Physics And Mathematics Of Quantum Many Body Systems

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Physics and Mathematics of Quantum Many-Body Systems

Hal Tasaki
Physics and Mathematics of Quantum Many Body Systems Book PDF

Author : Hal Tasaki
Publisher : Springer Nature
Page : 534 pages
File Size : 41,7 Mb
Release : 2020-05-07
Category : Technology & Engineering
ISBN : 9783030412654

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Physics and Mathematics of Quantum Many-Body Systems by Hal Tasaki Pdf

This book is a self-contained advanced textbook on the mathematical-physical aspects of quantum many-body systems, which begins with a pedagogical presentation of the necessary background information before moving on to subjects of active research, including topological phases of matter. The book explores in detail selected topics in quantum spin systems and lattice electron systems, namely, long-range order and spontaneous symmetry breaking in the antiferromagnetic Heisenberg model in two or higher dimensions (Part I), Haldane phenomena in antiferromagnetic quantum spin chains and related topics in topological phases of quantum matter (Part II), and the origin of magnetism in various versions of the Hubbard model (Part III). Each of these topics represents certain nontrivial phenomena or features that are invariably encountered in a variety of quantum many-body systems, including quantum field theory, condensed matter systems, cold atoms, and artificial quantum systems designed for future quantum computers. The book’s main focus is on universal properties of quantum many-body systems. The book includes roughly 50 problems with detailed solutions. The reader only requires elementary linear algebra and calculus to comprehend the material and work through the problems. Given its scope and format, the book is suitable both for self-study and as a textbook for graduate or advanced undergraduate classes.

The Quantum Mechanics of Many-Body Systems

D.J. Thouless
The Quantum Mechanics of Many Body Systems Book PDF

Author : D.J. Thouless
Publisher : Courier Corporation
Page : 256 pages
File Size : 49,7 Mb
Release : 2014-01-15
Category : Science
ISBN : 9780486493572

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The Quantum Mechanics of Many-Body Systems by D.J. Thouless Pdf

"Unabridged republication of the second edition of the work, originally published in the Pure and applied physics series by Academic Press, Inc., New York, in 1972"--Title page verso.

Mathematical Methods of Many-Body Quantum Field Theory

Detlef Lehmann
Mathematical Methods of Many Body Quantum Field Theory Book PDF

Author : Detlef Lehmann
Publisher : CRC Press
Page : 264 pages
File Size : 50,9 Mb
Release : 2004-08-30
Category : Mathematics
ISBN : 9781482286052

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Mathematical Methods of Many-Body Quantum Field Theory by Detlef Lehmann Pdf

Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theo

Quantum Many-Body Systems in One Dimension

Zachary N C Ha
Quantum Many Body Systems in One Dimension Book PDF

Author : Zachary N C Ha
Publisher : World Scientific
Page : 168 pages
File Size : 51,8 Mb
Release : 1996-09-13
Category : Science
ISBN : 9789814500371

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Quantum Many-Body Systems in One Dimension by Zachary N C Ha Pdf

The main theme of the book is the intimate connection between the two families of exactly solvable models: the inverse-square exchange (ISE) and the nearest-neighbor exchange (NNE) models. The latter are better known as the Bethe-Ansatz solvable models and include the Heisenberg spin chain, t–J models and Hubbard models. The former, the Calogero–Sutherland family of models, are simple to solve and contain essentially the same physics as the NNE family. The author introduces and discusses current topics, such as the Luttinger liquid concept, fractional statistics, and spin–charge separation, in the context of the explicit models. Contents:IntroductionHeisenberg Spin ChainThe 1D Hubbard ModelModels with Inverse-Square ExchangeStrings in Long-Range Interaction ModelElementary Excitations of t-J ModelFractional Statistics in One-Dimension: View from an Exactly Solvable ModelConcluding Remarks Readership: Graduate students, researchers in statistical mechanics, mathematical physics and condensed matter physics. keywords:Quantum;Many-Body;One;Inverse Square;Exchange;Luttinger;Fractional Statistics

Quantum Theory of Many-Body Systems

Alexandre Zagoskin
Quantum Theory of Many Body Systems Book PDF

Author : Alexandre Zagoskin
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461205951

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Quantum Theory of Many-Body Systems by Alexandre Zagoskin Pdf

Intended for graduates in physics and related fields, this is a self-contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, covers all the important diagram techniques for normal and superconducting systems, including the zero-temperature perturbation theory, and the Matsubara, Keldysh, and Nambu-Gorov formalisms. The aim is not to be exhaustive, but to present just enough detail to enable students to follow the current research literature or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum coherence is maintained throughout the volume, and which therefore provides an ideal testing ground for many-body theories. '

Mathematical Methods of Many-Body Quantum Field Theory

Detlef Lehmann
Mathematical Methods of Many Body Quantum Field Theory Book PDF

Author : Detlef Lehmann
Publisher : CRC Press
Page : 265 pages
File Size : 50,7 Mb
Release : 2004-08-30
Category : Science
ISBN : 9781420035018

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Mathematical Methods of Many-Body Quantum Field Theory by Detlef Lehmann Pdf

Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations. Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and when they break down. At the same time, its clear explanations and methodical, step-by-step calculations shed welcome light on the established physics literature.

