Download or read book C0 Groups Commutator Methods and Spectral Theory of N Body Hamiltonians written by Werner O. Amrein and published by Springer Science & Business Media. This book was released on 2013-11-26 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conjugate operator method is a powerful recently developed technique for studying spectral properties of self-adjoint operators. One of the purposes of this volume is to present a refinement of the original method due to Mourre leading to essentially optimal results in situations as varied as ordinary differential operators, pseudo-differential operators and N-body Schrödinger hamiltonians. Another topic is a new algebraic framework for the N-body problem allowing a simple and systematic treatment of large classes of many-channel hamiltonians. The monograph will be of interest to research mathematicians and mathematical physicists. The authors have made efforts to produce an essentially self-contained text, which makes it accessible to advanced students. Thus about one third of the book is devoted to the development of tools from functional analysis, in particular real interpolation theory for Banach spaces and functional calculus and Besov spaces associated with multi-parameter C0-groups. Certainly this monograph (containing a bibliography of 170 items) is a well-written contribution to this field which is suitable to stimulate further evolution of the theory. (Mathematical Reviews)
Download or read book Co groups Commutator Methods and Spectral Theory of N body Hamiltonians written by Werner O. Amrein and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Co groups Commutator Methods and Spectral Theory of N body Hamiltonians written by Werner O. Amrein and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Theory and Mathematical Physics written by Pablo Miranda and published by Springer Nature. This book was released on 2020-11-12 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains peer-reviewed, selected papers and surveys presented at the conference Spectral Theory and Mathematical Physics (STMP) 2018 which was held in Santiago, Chile, at the Pontifical Catholic University of Chile in December 2018. The original works gathered in this volume reveal the state of the art in the area and reflect the intense cooperation between young researchers in spectral theoryand mathematical physics and established specialists in this field. The list of topics covered includes: eigenvalues and resonances for quantum Hamiltonians; spectral shift function and quantum scattering; spectral properties of random operators; magnetic quantum Hamiltonians; microlocal analysis and its applications in mathematical physics. This volume can be of interest both to senior researchers and graduate students pursuing new research topics in Mathematical Physics.
Download or read book Partial Differential Equations and Spectral Theory written by Michael Demuth and published by Birkhäuser. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of the international conference PDE2000 was to bring together specialists from different areas of modern analysis, mathematical physics and geometry, to discuss not only the recent progress in their own fields but also the interaction between these fields. The special topics of the conference were spectral and scattering theory, semiclassical and asymptotic analysis, pseudodifferential operators and their relation to geometry, as well as partial differential operators and their connection to stochastic analysis and to the theory of semigroups. The scientific advisory board of the conference in Clausthal consisted of M. Ben-Artzi (Jerusalem), Chen Hua (Peking), M. Demuth (Clausthal), T. Ichinose (Kanazawa), L. Rodino (Turin), B.-W. Schulze (Potsdam) and J. Sjöstrand (Paris). The book is aimed at researchers in mathematics and mathematical physics with interests in partial differential equations and all its related fields.
Download or read book Spectral Theory and Partial Differential Equations written by James V Ralston and published by American Mathematical Soc.. This book was released on 2015 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the Conference on Spectral Theory and Partial Differential Equations, held in honor of James Ralston's 70th Birthday. Papers cover important topics in spectral theory and partial differential equations such as inverse problems, both analytical and algebraic; minimal partitions and Pleijel's Theorem; spectral theory for a model in Quantum Field Theory; and beams on Zoll manifolds.
