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Spectral And Scattering Theory For Quantum Magnetic Systems
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Book Synopsis Spectral and Scattering Theory for Quantum Magnetic Systems, July 7-11, 2008, CIRM, Luminy, Marseilles, France by : Philippe Briet
Download or read book Spectral and Scattering Theory for Quantum Magnetic Systems, July 7-11, 2008, CIRM, Luminy, Marseilles, France written by Philippe Briet and published by American Mathematical Soc.. This book was released on 2009 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Spectral and Scattering Theory for Quantum Magnetic Systems by : Philippe Briet
Download or read book Spectral and Scattering Theory for Quantum Magnetic Systems written by Philippe Briet and published by American Mathematical Soc.. This book was released on 2009 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spectral Theory and Mathematical Physics by : Marius Mantoiu
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.
Book Synopsis Multiparticle Quantum Scattering in Constant Magnetic Fields by : Christian Gérard
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.
Book Synopsis Multiparticle Quantum Scattering in Constant Magnetic Fields by : Christian Gérard
Download or read book Multiparticle Quantum Scattering in Constant Magnetic Fields written by Christian Gérard and published by . This book was released on 2014-05-22 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 an
Book Synopsis Spectral Theory and Geometric Analysis by : Mikhail Aleksandrovich Shubin
Download or read book Spectral Theory and Geometric Analysis written by Mikhail Aleksandrovich Shubin and published by American Mathematical Soc.. This book was released on 2011-02-10 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spectral Theory and Mathematical Physics by : Pablo Miranda
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.
Book Synopsis Dynamical Numbers: Interplay between Dynamical Systems and Number Theory by : S. F. Koli︠a︡da
Download or read book Dynamical Numbers: Interplay between Dynamical Systems and Number Theory written by S. F. Koli︠a︡da and published by American Mathematical Soc.. This book was released on 2010 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Multiparticle Quantum Scattering with Applications to Nuclear, Atomic and Molecular Physics by : Donald G. Truhlar
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.
Book Synopsis Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV by : Victor Ivrii
Download or read book Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV written by Victor Ivrii and published by Springer Nature. This book was released on 2019-09-11 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I, II and III are applied to the Schrödinger and Dirac operators in non-smooth settings and in higher dimensions.
Book Synopsis Microlocal Analysis, Sharp Spectral Asymptotics and Applications II by : Victor Ivrii
Download or read book Microlocal Analysis, Sharp Spectral Asymptotics and Applications II written by Victor Ivrii and published by Springer Nature. This book was released on 2019-09-11 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the local spectral asymptotics of Volume I in the regular part of the domain are combined with variational estimates in the vicinity of singularities, and global asymptotics are derived in the general form. They are then applied to multiple cases and asymptotics with respect to a spectral parameter. Finally, cases in which only general methods but not the results can be applied (non-standard asymptotics) are studied.
Book Synopsis From Complex Analysis to Operator Theory: A Panorama by : Malcolm Brown
Download or read book From Complex Analysis to Operator Theory: A Panorama written by Malcolm Brown and published by Springer Nature. This book was released on 2023-09-21 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Symplectic Topology and Measure Preserving Dynamical Systems by : Albert Fathi
Download or read book Symplectic Topology and Measure Preserving Dynamical Systems written by Albert Fathi and published by American Mathematical Soc.. This book was released on 2010-04-09 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Random Operators by : Michael Aizenman
Download or read book Random Operators written by Michael Aizenman and published by American Mathematical Soc.. This book was released on 2015-12-11 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.
Book Synopsis Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities by : Rupert L. Frank
Download or read book Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities written by Rupert L. Frank and published by Cambridge University Press. This book was released on 2022-11-17 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Set Theory and Its Applications by : Liljana Babinkostova
Download or read book Set Theory and Its Applications written by Liljana Babinkostova and published by American Mathematical Soc.. This book was released on 2011 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Operators and Representation Theory by : Palle E.T. Jorgensen
Download or read book Operators and Representation Theory written by Palle E.T. Jorgensen and published by Courier Dover Publications. This book was released on 2017-06-21 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