Many-Body Quantum Theory in Condensed Matter Physics

Henrik Bruus,Karsten Flensberg,ØRsted Laboratory Niels Bohr Institute Karsten Flensberg
Many Body Quantum Theory in Condensed Matter Physics Book PDF

Author : Henrik Bruus,Karsten Flensberg,ØRsted Laboratory Niels Bohr Institute Karsten Flensberg
Publisher : Oxford University Press
Page : 458 pages
File Size : 51,5 Mb
Release : 2004-09-02
Category : Science
ISBN : 9780198566335

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Many-Body Quantum Theory in Condensed Matter Physics by Henrik Bruus,Karsten Flensberg,ØRsted Laboratory Niels Bohr Institute Karsten Flensberg Pdf

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.

Quantum Field Theory of Many-Body Systems

Xiao-Gang Wen
Quantum Field Theory of Many Body Systems Book PDF

Author : Xiao-Gang Wen
Publisher : OUP Oxford
Page : 520 pages
File Size : 42,9 Mb
Release : 2004-06-04
Category : Science
ISBN : 9780191523960

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Quantum Field Theory of Many-Body Systems by Xiao-Gang Wen Pdf

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalisation, topological order, emergent gauge bosons and fermions, and string condensation. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and fermions in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods (which have fuelled the rapid developments) in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature. Topics covered are dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological and quantum order, spin liquids, and string condensation. Methods covered are the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, slave-boson theory, and exactly soluble models beyond one-dimension. This book is aimed at teaching graduate students and bringing them to the frontiers of research in condensed matter physics.

Many-Body Physics, Topology and Geometry

Siddhartha Sen,Kumar Sankar Gupta
Many Body Physics Topology and Geometry Book PDF

Author : Siddhartha Sen,Kumar Sankar Gupta
Publisher : World Scientific
Page : 220 pages
File Size : 53,6 Mb
Release : 2015-06-15
Category : Science
ISBN : 9789814678186

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Many-Body Physics, Topology and Geometry by Siddhartha Sen,Kumar Sankar Gupta Pdf

The book explains concepts and ideas of mathematics and physics that are relevant for advanced students and researchers of condensed matter physics. With this aim, a brief intuitive introduction to many-body theory is given as a powerful qualitative tool for understanding complex systems. The important emergent concept of a quasiparticle is then introduced as a way to reduce a many-body problem to a single particle quantum problem. Examples of quasiparticles in graphene, superconductors, superfluids and in a topological insulator on a superconductor are discussed. The mathematical idea of self-adjoint extension, which allows short distance information to be included in an effective long distance theory through boundary conditions, is introduced through simple examples and then applied extensively to analyse and predict new physical consequences for graphene. The mathematical discipline of topology is introduced in an intuitive way and is then combined with the methods of differential geometry to show how the emergence of gapless states can be understood. Practical ways of carrying out topological calculations are described. Contents:OverviewMany-Body TheoryTopology and GeometryBoundary Conditions and Self-Adjoint ExtensionsElectronic Properties of Graphene Readership: Graduate students and researchers in condensed matter physics and mathematical physics. Key Features:Topics are of current interest, e.g. graphene, topological insulators, Majorana fermionsIs self-contained and provides all the background material necessary to understand the physical or mathematical concepts discussedPractical ways of using topology, self-adjoint extensions as well as ways of making qualitative estimates in physics are explained and then illustrated by examplesKeywords:Condensed Matter Physics;Topology;Differential Geometry;Many-Body Problem;Graphene;Self-Adjoint Extensions;K-Theory;Quasiparticles;Superconductivity;Superfluidity;Topological Insulator;Mathematical Physics

Quantum Many-Body Physics in a Nutshell

Edward Shuryak
Quantum Many Body Physics in a Nutshell Book PDF

Author : Edward Shuryak
Publisher : Princeton University Press
Page : 306 pages
File Size : 45,9 Mb
Release : 2018-11-27
Category : Science
ISBN : 9780691175607

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Quantum Many-Body Physics in a Nutshell by Edward Shuryak Pdf

