Spectral And Scattering Theory For Quantum Magnetic Systems

Author : Philippe Briet,François Germinet,Georgi Raikov
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 41,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821858264

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Spectral and Scattering Theory for Quantum Magnetic Systems, July 7-11, 2008, CIRM, Luminy, Marseilles, France by Philippe Briet,François Germinet,Georgi Raikov Pdf

"This volume contains the proceedings of the conference on Spectral and Scattering Theory for Quantum Magnetic Systems, which took place at CIRM, Luminy, France, in July 2008. The main purpose of this conference was to bring together a number of specialists in the mathematical modelling of magnetic phenomena in quantum mechanics, to mark the recent progress as well as to outline the future development in this area. This volume contains original results presented by some of the invited speakers and surveys on recent advances in the mathematical theory of quantum magnetic Hamiltonians. Most of the talks at the conference, as well as the articles in this volume, have been dedicated to one of the following topics: Spectral and scattering theory for magnetic Schrödinger operators ; Magnetic Pauli and Dirac operators ; Magnetic operators on manifolds ; Microlocal analysis of magnetic Hamiltonians ; Random Schrödinger operators and quantum Hall effect ; Ginsburg-Landau equation, supraconductivity, magnetic bottles ; Bose-Einstein condensate, Gross-Pitaevski equation ; Magnetic Lieb-Thirring inequalities, stability of matter."--Publisher's website.

Author : Philippe Briet,François Germinet,Georgi Raikov
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 42,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847442

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Spectral and Scattering Theory for Quantum Magnetic Systems by Philippe Briet,François Germinet,Georgi Raikov Pdf

Contains the proceedings of the conference on Spectral and Scattering Theory for Quantum Magnetic Systems, which took place at CIRM, Luminy, France, in July 2008. This volume includes original results presented by some of the invited speakers and surveys on advances in the mathematical theory of quantum magnetic Hamiltonians.

Author : Christian Gérard,Izabella Łaba
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 48,9 Mb
Release : 2002
Category : Few-body problem
ISBN : 9780821829196

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Multiparticle Quantum Scattering in Constant Magnetic Fields by Christian Gérard,Izabella Łaba Pdf

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.

Author : Marius Mantoiu,Georgi Raikov,Rafael Tiedra de Aldecoa
Publisher : Birkhäuser
Page : 0 pages
File Size : 44,5 Mb
Release : 2016-07-01
Category : Mathematics
ISBN : 3319299905

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Spectral Theory and Mathematical Physics by Marius Mantoiu,Georgi Raikov,Rafael Tiedra de Aldecoa Pdf

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.

Author : Christian Gérard
Publisher : Unknown
Page : 258 pages
File Size : 47,7 Mb
Release : 2014-05-22
Category : SCIENCE
ISBN : 1470413175

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Multiparticle Quantum Scattering in Constant Magnetic Fields by Christian Gérard Pdf

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 an

Author : Mikhail Aleksandrovich Shubin,Maxim Braverman
Publisher : American Mathematical Soc.
Page : 223 pages
File Size : 42,9 Mb
Release : 2011-02-10
Category : Mathematics
ISBN : 9780821849484

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Spectral Theory and Geometric Analysis by Mikhail Aleksandrovich Shubin,Maxim Braverman Pdf

The papers in this volume cover important topics in spectral theory and geometric analysis such as resolutions of smooth group actions, spectral asymptotics, solutions of the Ginzburg-Landau equation, scattering theory, Riemann surfaces of infinite genus and tropical mathematics.

Author : S. F. Koli︠a︡da
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 55,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849583

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Dynamical Numbers: Interplay between Dynamical Systems and Number Theory by S. F. Koli︠a︡da Pdf

This volume contains papers from the special program and international conference on Dynamical Numbers which were held at the Max-Planck Institute in Bonn, Germany in 2009. These papers reflect the extraordinary range and depth of the interactions between ergodic theory and dynamical systems and number theory. Topics covered in the book include stationary measures, systems of enumeration, geometrical methods, spectral methods, and algebraic dynamical systems.

Author : Donald G. Truhlar,Barry Simon
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461218708

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Multiparticle Quantum Scattering with Applications to Nuclear, Atomic and Molecular Physics by Donald G. Truhlar,Barry Simon Pdf

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.

