TY - BOOK AU - Mattis,Daniel Charles TI - The Many-body problem: an encyclopedia of exactly solved models in one dimension SN - 9810209754 AV - QC174.17.P7 M36 1993 PY - 1993///] CY - Singapore, River Edge, NJ PB - World Scientific KW - Many-body problem N1 - Includes bibliographical references; -- Contents; Preface ; Acknowledgements ; Note to the Reader ; Ch. 1 Classical Statistical Mechanics ; A Simple Method for Treating the Statistical Mechanics of One-Dimensional Substances; / H. Takahashi; Sur l'Integrale de Configuration pour les Systemes de Particules a Une Dimension; / L. van Hove; Exact Partition Functions for some One-Dimensional Models via the Isobaric Ensemble; / M. Bishop, M. A. Boonstra; Molecular Distribution Functions in a One-Dimensional Fluid; / Z. W. Salsburg, R. W. Zwanzig, J. G. Kirkwood; Certain General Order-Disorder Models in the Limit of Long-Range Interactions; / G. A. Baker, Jr; On the van der Waals Theory of the Vapor-Liquid Equilibrium, I. Discussion of a One-Dimensional Model; / M. Kac, G. E. Uhlenbeck, P. C. Hemmer; On the van der Waals Theory of the Vapor-Liquid Equilibrium, III. Discussion of the Critical Region; / P. C. Hemmer, M. Kac, G. E. Uhlenbeck; Exact Statistical Mechanics of a One-Dimensional System with Coulomb Forces; / A. Lenard; One-Dimensional Plasma Model at Thermodynamic Equilibrium; / O. C. Eldridge, M. Feix; Statistical Mechanics of a One-Dimensional Coulomb System with a Uniform Charge Background; / R. J. Baxter; Ch. 2 Spectrum of Disordered and/or Anharmonic Chains of Oscillators ; The Dynamics of a Disordered Linear Chain; / F. J. Dyson; Disordered One-Dimensional Crystals; / H. Schmidt; Special Frequencies in the Vibrational Spectra of Disordered Chains; / H. Matsuda; Some Exact Results for the Vibrational Spectrum of a Disordered Chain; / R. E. Borland; Structure of the Spectra of Disordered Systems, I. Fundamental Theorems; / J. Hori, H. Matsuda; The Vibrational Spectrum of a Disordered Linear System; / R. L. Agacy; Vibrations of Glass-Like Disordered Chains; / P. Dean; Vibrations of a Chain with Nonlinear Interaction; / M. Toda; Wave Propagation in Anharmonic Lattices; / M. Toda; A Soliton and Two Solitons in an Exponential Lattice and Related Equations; / M. Toda, M. Wadati; Integrals of the Toda Lattice; / M. Henon; The Toda Lattice, II. Existence of Integrals; / H. Flaschka; Solution of a Three-Body Problem in One Dimension; / F. Calogero; Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials; / F. Calogero; A Brief History of the Quantum Soliton with New Results on the Quantization of the Toda Lattice; / B. Sutherland; Ch. 3 Electron Energy Bands in Ordered and Disordered "Crystals" ; The Approximate Solution of One-Dimensional Wave Equations; / C. Eckart; Quantum Mechanics of Electrons in Crystal Lattices; / R. de L. Kronig, W. G. Penney; New Soluble Energy Band Problem; / F. L. Scarf; Energy Bands and Wave Functions in Periodic Potentials; / H. M. James; Wave Propagation in One-Dimensional Structures; / J. M. Luttinger; Analytic Properties of Bloch Waves and Wannier Functions; / W. Kohn; A Theory of the Electrical Breakdown of Solid Dielectrics; / C. Zener; Electron Levels in a One-Dimensional Random Lattice; / H. L. Frisch, S. P. Lloyd; Existence of Energy Gaps in One-Dimensional Liquids; / R. E. Borland; The Electronic Structure of a One-Dimensional Random Alloy; / R. L. Agacy, R. E. Borland; Existence of Energy Gaps in the Spectrum of a One-Dimensional Atomic Chain; / L. Dworin; Saxon-Hutner Theorem for One-Dimensional General Alloys; / B. Y. Tong, S. Y. Tong; Short-Range versus Long-Range Order in a Model Binary Alloy; / M. Plischke, D. C. Mattis; The Statistics of One-Dimensional Resistances; / P. D. Kirkman, J. B. Pendry; Exact Solution of a Nonlinear Eigenvalue Problem; / F. J. Romeiras, G. Rowlands; Ch. 4 The Many-Fermion Problem ; Remarks on Bloch's Method of Sound Waves Applied to Many-Fermion Problems; / S. Tomonoga; Exact Solution of a Many-Fermion System and its Associated Boson Field; / D. C. Mattis, E. H. Lieb; Tomonaga's Model and the Threshold Singularity of X-Ray Spectra of Metals; / K. D. Schotte, U. Schotte; New Wave-Operator Identity Applied to the Study of Persistent Currents in 1D; / D. C. Mattis; Conductivity of One-Dimensional Interacting Fermions; / D. C. Mattis; Backward Scattering in the One-Dimensional Electron Gas; / A. Luther, V. J. Emery; Calculation of Critical Exponents in Two Dimensions from Quantum Field Theory in One Dimension; / A. Luther, I. Peschel; Generalization of the Landau Liquid Concept: Example of the Luttinger Liquids; / J. Carmelo, A. A. Ovchinnikov; Structure and Solution of the Massive Thirring Model; / H. Bergknoff, H. B. Thacker; One-Dimensional Backward-Scattering Fermion Model with Built-In Cutoff; / S. Rudin; Strange Solutions to Field Theories in One Spatial Dimension; / D. C. Mattis, B. Sutherland; Some Exact Results for the Many-Body Problem in One Dimension with Repulsive Delta-Function Interaction; / C. N. Yang; S Matrix for the One-Dimensional N-Body Problem with Repulsive or Attractive [delta]-Function Interaction; / C. N. Yang; Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension; / E. H. Lieb, F. Y. Wu; Theory of Ferromagnetism and the Ordering of Electronic Energy Levels; / E. H. Lieb, D. C. Mattis; Magnetic Properties of Some Itinerant-Electron Systems at T > 0; / M. Aizenman, E. H. Lieb; One-Dimensional Plasma as an Example of a Wigner Solid; / B. Sutherland; Soliton Excitations in Polyacetylene; / W. P. Su, J. R. Schrieffer, A. J. Heeger; Solitons with Fermion Number 1/2 in Condensed Matter and Relativistic Field Theories; / R. Jackiw, J. R. Schrieffer; Ch. 5 The Bose Gas ; Exact Analysis of an Interacting Bose Gas, I. The General Solution and the Ground State; / E. H. Lieb, W. Liniger; Exact Analysis of an Interacting Bose Gas, II. The Excitation Spectrum; / E. H. Lieb; Momentum Distribution in the Ground State of the One-Dimensional System of Impenetrable Bosons; / A. Lenard; One-Dimensional Impenetrable Bosons in Thermal Equilibrium; / A. Lenard; Study of Exactly Soluble One-Dimensional N-Body Problems; / J. B. McGuire; Quantum Critical Phenomena in One-Dimensional Bose Systems; / G. G. Batrouni, R. T. Scalettar, G. T. Zimanyi; Thermodynamics of a One-Dimensional System of Bosons with Repulsive Delta-Function Interaction; / C. N. Yang, C. P. Yang; Ch. 6 Magnetism ; On the Theory of Metals, I. Eigenvalues and Eigenfunctions of a Linear Chain of Atoms (English Translation); / H. Bethe; Linear Magnetic Chains with Anisotropic Coupling; / J. C. Bonner, M. E. Fisher; Magnetization Curve at Zero Temperature for the Antiferromagnetic Heisenberg Linear Chain; / R. B. Griffiths; What is the Spin of a Spin Wave?; / L. D. Faddeev, L. A. Takhtajan ; A Survey of Results for the 1-D Heisenberg Magnets; / J. D. Johnson; Two Soluble Models of an Antiferromagnetic Chain; / E. Lieb, T. Schultz, D. Mattis; Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Neel State; / F. D. M. Haldane; Comment on "Ground State Properties of a Spin-1 Antiferromagnetic Chain"; / D. C. Mattis; Rigorous Results on Valence-Bond Ground States in Antiferromagnets; / I. Affleck, T. Kennedy, E. H. Lieb, H. Tasaki; Quantum Spin Chains and the Haldane Gap; / I. Affleck; Ch. 7 Time-Dependent Phenomena and the Approach to Equilibrium ; Studies of Nonlinear Problems. I; / E. Fermi, J. Pasta, S. Ulam, M. Tsingou; The Fermi-Pasta-Ulam Problem: Paradox Turns Discovery; / J. Ford; Statistical Mechanics of Assemblies of Coupled Oscillators; / G. W. Ford, M. Kac, P. Mazur; Korteweg-de Vries Equation and Generalizations, VI. Methods for Exact Solution; / C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura ER -