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The Many-body problem : an encyclopedia of exactly solved models in one dimension /
The Many-body problem : an encyclopedia of exactly solved models in one dimension /
edited by Daniel C. Mattis
- xxiii, 958 pages : illustrations ; 26 cm
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 Sur l'Integrale de Configuration pour les Systemes de Particules a Une Dimension Exact Partition Functions for some One-Dimensional Models via the Isobaric Ensemble Molecular Distribution Functions in a One-Dimensional Fluid Certain General Order-Disorder Models in the Limit of Long-Range Interactions On the van der Waals Theory of the Vapor-Liquid Equilibrium, I. Discussion of a One-Dimensional Model On the van der Waals Theory of the Vapor-Liquid Equilibrium, III. Discussion of the Critical Region Exact Statistical Mechanics of a One-Dimensional System with Coulomb Forces One-Dimensional Plasma Model at Thermodynamic Equilibrium Statistical Mechanics of a One-Dimensional Coulomb System with a Uniform Charge Background Ch. 2 Spectrum of Disordered and/or Anharmonic Chains of Oscillators The Dynamics of a Disordered Linear Chain Disordered One-Dimensional Crystals Special Frequencies in the Vibrational Spectra of Disordered Chains Some Exact Results for the Vibrational Spectrum of a Disordered Chain Structure of the Spectra of Disordered Systems, I. Fundamental Theorems The Vibrational Spectrum of a Disordered Linear System Vibrations of Glass-Like Disordered Chains Vibrations of a Chain with Nonlinear Interaction Wave Propagation in Anharmonic Lattices A Soliton and Two Solitons in an Exponential Lattice and Related Equations Integrals of the Toda Lattice The Toda Lattice, II. Existence of Integrals Solution of a Three-Body Problem in One Dimension Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials A Brief History of the Quantum Soliton with New Results on the Quantization of the Toda Lattice Ch. 3 Electron Energy Bands in Ordered and Disordered "Crystals" The Approximate Solution of One-Dimensional Wave Equations Quantum Mechanics of Electrons in Crystal Lattices New Soluble Energy Band Problem Energy Bands and Wave Functions in Periodic Potentials Wave Propagation in One-Dimensional Structures Analytic Properties of Bloch Waves and Wannier Functions A Theory of the Electrical Breakdown of Solid Dielectrics Electron Levels in a One-Dimensional Random Lattice Existence of Energy Gaps in One-Dimensional Liquids The Electronic Structure of a One-Dimensional Random Alloy Existence of Energy Gaps in the Spectrum of a One-Dimensional Atomic Chain Saxon-Hutner Theorem for One-Dimensional General Alloys Short-Range versus Long-Range Order in a Model Binary Alloy The Statistics of One-Dimensional Resistances Exact Solution of a Nonlinear Eigenvalue Problem Ch. 4 The Many-Fermion Problem Remarks on Bloch's Method of Sound Waves Applied to Many-Fermion Problems Exact Solution of a Many-Fermion System and its Associated Boson Field Tomonaga's Model and the Threshold Singularity of X-Ray Spectra of Metals New Wave-Operator Identity Applied to the Study of Persistent Currents in 1D Conductivity of One-Dimensional Interacting Fermions Backward Scattering in the One-Dimensional Electron Gas Calculation of Critical Exponents in Two Dimensions from Quantum Field Theory in One Dimension Generalization of the Landau Liquid Concept: Example of the Luttinger Liquids Structure and Solution of the Massive Thirring Model One-Dimensional Backward-Scattering Fermion Model with Built-In Cutoff Strange Solutions to Field Theories in One Spatial Dimension Some Exact Results for the Many-Body Problem in