Beautiful Models

70 Years of Exactly Solved Quantum Many-body Problems

Author: Bill Sutherland

Publisher: World Scientific

ISBN: 9789812388971

Category: Science

Page: 381

View: 4955

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Key Features; An original book - not just a collection of reprints - by an expert, and in many cases the originator, in the field; Although most of the important results are derived, the book also discusses in depth the motivation and meaning of these results; The intrinisic beauty of these models and their solution is emphasized throughout the text, in part by unique full-color figures Readership: Advanced undergraduates and graduate students in physics; non-experts interested in exactly solved quantum many-body systems.

Introduction to the Statistical Physics of Integrable Many-body Systems

Author: Ladislav Šamaj,Zoltán Bajnok

Publisher: Cambridge University Press

ISBN: 1107030439

Category: Science

Page: 523

View: 1194

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"Including topics not traditionally covered in the literature, such as (1 + 1)- dimensional quantum field theory and classical two-dimensional Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which theycan be applied. "--

Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems

Author: Laurens Vanderstraeten

Publisher: Springer

ISBN: 3319641913

Category: Science

Page: 219

View: 9406

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This thesis develops new techniques for simulating the low-energy behaviour of quantum spin systems in one and two dimensions. Combining these developments, it subsequently uses the formalism of tensor network states to derive an effective particle description for one- and two-dimensional spin systems that exhibit strong quantum correlations. These techniques arise from the combination of two themes in many-particle physics: (i) the concept of quasiparticles as the effective low-energy degrees of freedom in a condensed-matter system, and (ii) entanglement as the characteristic feature for describing quantum phases of matter. Whereas the former gave rise to the use of effective field theories for understanding many-particle systems, the latter led to the development of tensor network states as a description of the entanglement distribution in quantum low-energy states.

Encyclopedia of mathematical physics

Author: Sheung Tsun Tsou

Publisher: Academic Pr

ISBN: 9780125126601

Category: Science

Page: 3500

View: 7799

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The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originated from work in mathematical physics by providing them with focused high quality background information. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise * Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking.

A Career in Theoretical Physics

Author: Philip W. Anderson

Publisher: World Scientific

ISBN: 9789810217181

Category: Science

Page: 678

View: 8729

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Theory of ferroelectric behaviour of barium titanate. Use of stochastic methods in line broadening problems. Theory of dirty superconductors.

CERN Courier

Author: European Organization for Nuclear Research

Publisher: N.A

ISBN: N.A

Category: Nuclear energy

Page: N.A

View: 7770

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Quantum Theory of the Electron Liquid

Author: Gabriele Giuliani,Giovanni Vignale

Publisher: Cambridge University Press

ISBN: 9780521821124

Category: Science

Page: 777

View: 7696

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Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron liquid. This book provides an in-depth introduction to the physics of the interacting electron liquid in a broad variety of systems, including metals, semiconductors, artificial nano-structures, atoms and molecules. One, two and three dimensional systems are treated separately and in parallel. Different phases of the electron liquid, from the Landau Fermi liquid to the Wigner crystal, from the Luttinger liquid to the quantum Hall liquid are extensively discussed. Both static and time-dependent density functional theory are presented in detail. Although the emphasis is on the development of the basic physical ideas and on a critical discussion of the most useful approximations, the formal derivation of the results is highly detailed and based on the simplest, most direct methods.

Solvable Models in Quantum Mechanics

Author: Sergio Albeverio,Friedrich Gesztesy,Raphael Hoegh-Krohn,H. Holden

Publisher: Springer Science & Business Media

ISBN: 3642882013

Category: Science

Page: 452

View: 2343

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Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrödinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.

Exploring Quantum Mechanics

A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers

Author: Viktor Mikhaĭlovich Galit︠s︡kiĭ,Victor Galitski,Boris Karnakov,Vladimir Ilʹich Kogan,Vladimir Kogan

Publisher: Oxford University Press

ISBN: 0199232725

Category: Science

Page: 881

View: 3320

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It is notoriously difficult to come up with a new quantum-mechanical problem that would be solvable with a pencil and paper within a finite amount of time and that would provide a useful insight into the fascinating world of quantum physics. Any person who has taught quantum mechanics is certainly aware that there is a lack of such solvable problems in quantum mechanics. In fact, it is exactly this deficit of illuminating examples and practical exercises that make learning and teaching quantum physics so complicated. It is very difficult to understand fundamentally new concepts without real-life examples. Despite this difficulty, this book remarkably presents some 700+ problems in quantum mechanics together with solutions. They are largely new to the English-speaking audience. The problems have been collected over about 60 years, first by the lead author, the late Prof. Victor Galitski, Sr. Over the years, new problems were added and the material polished by Prof. Karnakov.Finally, the translator Prof. Victor Galitski, Jr, has edited the material for the modern English-speaking audience and extended it with new problems particularly relevant to modern science.

