Download or read book Exactly Solvable Models in Many Body Theory written by N H March and published by World Scientific. This book was released on 2016-05-27 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed. The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments. Contents:Low-Order Density MatricesSolvable Models for Small Clusters of FermionsSmall Clusters of BosonsAnyon Statistics with ModelsSuperconductivity and SuperfluidityExact Results for an Isolated Impurity in a SolidPair Potential and Many-Body Force Models for LiquidsAnderson Localization in Disordered SystemsStatistical Field Theory: Especially Models of Critical ExponentsRelativistic FieldsTowards Quantum GravityAppendices Readership: Graduate students and researchers in condensed matter theory.
Download or read book Exactly Solvable Models for Cluster and Many body Condensed Matter Systems written by Norman Henry March and published by . This book was released on 2016 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exactly Solved Models in Statistical Mechanics written by Rodney J. Baxter and published by Elsevier. This book was released on 2016-06-12 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exactly Solved Models in Statistical Mechanics
Download or read book Solvable Models in Quantum Mechanics written by Sergio Albeverio and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Many body Problem written by Daniel Charles Mattis and published by World Scientific. This book was released on 1993 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book differs from its predecessor, Lieb & Mattis Mathematical Physics in One Dimension, in a number of important ways. Classic discoveries which once had to be omitted owing to lack of space ? such as the seminal paper by Fermi, Pasta and Ulam on lack of ergodicity of the linear chain, or Bethe's original paper on the Bethe ansatz ? can now be incorporated. Many applications which did not even exist in 1966 (some of which were originally spawned by the publication of Lieb & Mattis) are newly included. Among these, this new book contains critical surveys of a number of important developments: the exact solution of the Hubbard model, the concept of spinons, the Haldane gap in magnetic spin-one chains, bosonization and fermionization, solitions and the approach to thermodynamic equilibrium, quantum statistical mechanics, localization of normal modes and eigenstates in disordered chains, and a number of other contemporary concerns.
Download or read book Exactly Solvable Models of Strongly Correlated Electrons written by Vladimir E. Korepin and published by World Scientific. This book was released on 1994 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Exactly Solvable Models of Strongly Correlated Electrons written by Vladimir E Korepin and published by World Scientific. This book was released on 1994-05-24 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems of strongly correlated electrons are at the heart of recent developments in condensed matter theory. They have applications to phenomena like high-Tc 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. Contents:One-Dimensional Hubbard ModelThe Supersymmetric t-J ModelOther Models of Strongly Correlated Electrons: Models with Local InteractionModels with Long-Range Interaction Readership: Mathematical physicists and condensed matter physicists. keywords:Hubbard Model;Bethe Ansatz;t-J Model;Charge and Spin Separation;Thermodynamics;Magnetism;Correlation Functions;Cattering Matrix;Luttinger Liqud;Confomal Field Theory
Download or read book Beautiful Models written by Bill Sutherland and published by World Scientific. This book was released on 2004 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Beautiful Models written by Bill Sutherland and published by World Scientific Publishing Company. This book was released on 2004-06-21 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book provides a broad introduction to the fascinating and beautiful subject of many-body quantum systems that can be solved exactly. The subject began with Bethe's famous solution of the one-dimensional Heisenberg magnet more than 70 years ago, soon after the invention of quantum mechanics. Since then, the diversity and scope of such systems have been steadily growing. Beautiful Models is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and even ambitious undergraduates in physics. It is also suitable for the non-experts in physics who wish to have an overview of some of the classic and fundamental models in the subject. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.
Download or read book Many Particle Physics written by Gerald D. Mahan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first, second, and third editions of this book seem to occur at ten year intervals. The intent is to keep the book up-to-date. Many-body theory is a field which continually evolves in time. Journals only publish new results, conferences only invite speakers to report new phenomena, and agencies only fund scientists to do new physics. Today's physics is old hat by tomorrow. Students want to learn new material, and textbooks must be modified to keep up with the times. The early chapters in this book teach the techniques of many-body theory. They are largely unchanged in format. The later chapters apply the techniques to specific problems. The third edition increases the number of applications. New sections have been added, while old sections have been modified to include recent applications. The previous editions were set in type using pre-computer technology. No computer file existed of the prior editions. The publisher scanned the second edition and gave me a disk with the contents. This scan recorded the words accurately and scrambled the equations into unintelligible form. So I retyped the equations using LaTeX. Although tedious, it allowed me to correct the infinite numbers of typographical errors in the previous edition. The earlier typesetting methods did not permit such corrections. The entire book was edited sentence-by sentence. Most old sections of the book were shortened by editing sentences and paragraphs.
