Condensed Matter Physics and Exactly Soluble Models

Condensed Matter Physics and Exactly Soluble Models

Author: Elliott H. Lieb

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 645

ISBN-13: 3662063905

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This is the third Selecta of publications of Elliott Lieb, the first two being Stabil ity of Matter: From Atoms to Stars, edited by Walter Thirring, and Inequalities, edited by Michael Loss and Mary Beth Ruskai. A companion fourth Selecta on Statistical Mechanics is also edited by us. Elliott Lieb has been a pioneer of the discipline of mathematical physics as it is nowadays understood and continues to lead several of its most active directions today. For the first part of this selecta we have made a selection of Lieb's works on Condensed Matter Physics. The impact of Lieb's work in mathematical con densed matter physics is unrivaled. It is fair to say that if one were to name a founding father of the field, Elliott Lieb would be the only candidate to claim this singular position. While in related fields, such as Statistical Mechanics and Atomic Physics, many key problems are readily formulated in unambiguous mathematical form, this is less so in Condensed Matter Physics, where some say that rigor is "probably impossible and certainly unnecessary". By carefully select ing the most important questions and formulating them as well-defined mathemat ical problems, and then solving a good number of them, Lieb has demonstrated the quoted opinion to be erroneous on both counts. What is true, however, is that many of these problems turn out to be very hard. It is not unusual that they take a decade (even several decades) to solve.


Quantum Field Theory of Many-Body Systems

Quantum Field Theory of Many-Body Systems

Author: Xiao-Gang Wen

Publisher: OUP Oxford

Published: 2004-06-04

Total Pages: 520

ISBN-13: 0191523968

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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.


Thermodynamics of One-Dimensional Solvable Models

Thermodynamics of One-Dimensional Solvable Models

Author: Minoru Takahashi

Publisher: Cambridge University Press

Published: 1999-03-28

Total Pages: 268

ISBN-13: 9780521551434

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Exactly solvable models are very important in physics from a theoretical point of view and also from the experimentalist's perspective, because in such cases theoretical results and experimental results can be compared without ambiguity. This is a book about an important class of exactly solvable models in physics. The subject area is the Bethe-ansatz approach for a number of one-dimensional models, and the setting up of equations within this approach to determine the thermodynamics of these systems. It is a topic that crosses the boundaries among condensed matter physics, mathematics and field theory. The derivation and application of thermodynamic Bethe-ansatz equations for one-dimensional models are explained in detail. This technique is indispensable for physicists studying the low-temperature properties of one-dimensional substances. Written by the originator of much of the work in the subject, this book will be of great interest to theoretical condensed matter physicists.


Many-Body Quantum Theory in Condensed Matter Physics

Many-Body Quantum Theory in Condensed Matter Physics

Author: Henrik Bruus

Publisher: Oxford University Press

Published: 2004-09-02

Total Pages: 458

ISBN-13: 0198566336

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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.


Classical And Quantum Field Theory Of Exactly Soluble Nonlinear Systems

Classical And Quantum Field Theory Of Exactly Soluble Nonlinear Systems

Author: Piotr Garbaczewski

Publisher: World Scientific

Published: 1985-07-01

Total Pages: 260

ISBN-13: 9814513571

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Contents:Nonlinear Problems in 1 + 1 and Their LinearizationClassical Field Theory ModelsHamiltonian Formulation, Action-Angle Variables, Solitons, Classical Lattice Models and Lattice Approximants of Classical FieldsQuantization on a Lattice: Relationship Classical-QuantumQuantization on a Lattice: Simple Bose ModelsSpin 1/2 Lattice Systems Related to Nonlinear Bose Problems: Lattice FermionsQuantization in Continuum: Joint Bose-Fermi Spectral Problems in 1 + 1Quantum Meaning of Classical Field Theory for Fermi SystemsOn Infinite Constituent “Elementary” Systems: Canonical (Constituent) Quantization of Soliton FieldsTowards 1 + 3: Problems and Prospects Readership: Mathematical physicists and physicists. Keywords:Nonlinear Fields;Integrability;Solvable Models;Solitons;Continuum and Lattice Models;Quantization;Fermi Fields And Their Classical Counterparts;Relationship Classical-Quantum;Boson-Fermion Reciprocity (Bosonization)


Statistical Mechanics

Statistical Mechanics

Author: E.H. Lieb

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 491

ISBN-13: 3662100185

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In Statistical Physics one of the ambitious goals is to derive rigorously, from statistical mechanics, the thermodynamic properties of models with realistic forces. Elliott Lieb is a mathematical physicist who meets the challenge of statistical mechanics head on, taking nothing for granted and not being content until the purported consequences have been shown, by rigorous analysis, to follow from the premises. The present volume contains a selection of his contributions to the field, in particular papers dealing with general properties of Coulomb systems, phase transitions in systems with a continuous symmetry, lattice crystals, and entropy inequalities. It also includes work on classical thermodynamics, a discipline that, despite many claims to the contrary, is logically independent of statistical mechanics and deserves a rigorous and unambiguous foundation of its own. The articles in this volume have been carefully annotated by the editors.


Topological Aspects of Condensed Matter Physics

Topological Aspects of Condensed Matter Physics

Author: Claudio Chamon

Publisher: Oxford University Press

Published: 2017-02-16

Total Pages: 705

ISBN-13: 019108879X

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This book contains lecture notes by world experts on one of the most rapidly growing fields of research in physics. Topological quantum phenomena are being uncovered at unprecedented rates in novel material systems. The consequences are far reaching, from the possibility of carrying currents and performing computations without dissipation of energy, to the possibility of realizing platforms for topological quantum computation.The pedagogical lectures contained in this book are an excellent introduction to this blooming field. The lecture notes are intended for graduate students or advanced undergraduate students in physics and mathematics who want to immerse in this exciting XXI century physics topic. This Les Houches Summer School presents an overview of this field, along with a sense of its origins and its placement on the map of fundamental physics advancements. The School comprised a set of basic lectures (part 1) aimed at a pedagogical introduction of the fundamental concepts, which was accompanied by more advanced lectures (part 2) covering individual topics at the forefront of today's research in condensed-matter physics.


Quantum Field Theory I: Basics in Mathematics and Physics

Quantum Field Theory I: Basics in Mathematics and Physics

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

Published: 2007-04-18

Total Pages: 1060

ISBN-13: 354034764X

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This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.


Low-dimensional Quantum Field Theories For Condensed Matter Physicists - Lecture Notes Of Ictp Summer Course

Low-dimensional Quantum Field Theories For Condensed Matter Physicists - Lecture Notes Of Ictp Summer Course

Author: Lu Yu

Publisher: World Scientific

Published: 1995-02-28

Total Pages: 625

ISBN-13: 9814556831

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This volume contains a set of pedagogical reviews covering the most recent applications of low-dimensional quantum field theory in condensed matter physics, written by experts who have made major contributions to this rapidly developing field of research. The main purpose is to introduce active young researchers to new ideas and new techniques which are not covered by the standard textbooks.