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Introduction To The Statistical Physics Of Integrable Many Body Systems

Author: Ladislav Šamaj
Publisher: Cambridge University Press
ISBN: 1107030439
Size: 44.89 MB
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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. "--

Quantum Many Body Systems In One Dimension

Author: Zachary N C Ha
Publisher: World Scientific
ISBN: 9814500372
Size: 15.95 MB
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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

Lattice Statistics And Mathematical Physics

Author: Jacques H. H. Perk
Publisher: World Scientific
ISBN: 9789812776358
Size: 16.27 MB
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This book contains thirty-six short papers on recent progress in a variety of subjects in mathematical and theoretical physics, written for the proceedings of a symposium in honor of the seventieth birthday of Professor F Y Wu, held at the Nankai Institute of Mathematics, October 7OCo11, 2001. The collection of papers is aimed at researchers, including graduate students, with an interdisciplinary interest and gives a brief introduction to many of the topics of current interest. These include new results on exactly solvable models in statistical mechanics, integrable through the YangOCoBaxter equations, quantum groups, fractional statistics, random matrices, index theorems on the lattice, combinatorics, and other related topics."

New Developments Of Integrable Systems And Long Ranged Interaction Models

Author: Ge Mo-lin
Publisher: World Scientific
ISBN: 9814549754
Size: 49.80 MB
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This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; (3) topology and differential geometry.The following are noteworthy features of this book: the style of exposition is a fusion of those common in the standard physics and mathematics literatures; the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience; despite the diversity of the topics covered, there is a strong degree of thematic unity; much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.

Integrable Quantum Field Theories And Their Applications

Author: Changrim Ahn
Publisher: World Scientific
ISBN: 9814490180
Size: 22.35 MB
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This volume includes several lecture notes on the fundamentals and elementary techniques of integrable field theories and on their applications to low-dimensional physics systems contributed by leading scientists in the respective fields. The main topics covered are various aspects of the thermodynamic Bethe ansatz, form factors, Calogero (and related) models, sigma models, conformal boundary conditions, etc. The volume presents both pedagogical material and a current research trend in the field. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) Contents:Applications of Reflection Amplitudes in Toda-Type Theories (C Ahn et al.)Lax Pairs and Involutive Hamiltonians for CN and BCN Ruijsenaars–Schneider Models (K Chen et al.)Fateev's Models and Their Applications (D Controzzi & A M Tsvelik)The ODE/IM Correspondence (P Dorey et al.)Integrable Sigma Models (P Fendley)Lorentz Lattice Gases and Spin Chains (M J Martins)Quantum Calogero–Moser Models for Any Root System (R Sasaki)Quasi-Particles in Conformal Field Theories for Fractional Quantum Hall Systems (K Schoutens & R A J van Elburg)Towards Form Factors in Finite Volume (F A Smirnov)Static and Dynamic Properties of Trapped Bose–Einstein Condensates (T Tsurumi et al.)Integrability of the Calogero Model: Conserved Quantities, the Classical General Solution and the Quantum Orthogonal Basis (H Ujino et al.)Conformal Boundary Conditions (J B Zuber) Readership: Quantum field theorists, mathematical, theoretical, high energy and condensed matter physicists. Keywords:Proceedings;Quantum Field Theories;Cheju Island (Republic of Korea);Winter School

Introduction To Nonextensive Statistical Mechanics

Author: Constantino Tsallis
Publisher: Springer Science & Business Media
ISBN: 0387853588
Size: 33.27 MB
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Metaphors, generalizations and unifications are natural and desirable ingredients of the evolution of scientific theories and concepts. Physics, in particular, obviously walks along these paths since its very beginning. This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics, one of the greatest monuments of contemporary physics. Conceived more than 130 years ago by Maxwell, Boltzmann and Gibbs, the BG theory exhibits uncountable – some of them impressive – successes in physics, chemistry, mathematics, and computational sciences, to name a few. Presently, more than two thousand publications, by over 1800 scientists around the world, have been dedicated to the nonextensive generalization. Remarkable applications have emerged, and its mathematical grounding is by now relatively well established. A pedagogical introduction to its concepts – nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, generalization of the standard CLT’s, among others – is presented in this book as well as a selection of paradigmatic applications in various sciences together with diversified experimental verifications of some of its predictions. This is the first pedagogical book on the subject, written by the proponent of the theory Presents many applications to interdisciplinary complex phenomena in virtually all sciences, ranging from physics to medicine, from economics to biology, through signal and image processing and others Offers a detailed derivation of results, illustrations and for the first time detailed presentation of Nonextensive Statistical Mechanics

Integrable Quantum Field Theories And Their Application

Author: Changrim Ahn
Publisher: World Scientific
ISBN: 9789812799739
Size: 76.37 MB
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Applications of reflection amplitudes in Toda-type theories / C. Ahn, C. Kim and C. Rim -- Lax pairs and involutive Hamiltonians for CN and BCN Ruijsenaars-Schneider models / Kai Chen, B.-Y. Hou and W.-L. Yang -- Fateev's models and their applications / D. Controzzi and A.M. Tsvelik -- The ODE/IM correspondence / P. Dorey, C. Dunning and R. Tateo -- Integrable sigma models / P. Fendley -- Lorentz lattice gases and spin chains / M.J. Martins -- Quantum Calogero-Moser models for any root system / R. Sasaki -- Quasi-particles in conformal field theories for fractional quantum Hall systems / K. Schoutens and R.A.J. van Elburg -- Towards form factors in finite volume / F.A. Smirnov -- Static and dynamic properties of trapped Bose-Einstein condensates / T. Tsurumi, H. Morise and M. Wadati -- Integrability of the Calogero Model: Conserved quantities, the classical general solution and the quantum orthogonal basis / H. Ujino, A. Nishino and M. Wadati -- Conformal boundary conditions / J.-B. Zuber

Classical And Quantum Nonlinear Integrable Systems

Author: A Kundu
Publisher: CRC Press
ISBN: 9781420034615
Size: 70.72 MB
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Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories and applications and another on quantum aspects, Classical and Quantum Nonlinear Integrable Systems: Theory and Application reviews the advances made in nonlinear integrable systems, with emphasis on the underlying concepts rather than technical details. It forms an outstanding introductory textbook as well as a useful reference for specialists.