One Dimension with Repulsive Delta-Function Interaction S Matrix for the One-Dimensional N-Body Problem with Repulsive or Attractive [delta]-Function Interaction Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension Theory of Ferromagnetism and the Ordering of Electronic Energy Levels Magnetic Properties of Some Itinerant-Electron Systems at T > 0 One-Dimensional Plasma as an Example of a Wigner Solid Soliton Excitations in Polyacetylene Solitons with Fermion Number 1/2 in Condensed Matter and Relativistic Field Theories Ch. 5 The Bose Gas Exact Analysis of an Interacting Bose Gas, I. The General Solution and the Ground State Exact Analysis of an Interacting Bose Gas, II. The Excitation Spectrum Momentum Distribution in the Ground State of the One-Dimensional System of Impenetrable Bosons One-Dimensional Impenetrable Bosons in Thermal Equilibrium Study of Exactly Soluble One-Dimensional N-Body Problems Quantum Critical Phenomena in One-Dimensional Bose Systems Thermodynamics of a One-Dimensional System of Bosons with Repulsive Delta-Function Interaction Ch. 6 Magnetism On the Theory of Metals, I. Eigenvalues and Eigenfunctions of a Linear Chain of Atoms (English Translation) Linear Magnetic Chains with Anisotropic Coupling Magnetization Curve at Zero Temperature for the Antiferromagnetic Heisenberg Linear Chain What is the Spin of a Spin Wave? A Survey of Results for the 1-D Heisenberg Magnets Two Soluble Models of an Antiferromagnetic Chain Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Neel State Comment on "Ground State Properties of a Spin-1 Antiferromagnetic Chain" Rigorous Results on Valence-Bond Ground States in Antiferromagnets Quantum Spin Chains and the Haldane Gap Ch. 7 Time-Dependent Phenomena and the Approach to Equilibrium Studies of Nonlinear Problems. I The Fermi-Pasta-Ulam Problem: Paradox Turns Discovery Statistical Mechanics of Assemblies of Coupled Oscillators Korteweg-de Vries Equation and Generalizations, VI. Methods for Exact Solution / H. Takahashi / L. van Hove / M. Bishop, M. A. Boonstra / Z. W. Salsburg, R. W. Zwanzig, J. G. Kirkwood / G. A. Baker, Jr. / M. Kac, G. E. Uhlenbeck, P. C. Hemmer / P. C. Hemmer, M. Kac, G. E. Uhlenbeck / A. Lenard / O. C. Eldridge, M. Feix / R. J. Baxter / F. J. Dyson / H. Schmidt / H. Matsuda / R. E. Borland / J. Hori, H. Matsuda / R. L. Agacy / P. Dean / M. Toda / M. Toda / M. Toda, M. Wadati / M. Henon / H. Flaschka / F. Calogero / F. Calogero / B. Sutherland / C. Eckart / R. de L. Kronig, W. G. Penney / F. L. Scarf / H. M. James / J. M. Luttinger / W. Kohn / C. Zener / H. L. Frisch, S. P. Lloyd / R. E. Borland / R. L. Agacy, R. E. Borland / L. Dworin / B. Y. Tong, S. Y. Tong / M. Plischke, D. C. Mattis / P. D. Kirkman, J. B. Pendry / F. J. Romeiras, G. Rowlands / S. Tomonoga / D. C. Mattis, E. H. Lieb / K. D. Schotte, U. Schotte / D. C. Mattis / D. C. Mattis / A. Luther, V. J. Emery / A. Luther, I. Peschel / J. Carmelo, A. A. Ovchinnikov / H. Bergknoff, H. B. Thacker / S. Rudin / D. C. Mattis, B. Sutherland / C. N. Yang / C. N. Yang / E. H. Lieb, F. Y. Wu / E. H. Lieb, D. C. Mattis / M. Aizenman, E. H. Lieb / B. Sutherland / W. P. Su, J. R. Schrieffer, A. J. Heeger / R. Jackiw, J. R. Schrieffer / E. H. Lieb, W. Liniger / E. H. Lieb / A. Lenard / A. Lenard / J. B. McGuire / G. G. Batrouni, R. T. Scalettar, G. T. Zimanyi / C. N. Yang, C. P. Yang / H. Bethe / J. C. Bonner, M. E. Fisher / R. B. Griffiths / L. D. Faddeev, L. A. Takhtajan / J. D. Johnson / E. Lieb, T. Schultz, D. Mattis / F. D. M. Haldane / D. C. Mattis / I. Affleck, T. Kennedy, E. H. Lieb, H. Tasaki / I. Affleck / E. Fermi, J. Pasta, S. Ulam, M. Tsingou / J. Ford / G. W. Ford, M. Kac, P. Mazur / C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura
9810209754
Many-body problem
QC174.17.P7 / M36 1993
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 Sur l'Integrale de Configuration pour les Systemes de Particules a Une Dimension Exact Partition Functions for some One-Dimensional Models via the Isobaric Ensemble Molecular Distribution Functions in a One-Dimensional Fluid Certain General Order-Disorder Models in the Limit of Long-Range Interactions On the van der Waals Theory of the Vapor-Liquid Equilibrium, I. Discussion of a One-Dimensional Model On the van der Waals Theory of the Vapor-Liquid Equilibrium, III. Discussion of the Critical Region Exact Statistical Mechanics of a One-Dimensional System with Coulomb Forces One-Dimensional Plasma Model at Thermodynamic Equilibrium Statistical Mechanics of a One-Dimensional Coulomb System with a Uniform Charge Background Ch. 2 Spectrum of Disordered and/or Anharmonic Chains of Oscillators The Dynamics of a Disordered Linear Chain Disordered One-Dimensional Crystals Special Frequencies in the Vibrational Spectra of Disordered Chains Some Exact Results for the Vibrational Spectrum of a Disordered Chain Structure of the Spectra of Disordered Systems, I. Fundamental Theorems The Vibrational Spectrum of a Disordered Linear System Vibrations of Glass-Like Disordered Chains Vibrations of a Chain with Nonlinear Interaction Wave Propagation in Anharmonic Lattices A Soliton and Two Solitons in an Exponential Lattice and Related Equations Integrals of the Toda Lattice The Toda Lattice, II. Existence of Integrals Solution of a Three-Body Problem in One Dimension Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials A Brief History of the Quantum Soliton with New Results on the Quantization of the Toda Lattice Ch. 3 Electron Energy Bands in Ordered and Disordered "Crystals" The Approximate Solution of One-Dimensional Wave Equations Quantum Mechanics of Electrons in Crystal Lattices New Soluble Energy Band Problem Energy Bands and Wave Functions in Periodic Potentials Wave Propagation in One-Dimensional Structures Analytic Properties of Bloch Waves and Wannier Functions A Theory of the Electrical Breakdown of Solid Dielectrics Electron Levels in a One-Dimensional Random Lattice Existence of Energy Gaps in One-Dimensional Liquids The Electronic Structure of a One-Dimensional Random Alloy Existence of Energy Gaps in the Spectrum of a One-Dimensional Atomic Chain Saxon-Hutner Theorem for One-Dimensional General Alloys Short-Range versus Long-Range Order in a Model Binary Alloy The Statistics of One-Dimensional Resistances Exact Solution of a Nonlinear Eigenvalue Problem Ch. 4 The Many-Fermion Problem Remarks on Bloch's Method of Sound Waves Applied to Many-Fermion Problems Exact Solution of a Many-Fermion System and its Associated Boson Field Tomonaga's Model and the Threshold Singularity of X-Ray Spectra of Metals New Wave-Operator Identity Applied to the Study of Persistent Currents in 1D Conductivity of One-Dimensional Interacting Fermions Backward Scattering in the One-Dimensional Electron Gas Calculation of Critical Exponents in Two Dimensions from Quantum Field Theory in One Dimension Generalization of the Landau Liquid Concept: Example of the Luttinger Liquids Structure and Solution of the Massive Thirring Model One-Dimensional Backward-Scattering Fermion Model with Built-In Cutoff Strange Solutions to Field Theories in One Spatial Dimension Some Exact Results for the Many-Body Problem in One Dimension with Repulsive Delta-Function Interaction S Matrix for the One-Dimensional N-Body Problem with Repulsive or Attractive [delta]-Function