Author : Albert Fathi,Yong-Geun Oh,Claude Viterbo
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 55,7 Mb
Release : 2010-04-09
Category : Mathematics
ISBN : 9780821848920

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Symplectic Topology and Measure Preserving Dynamical Systems by Albert Fathi,Yong-Geun Oh,Claude Viterbo Pdf

The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference on Symplectic Topology and Measure Preserving Dynamical Systems held in Snowbird, Utah in July 2007. The aim of the conference was to bring together specialists of symplectic topology and of measure preserving dynamics to try to connect these two subjects. One of the motivating conjectures at the interface of these two fields is the question of whether the group of area preserving homeomorphisms of the 2-disc is or is not simple. For diffeomorphisms it was known that the kernel of the Calabi invariant is a normal proper subgroup, so the group of area preserving diffeomorphisms is not simple. Most articles are related to understanding these and related questions in the framework of modern symplectic topology.

Author : Malcolm Brown,Fritz Gesztesy,Pavel Kurasov,Ari Laptev,Barry Simon,Gunter Stolz,Ian Wood
Publisher : Springer Nature
Page : 731 pages
File Size : 54,6 Mb
Release : 2023-09-21
Category : Mathematics
ISBN : 9783031311390

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From Complex Analysis to Operator Theory: A Panorama by Malcolm Brown,Fritz Gesztesy,Pavel Kurasov,Ari Laptev,Barry Simon,Gunter Stolz,Ian Wood Pdf

This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.

Author : Rupert L. Frank,Ari Laptev,Timo Weidl
Publisher : Cambridge University Press
Page : 524 pages
File Size : 55,9 Mb
Release : 2022-11-17
Category : Mathematics
ISBN : 9781009218443

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Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities by Rupert L. Frank,Ari Laptev,Timo Weidl Pdf

The analysis of eigenvalues of Laplace and Schrödinger operators is an important and classical topic in mathematical physics with many applications. This book presents a thorough introduction to the area, suitable for masters and graduate students, and includes an ample amount of background material on the spectral theory of linear operators in Hilbert spaces and on Sobolev space theory. Of particular interest is a family of inequalities by Lieb and Thirring on eigenvalues of Schrödinger operators, which they used in their proof of stability of matter. The final part of this book is devoted to the active research on sharp constants in these inequalities and contains state-of-the-art results, serving as a reference for experts and as a starting point for further research.

Author : Liljana Babinkostova
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 43,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821848128

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Set Theory and Its Applications by Liljana Babinkostova Pdf

This book consists of several survey and research papers covering a wide range of topics in active areas of set theory and set theoretic topology. Some of the articles present, for the first time in print, knowledge that has been around for several years and known intimately to only a few experts. The surveys bring the reader up to date on the latest information in several areas that have been surveyed a decade or more ago. Topics covered in the volume include combinatorial and descriptive set theory, determinacy, iterated forcing, Ramsey theory, selection principles, set-theoretic topology, and universality, among others. Graduate students and researchers in logic, especially set theory, descriptive set theory, and set-theoretic topology, will find this book to be a very valuable reference.

Author : Palle E.T. Jorgensen
Publisher : Courier Dover Publications
Page : 307 pages
File Size : 54,5 Mb
Release : 2017-06-21
Category : Science
ISBN : 9780486815725

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Operators and Representation Theory by Palle E.T. Jorgensen Pdf

Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 51,7 Mb
Release : 2024-06-17
Category : Electronic
ISBN : 9789814465052

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XVIth International Congress on Mathematical Physics by Anonim Pdf

Author : A. Kechris,N. Makarov,D. Ramakrishnan,X. Zhu
Publisher : American Mathematical Soc.
Page : 221 pages
File Size : 41,9 Mb
Release : 2021-09-24
Category : Education
ISBN : 9781470454906

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Nine Mathematical Challenges: An Elucidation by A. Kechris,N. Makarov,D. Ramakrishnan,X. Zhu Pdf

This volume stems from the Linde Hall Inaugural Math Symposium, held from February 22–24, 2019, at California Institute of Technology, Pasadena, California. The content isolates and discusses nine mathematical problems, or sets of problems, in a deep way, but starting from scratch. Included among them are the well-known problems of the classification of finite groups, the Navier-Stokes equations, the Birch and Swinnerton-Dyer conjecture, and the continuum hypothesis. The other five problems, also of substantial importance, concern the Lieb–Thirring inequalities, the equidistribution problems in number theory, surface bundles, ramification in covers and curves, and the gap and type problems in Fourier analysis. The problems are explained succinctly, with a discussion of what is known and an elucidation of the outstanding issues. An attempt is made to appeal to a wide audience, both in terms of the field of expertise and the level of the reader.