Properties of Light

A Novel of Love, Betrayal, and Quantum Physics

Author: Rebecca Goldstein

Publisher: Houghton Mifflin Harcourt

ISBN: 9780547561622

Category: Fiction

Page: 256

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A grand gothic novel of the outer reaches of passion -- of the body and of the mind -- PROPERTIES OF LIGHT is a mesmerizing tale of consuming love and murderous professional envy that carries the reader into the very heart of a physics problem so huge and perplexing it thwarted even Einstein: the nature of light. Caught in the entanglements of erotic and intellectual passion are three physicists: Samuel Mallach is a brilliant theoretician unhinged by the professional glory he feels has been stolen from him; Dana is his intriguing and gifted daughter, whose desperate devotion to her father contributes to the tragic undoing of Justin Childs, her lover and her father's protege. All three are working together to solve some of the deepest and most controversial problems in quantum mechanics, problems that challenge our understanding of the "real world" and of the nature of time. The book grapples with these elusive mysteries, but at its heart is a fiery love story of startling urgency. Insights into quantum mechanics and relativity theory are attached to the nerve fibers of human emotions, and these connections are alive with poignancy and pathos. For these characters, the passion to know and understand, like the desire for love, is full of terrible risk, holding out possibilities for heartbreak as well as for ecstasy. The true subject of Properties of Light is the ecstatic response to reality, perhaps the only response that can embrace the erotic and the poetic, the scientific and the spiritual. Written with, and about, a rare form of passion, this incandescent novel is fiction at its most daring and utterly original.

Quantum Field Theory of Many-Body Systems

From the Origin of Sound to an Origin of Light and Electrons

Author: Xiao-Gang Wen

Publisher: Oxford University Press on Demand

ISBN: 0198530943

Category: Science

Page: 505

View: 9449

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This book is a pedagogical and systematic introduction to new concepts and quantum field theoretical methods in condensed matter physics, which may have an impact on our understanding of the origin of light, electrons and other elementary particles in the universe. Emphasis is on clear physical principles, while at the same time bringing students to the fore of today's research.

Quantum Models of Cognition and Decision

Author: Jerome R. Busemeyer,Peter D. Bruza

Publisher: Cambridge University Press

ISBN: 1139536486

Category: Psychology

Page: N.A

View: 8220

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Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modeling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.

Exactly Solvable Models of Strongly Correlated Electrons

Author: Vladimir E. Korepin,Fabian H. L. Essler

Publisher: World Scientific

ISBN: 9789810215347

Category: Technology & Engineering

Page: 490

View: 6282

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Systems of strongly correlated electrons are at the heart of recent developments in condensed matter theory. They have applications to phenomena like high-c superconductivity and the fractional quantum hall effect. Analytical solutions to such models, though mainly limited to one spatial dimension, provide a complete and unambiguous picture of the dynamics involved. This volume is devoted to such solutions obtained using the Bethe Ansatz, and concentrates on the most important of such models, the Hubbard model. The reprints are complemented by reviews at the start of each chapter and an extensive bibliography.

Mathematical Physics in One Dimension

Exactly Soluble Models of Interacting Particles

Author: Elliott H. Lieb,Daniel C. Mattis

Publisher: Academic Press

ISBN: 1483218562

Category: Science

Page: 580

View: 7750

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Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles covers problems of mathematical physics with one-dimensional analogs. The book discusses classical statistical mechanics and phase transitions; the disordered chain of harmonic oscillators; and electron energy bands in ordered and disordered crystals. The text also describes the many-fermion problem; the theory of the interacting boson gas; the theory of the antiferromagnetic linear chains; and the time-dependent phenomena of many-body systems (i.e., classical or quantum-mechanical dynamics). Physicists and mathematicians will find the book invaluable.

Many-body Theory Exposed!

Propagator Description of Quantum Mechanics in Many-body Systems

Author: Willem Hendrik Dickhoff,Dimitri Van Neck

Publisher: World Scientific

ISBN: 9812813799

Category: Science

Page: 831

View: 9958

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This comprehensive textbook on the quantum mechanics of identical particles includes a wealth of valuable experimental data, in particular recent results from direct knockout reactions directly related to the single-particle propagator in many-body theory. The comparison with data is incorporated from the start, making the abstract concept of propagators vivid and accessible. Results of numerical calculations using propagators or Green's functions are also presented. The material has been thoroughly tested in the classroom and the introductory chapters provide a seamless connection with a one-year graduate course in quantum mechanics. While the majority of books on many-body theory deal with the subject from the viewpoint of condensed matter physics, this book emphasizes finite systems as well and should be of considerable interest to researchers in nuclear, atomic, and molecular physics. A unified treatment of many different many-body systems is presented using the approach of self-consistent Green's functions. The second edition contains an extensive presentation of finite temperature propagators and covers the technique to extract the self-energy from experimental data as developed in the dispersive optical model.The coverage proceeds systematically from elementary concepts, such as second quantization and mean-field properties, to a more advanced but self-contained presentation of the physics of atoms, molecules, nuclei, nuclear and neutron matter, electron gas, quantum liquids, atomic Bose-Einstein and fermion condensates, and pairing correlations in finite and infinite systems, including finite temperature.