Interaction Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension Theory of Ferromagnetism and the Ordering of Electronic Energy Levels Magnetic Properties of Some Itinerant-Electron Systems at T > 0 One-Dimensional Plasma as an Example of a Wigner Solid Soliton Excitations in Polyacetylene Solitons with Fermion Number 1/2 in Condensed Matter and Relativistic Field Theories Ch. 5 The Bose Gas Exact Analysis of an Interacting Bose Gas, I. The General Solution and the Ground State Exact Analysis of an Interacting Bose Gas, II. The Excitation Spectrum Momentum Distribution in the Ground State of the One-Dimensional System of Impenetrable Bosons One-Dimensional Impenetrable Bosons in Thermal Equilibrium Study of Exactly Soluble One-Dimensional N-Body Problems Quantum Critical Phenomena in One-Dimensional Bose Systems Thermodynamics of a One-Dimensional System of Bosons with Repulsive Delta-Function Interaction Ch. 6 Magnetism On the Theory of Metals, I. Eigenvalues and Eigenfunctions of a Linear Chain of Atoms (English Translation) Linear Magnetic Chains with Anisotropic Coupling Magnetization Curve at Zero Temperature for the Antiferromagnetic Heisenberg Linear Chain What is the Spin of a Spin Wave? A Survey of Results for the 1-D Heisenberg Magnets Two Soluble Models of an Antiferromagnetic Chain Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Neel State Comment on "Ground State Properties of a Spin-1 Antiferromagnetic Chain" Rigorous Results on Valence-Bond Ground States in Antiferromagnets Quantum Spin Chains and the Haldane Gap Ch. 7 Time-Dependent Phenomena and the Approach to Equilibrium Studies of Nonlinear Problems. I The Fermi-Pasta-Ulam Problem: Paradox Turns Discovery Statistical Mechanics of Assemblies of Coupled Oscillators Korteweg-de Vries Equation and Generalizations, VI. Methods for Exact Solution / H. Takahashi / L. van Hove / M. Bishop, M. A. Boonstra / Z. W. Salsburg, R. W. Zwanzig, J. G. Kirkwood / G. A. Baker, Jr. / M. Kac, G. E. Uhlenbeck, P. C. Hemmer / P. C. Hemmer, M. Kac, G. E. Uhlenbeck / A. Lenard / O. C. Eldridge, M. Feix / R. J. Baxter / F. J. Dyson / H. Schmidt / H. Matsuda / R. E. Borland / J. Hori, H. Matsuda / R. L. Agacy / P. Dean / M. Toda / M. Toda / M. Toda, M. Wadati / M. Henon / H. Flaschka / F. Calogero / F. Calogero / B. Sutherland / C. Eckart / R. de L. Kronig, W. G. Penney / F. L. Scarf / H. M. James / J. M. Luttinger / W. Kohn / C. Zener / H. L. Frisch, S. P. Lloyd / R. E. Borland / R. L. Agacy, R. E. Borland / L. Dworin / B. Y. Tong, S. Y. Tong / M. Plischke, D. C. Mattis / P. D. Kirkman, J. B. Pendry / F. J. Romeiras, G. Rowlands / S. Tomonoga / D. C. Mattis, E. H. Lieb / K. D. Schotte, U. Schotte / D. C. Mattis / D. C. Mattis / A. Luther, V. J. Emery / A. Luther, I. Peschel / J. Carmelo, A. A. Ovchinnikov / H. Bergknoff, H. B. Thacker / S. Rudin / D. C. Mattis, B. Sutherland / C. N. Yang / C. N. Yang / E. H. Lieb, F. Y. Wu / E. H. Lieb, D. C. Mattis / M. Aizenman, E. H. Lieb / B. Sutherland / W. P. Su, J. R. Schrieffer, A. J. Heeger / R. Jackiw, J. R. Schrieffer / E. H. Lieb, W. Liniger / E. H. Lieb / A. Lenard / A. Lenard / J. B. McGuire / G. G. Batrouni, R. T. Scalettar, G. T. Zimanyi / C. N. Yang, C. P. Yang / H. Bethe / J. C. Bonner, M. E. Fisher / R. B. Griffiths / L. D. Faddeev, L. A. Takhtajan / J. D. Johnson / E. Lieb, T. Schultz, D. Mattis / F. D. M. Haldane / D. C. Mattis / I. Affleck, T. Kennedy, E. H. Lieb, H. Tasaki / I. Affleck / E. Fermi, J. Pasta, S. Ulam, M. Tsingou / J. Ford / G. W. Ford, M. Kac, P. Mazur / C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura
9810209754
Many-body problem
QC174.17.P7 / M36 1993
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