee biaise par l'utilisation d'un langage qui ne convient pas a la mecanique quantique. Seule une attention soutenue aux concepts propres a la mecanique quantique et a son langage peut nous permettre de saisir ce qu'elle nous invite a faire: revoir une bonne partie de notre systeme conceptuel et penser differemment.
Author : A Kundu
Publisher : CRC Press
ISBN 13 : 9781420034615
Total Pages : 320 pages
Book Rating : 4.0/5 (346 download)
Download or read book Classical and Quantum Nonlinear Integrable Systems written by A Kundu and published by CRC Press. This book was released on 2019-04-23 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories
Author : Stéphane Attal
Publisher : Springer Science & Business Media
ISBN 13 : 3540309926
Total Pages : 254 pages
Book Rating : 4.5/5 (43 download)
Download or read book Open Quantum Systems II written by Stéphane Attal and published by Springer Science & Business Media. This book was released on 2006-06-07 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.
Author : Claude Aslangul
Publisher : De Boeck Supérieur
ISBN 13 : 2804168352
Total Pages : 185 pages
Book Rating : 4.8/5 (41 download)
Download or read book Mécanique quantique written by Claude Aslangul and published by De Boeck Supérieur. This book was released on 2011-11-22 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: L'essentiel de la mécanique quantique en moins de 130 pages. Une synthèse pour réviser ou découvrir les points fondamentaux de la discipline. Cette synthèse a un double objectif : d'une part permettre aux étudiants ayant acquis des connaissances approfondies d'effectuer des révisions rapides ; d'autre part, donner la possibilité à des lecteurs néophytes de se familiariser avec la théorie quantique grâce à un exposé clair des concepts et des idées. Un index en fin d'ouvrage vous permettra de retrouver rapidement les notions sur lesquelles vous souhaitez faire le point, et une bibliographie vous orientera pour un approfondissement des sujets.