The ideal textbook for a one-semester introductory course for graduate students or advanced undergraduates This book provides an essential introduction to the physics of quantum many-body systems, which are at the heart of atomic and nuclear physics, condensed matter, and particle physics. Unlike other textbooks on the subject, it covers topics across a broad range of physical fields—phenomena as well as theoretical tools—and does so in a simple and accessible way. Edward Shuryak begins with Feynman diagrams of the quantum and statistical mechanics of a particle; in these applications, the diagrams are easy to calculate and there are no divergencies. He discusses the renormalization group and illustrates its uses, and covers systems such as weakly and strongly coupled Bose and Fermi gases, electron gas, nuclear matter, and quark-gluon plasmas. Phenomena include Bose condensation and superfluidity. Shuryak also looks at Cooper pairing and superconductivity for electrons in metals, liquid 3He, nuclear matter, and quark-gluon plasma. A recurring topic throughout is topological matter, ranging from ensembles of quantized vortices in superfluids and superconductors to ensembles of colored (QCD) monopoles and instantons in the QCD vacuum. Proven in the classroom, Quantum Many-Body Physics in a Nutshell is the ideal textbook for a one-semester introductory course for graduate students or advanced undergraduates. Teaches students how quantum many-body systems work across many fields of physics Uses path integrals from the very beginning Features the easiest introduction to Feynman diagrams available Draws on the most recent findings, including trapped Fermi and Bose atomic gases Guides students from traditional systems, such as electron gas and nuclear matter, to more advanced ones, such as quark-gluon plasma and the QCD vacuum

Introduction to Many-Body Physics

Piers Coleman
Introduction to Many Body Physics Book PDF

Author : Piers Coleman
Publisher : Cambridge University Press
Page : 815 pages
File Size : 45,8 Mb
Release : 2015-11-26
Category : Science
ISBN : 9780521864886

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Introduction to Many-Body Physics by Piers Coleman Pdf

This book explains the tools and concepts needed for a research-level understanding of the subject, for graduate students in condensed matter physics.

Quantum Field Theory of Many-Body Systems

Xiao-Gang Wen
Quantum Field Theory of Many Body Systems Book PDF

Author : Xiao-Gang Wen
Publisher : Oxford University Press
Page : 520 pages
File Size : 47,6 Mb
Release : 2004-06-03
Category : Science
ISBN : 9780198530947

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Quantum Field Theory of Many-Body Systems by Xiao-Gang Wen Pdf

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalisation, topological order, emergent gauge bosons andfermions, and string condensation. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and fermions in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods(which have fuelled the rapid developments) in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature. Topics covered are dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phasetransitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological and quantum order, spin liquids, and string condensation. Methods covered are the path integral, Green's functions, mean-field theory, effective theory, renormalization group,bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, slave-boson theory, and exactly soluble models beyond one-dimension. This book is aimed at teaching graduate students and bringing them to the frontiers of research in condensed matterphysics.

Many-Body Boson Systems

André F. Verbeure
Many Body Boson Systems Book PDF

Author : André F. Verbeure
Publisher : Springer
Page : 190 pages
File Size : 41,8 Mb
Release : 2010-11-25
Category : Mathematics
ISBN : 9780857291097

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Many-Body Boson Systems by André F. Verbeure Pdf

This book offers a modern way of dealing with the problems of equilibrium states of Bose systems. Starting with the variation principle of statistical mechanics and the energy-entropy balance principle as equilibrium criteria, results for general boson systems and models are explicitly derived using simple functional analytic calculus. Bridging the gap between general theoretical physics and the phenomenological research in the field of Bose systems, this book provides an insight into the fascinating quantum world of bosons. Key topics include the occurrence of BEC and its intimate structural relation with the phenomena of spontaneous symmetry breaking and off-diagonal long range order; the condensate equation; the issue concerning the choice of boundary conditions; solvable versus non-solvable boson models; the set of quasi-free boson states; the role of dissipative perturbations; and the surprising but general relation between general quantum fluctuations and boson systems. Only some knowledge of quantum mechanics and undergraduate algebra and analysis is assumed. This textbook brings students and researchers smoothly from general concepts to vivid applications.

Advanced Quantum Condensed Matter Physics

Michael El-Batanouny
Advanced Quantum Condensed Matter Physics Book PDF

Author : Michael El-Batanouny
Publisher : Cambridge University Press
Page : 839 pages
File Size : 54,9 Mb
Release : 2020-03-26
Category : Science
ISBN : 9781108480840

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Advanced Quantum Condensed Matter Physics by Michael El-Batanouny Pdf

Based on an established course, this comprehensive textbook on advanced quantum condensed matter physics covers one-body, many-body and topological perspectives. Discussing modern topics and containing end-of-chapter exercises throughout, it is ideal for graduate students studying advanced condensed matter physics.

Mathematics of Classical and Quantum Physics

Frederick W. Byron,Robert W. Fuller
Mathematics of Classical and Quantum Physics Book PDF

Author : Frederick W. Byron,Robert W. Fuller
Publisher : Courier Corporation
Page : 674 pages
File Size : 50,8 Mb
Release : 2012-04-26
Category : Science
ISBN : 9780486135069

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Mathematics of Classical and Quantum Physics by Frederick W. Byron,Robert W. Fuller Pdf

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.