The Many-body problem : an encyclopedia of exactly solved models in one dimension / edited by Daniel C. Mattis

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