Download or read book Off Diagonal Bethe Ansatz for Exactly Solvable Models written by Yupeng Wang and published by Springer. This book was released on 2015-04-21 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introduction of the off-diagonal Bethe Ansatz method, an analytic theory for the eigenvalue problem of quantum integrable models. It also presents some fundamental knowledge about quantum integrability and the algebraic Bethe Ansatz method. Based on the intrinsic properties of R-matrix and K-matrices, the book introduces a systematic method to construct operator identities of transfer matrix. These identities allow one to establish the inhomogeneous T-Q relation formalism to obtain Bethe Ansatz equations and to retrieve corresponding eigenstates. Several longstanding models can thus be solved via this method since the lack of obvious reference states is made up. Both the exact results and the off-diagonal Bethe Ansatz method itself may have important applications in the fields of quantum field theory, low-dimensional condensed matter physics, statistical physics and cold atom systems.
Download or read book Many Particle Physics written by Gerald D. Mahan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 1042 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is for a course in advanced solid-state theory. It is aimed at graduate students in their third or fourth year of study who wish to learn the advanced techniques of solid-state theoretical physics. The method of Green's functions is introduced at the beginning and used throughout. Indeed, it could be considered a book on practical applications of Green's functions, although I prefer to call it a book on physics. The method of Green's functions has been used by many theorists to derive equations which, when solved, provide an accurate numerical description of many processes in solids and quantum fluids. In this book I attempt to summarize many of these theories in order to show how Green's functions are used to solve real problems. My goal, in writing each section, is to describe calculations which can be compared with experiments and to provide these comparisons whenever available. The student is expected to have a background in quantum mechanics at the level acquired from a graduate course using the textbook by either L. I. Schiff, A. S. Davydov, or I. Landau and E. M. Lifshiftz. Similarly, a prior course in solid-state physics is expected, since the reader is assumed to know concepts such as Brillouin zones and energy band theory. Each chapter has problems which are an important part of the lesson; the problems often provide physical insights which are not in the text. Sometimes the answers to the problems are provided, but usually not.
Download or read book Many body Approaches at Different Scales written by G.G.N Angilella and published by Springer. This book was released on 2018-03-24 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of invited research and review contributions on recent advances in (mainly) theoretical condensed matter physics, theoretical chemistry, and theoretical physics. The volume celebrates the 90th birthday of N.H. March (Emeritus Professor, Oxford University, UK), a prominent figure in all of these fields. Given the broad range of interests in the research activity of Professor March, who collaborated with a number of eminent scientists in physics and chemistry, the volume embraces quite diverse topics in physics and chemistry, at various dimensions and energy scales. One thread connecting all these topics is correlation in aggregated states of matter, ranging from nuclear physics to molecules, clusters, disordered condensed phases such as the liquid state, and solid state physics, and the various phase transitions, both structural and electronic, occurring therein. A final chapter leaps to an even larger scale of matter aggregation, namely the universe and gravitation. A further no less important common thread is methodological, with the application of theoretical physics and chemistry, particularly density functional theory and statistical field theory, to both nuclear and condensed matter.
Download or read book Many Body Quantum Theory in Condensed Matter Physics written by Henrik Bruus and published by Oxford University Press. This book was released on 2004-09-02 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Many Body Boson Systems written by André F. Verbeure and published by Springer. This book was released on 2010-11-25 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Many body Systems in One Dimension written by Zachary Nyong-Chol Ha and published by World Scientific. This book was released on 1996 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Inverse Scattering Method and Correlation Functions written by V. E. Korepin and published by Cambridge University Press. This book was released on 1997-03-06 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.