Download or read book Many Body Schr dinger Equation written by Hiroshi Isozaki and published by Springer Nature. This book was released on 2023-08-28 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral properties for Schrödinger operators are a major concern in quantum mechanics both in physics and in mathematics. For the few-particle systems, we now have sufficient knowledge for two-body systems, although much less is known about N-body systems. The asymptotic completeness of time-dependent wave operators was proved in the 1980s and was a landmark in the study of the N-body problem. However, many problems are left open for the stationary N-particle equation. Due to the recent rapid development of computer power, it is now possible to compute the three-body scattering problem numerically, in which the stationary formulation of scattering is used. This means that the stationary theory for N-body Schrödinger operators remains an important problem of quantum mechanics. It is stressed here that for the three-body problem, we have a satisfactory stationary theory. This book is devoted to the mathematical aspects of the N-body problem from both the time-dependent and stationary viewpoints. The main themes are:(1) The Mourre theory for the resolvent of self-adjoint operators(2) Two-body Schrödinger operators—Time-dependent approach and stationary approach(3) Time-dependent approach to N-body Schrödinger operators(4) Eigenfunction expansion theory for three-body Schrödinger operatorsCompared with existing books for the many-body problem, the salient feature of this book consists in the stationary scattering theory (4). The eigenfunction expansion theorem is the physical basis of Schrödinger operators. Recently, it proved to be the basis of inverse problems of quantum scattering. This book provides necessary background information to understand the physical and mathematical basis of Schrödinger operators and standard knowledge for future development.
Download or read book Spectral Theory and Mathematical Physics written by Marius Mantoiu and published by Birkhäuser. This book was released on 2016-06-30 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schrödinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.
Download or read book Multiparticle Quantum Scattering in Constant Magnetic Fields written by Christian Gérard and published by American Mathematical Soc.. This book was released on 2002 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers a rigorous mathematical treatment of the scattering theory of quantum N-particle systems in an external constant magnetic field. In particular, it addresses the question of asymptotic completeness, a classification of all possible trajectories of such systems according to their asymptotic behaviour. The book adopts the so-called time-dependent approach to scattering theory, which relies on a direct study of the Schrodinger unitary group for large times. The modern methods of spectral and scattering theory introduced in the 1980's and 1990's, including the Mourre theory of positive commutators, propagation estimates, and geometrical techniques, are presented and heavily used. Additionally, new methods were developed by the authors in order to deal with the (much less understood) phenomena due to the presence of the magnetic field. The book is a good starting point for graduate students and researchers in mathematical physics who wish to move into this area of research. It includes expository material, research work previously available only in the form of journal articles, as well as some new unpublished results. The treatment of the subject is comprehensive and largely self-contained, and the text is carefully written with attention to detail.
Download or read book Mathematical Results in Quantum Mechanics written by Pavel Exner and published by American Mathematical Soc.. This book was released on 2002 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work contains contributions presented at the conference, QMath-8: Mathematical Results in Quantum Mechanics'', held at Universidad Nacional Autonoma de Mexico in December 2001. The articles cover a wide range of mathematical problems and focus on various aspects of quantum mechanics, quantum field theory and nuclear physics. Topics vary from spectral properties of the Schrodinger equation of various quantum systems to the analysis of quantum computation algorithms. The book should be suitable for graduate students and research mathematicians interested in the mathematical aspects of quantum mechanics.
Download or read book Introduction to Liaison Theory and Deficiency Modules written by Juan C. Migliore and published by Springer Science & Business Media. This book was released on 1998-08-25 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the fall of 1992 I was invited by Professor Changho Keem to visit Seoul National University and give a series of talks. I was asked to write a monograph based on my talks, and the result was published by the Global Analysis Research Center of that University in 1994. The monograph treated deficiency modules and liaison theory for complete intersections. Over the next several years I continually thought of improvements and additions that I would like to make to the manuscript, and at the same time my research led me in directions that gave me a fresh perspective on much of the material, especially in the direction of liaison theory. This re sulted in a dramatic change in the focus of this manuscript, from complete intersections to Gorenstein ideals, and a substantial amount of additions and revisions. It is my hope that this book now serves not only as an introduction to a beautiful subject, but also gives the reader a glimpse at very recent developments and an idea of the direction in which liaison theory is going, at least from my perspective. One theme which I have tried to stress is the tremendous amount of geometry which lies at the heart of the subject, and the beautiful interplay between algebra and geometry. Whenever possible I have given remarks and examples to illustrate this interplay, and I have tried to phrase the results in as geometric a way as possible.
Download or read book Multiparticle Quantum Scattering with Applications to Nuclear Atomic and Molecular Physics written by Donald G. Truhlar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the outcome of a workshop held at the Institute for Mathematics and Its Applications. This institute was founded to promote the interchange of ideas between applied mathematics and the other sciences, and this volume fits into that framework by bringing together the ideas of mathematicians, physicists and chemists in the area of multiparticle scattering theory. The correct formulation of scattering theory for two-body collisions is now well worked out, but systems with three or more particles still present fundamental challenges, both in the formulations of the problem and in the interpretation of computational results. The book begins with two tutorials, one on mathematical issues, including cluster decompositions and asymptotic completeness in N-body quantum systems, and the other on computational approaches to quantum mechanics and time evolution operators, classical action, collisions in laser fields and in magnetic fields, laser-induced processes, barrier resonances, complex dilated expansions, effective potentials for nuclear collisions, long-range potentials, and the Pauli Principle.
Download or read book Harmonic Analysis on the Heisenberg Group written by Sundaram Thangavelu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable.
Download or read book Regulators in Analysis Geometry and Number Theory written by Alexander Reznikov and published by Springer Science & Business Media. This book was released on 2000 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This work is an outgrowth of a conference held at the Hebrew University in Jerusalem on Regulators in Analysis, Geometry and Number Theory, and should appeal to a broad audience of graduate students and research mathematicians."--BOOK JACKET.
Download or read book Compactifications of Symmetric Spaces written by Yves Guivarc'h and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of symmetric space is of central importance in many branches of mathematics. Compactifications of these spaces have been studied from the points of view of representation theory, geometry, and random walks. This work is devoted to the study of the interrelationships among these various compactifications and, in particular, focuses on the martin compactifications. It is the first exposition to treat compactifications of symmetric spaces systematically and to uniformized the various points of view. The work is largely self-contained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students.
Download or read book Geodesic Flows written by Gabriel P. Paternain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present the fundamental concepts and properties of the geodesic flow of a closed Riemannian manifold. The topics covered are close to my research interests. An important goal here is to describe properties of the geodesic flow which do not require curvature assumptions. A typical example of such a property and a central result in this work is Mane's formula that relates the topological entropy of the geodesic flow with the exponential growth rate of the average numbers of geodesic arcs between two points in the manifold. The material here can be reasonably covered in a one-semester course. I have in mind an audience with prior exposure to the fundamentals of Riemannian geometry and dynamical systems. I am very grateful for the assistance and criticism of several people in preparing the text. In particular, I wish to thank Leonardo Macarini and Nelson Moller who helped me with the writing of the first two chapters and the figures. Gonzalo Tomaria caught several errors and contributed with helpful suggestions. Pablo Spallanzani wrote solutions to several of the exercises. I have used his solutions to write many of the hints and answers. I also wish to thank the referee for a very careful reading of the manuscript and for a large number of comments with corrections and suggestions for improvement.
Download or read book Advances in Geometry written by Jean-Luc Brylinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outgrowth of the activities of the Center for Geometry and Mathematical Physics (CGMP) at Penn State from 1996 to 1998. The Center was created in the Mathematics Department at Penn State in the fall of 1996 for the purpose of promoting and supporting the activities of researchers and students in and around geometry and physics at the university. The CGMP brings many visitors to Penn State and has ties with other research groups; it organizes weekly seminars as well as annual workshops The book contains 17 contributed articles on current research topics in a variety of fields: symplectic geometry, quantization, quantum groups, algebraic geometry, algebraic groups and invariant theory, and character istic classes. Most of the 20 authors have talked at Penn State about their research. Their articles present new results or discuss interesting perspec tives on recent work. All the articles have been refereed in the regular fashion of excellent scientific journals. Symplectic geometry, quantization and quantum groups is one main theme of the book. Several authors study deformation quantization. As tashkevich generalizes Karabegov's deformation quantization of Kahler manifolds to symplectic manifolds admitting two transverse polarizations, and studies the moment map in the case of semisimple coadjoint orbits. Bieliavsky constructs an explicit star-product on holonomy reducible sym metric coadjoint orbits of a simple Lie group, and he shows how to con struct a star-representation which has interesting holomorphic properties.
