Mathematical Physics in One Dimension. Exactly Soluble Models of Interacting Particles

Content: 
PERSPECTIVES IN PHYSICS: A Series of Reprint Collections, Page ii
Front Matter, Page iii
Copyright, Page iv
Foreword, Pages v-viii
Chapter 1 - Classical Statistical Mechanics, Pages 3-24
A Simple Method for Treating the Statistical Mechanics of One-Dimensional Substances,, Pages 25-27
SUR L'INTÉGRALE DE CONFIGURATION POUR LES SYSTÉMES DE PARTICULES Á UNE DIMENSION, Pages 28-34
Molecular Distribution Functions in a One-Dimensional Fluid, Pages 35-44
Certain General Order-Disorder Models in the Limit of Long-Range Interactions, Pages 45-52
On the van der Waals Theory of the Vapor–Liquid Equilibrium. I. Discussion of a One-Dimensional Model, Pages 53-65
On the van der Waals Theory of the Vapor–Liquid Equilibrium. III. Discussion of the Critical Region, Pages 66-80
One-Dimensional Phase Transition in the Spherical Model of a Gas, Pages 81-90
Exact Statistical Mechanics of a One-Dimensional System with Coulomb Forces, Pages 91-102
One-Dimensional Plasma Model at Thermodynamic Equilibrium, Pages 103-107
Statistical mechanics of a one-dimensional Coulomb system with a uniform charge background, Pages 108-116
Chapter 2 - The Disordered Chain of Harmonic Oscillators, Pages 119-131
The Dynamics of a Disordered Linear Chain, Pages 132-139
Disordered One-Dimensional Crystals, Pages 140-156
Special Frequencies in the Vibrational Spectra of Disordered Chains, Pages 157-158
Some exact results for the vibrational spectrum of a disordered chain, Pages 159-164
Structure of the Spectra of Disordered Systems. I: —– Fundamental Theorems —–, Pages 165-171
The vibrational spectrum of a disordered linear system, Pages 172-177
Vibrations of glass-like disordered chains, Pages 178-195
Theory of Normal Vibrations of Chain Molecules with Finite Length, Pages 196-210
Chapter 3 - Electron Energy Bands in Ordered and Disordered Crystals, Pages 213-223
The Approximate Solution of One-Dimensional Wave Equations, Pages 224-242
Quantum Mechanics of Electrons in Crystal Lattices, Pages 243-257
New Soluble Energy Band Problem, Pages 258-261
Energy Bands and Wave Functions in Periodic Potentials, Pages 262-270
WAVE PROPAGATION IN ONE-DIMENSIONAL STRUCTURES, Pages 271-278
Analytic Properties of Bloch Waves and Wannier Functions, Pages 279-291
A Theory of the Electrical Breakdown of Solid Dielectrics., Pages 292-298
Electron Levels in a One-Dimensional Random Lattice, Pages 299-313
Existence of Energy Gaps in One-Dimensional Liquids, Pages 314-319
The electronic structure of a one-dimensional random alloy, Pages 320-329
Existence of Energy Gaps in the Spectrum of a One-Dimensional Atomic Chain, Pages 330-335
Chapter 4 - The Many-Fermion Problem, Pages 339-348
Remarks on Bloch's Method of Sound Waves applied to Many-Fermion Problems, Pages 349-374
Exact Solution of a Many-Fermion System and Its Associated Boson Field, Pages 375-383
Theory of Ferromagnetism and the Ordering of Electronic Energy Levels, Pages 384-392
Chapter 5 - The Bose Gas, Pages 395-403
Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State, Pages 404-415
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum, Pages 416-424
Momentum Distribution in the Ground State of the One-Dimensional System of Impenetrable Bosons, Pages 425-438
Study of Exactly Soluble One-Dimensional N-Body Problems, Pages 439-453
Chapter 6 - Magnetism, Pages 457-465
Two Soluble Models of an Antiferromagnetic Chain, Pages 466-486
Linear Magnetic Chains with Anisotropic Coupling, Pages 487-505
Spin-Wave Spectrum of the Antiferromagnetic Linear Chain, Pages 506-510
Magnetization Curve at Zero Temperature for the Antiferromagnetic Heisenberg Linear Chain, Pages 511-518
Chapter 7 - Time-Dependent Phenomena, Pages 521-523
Statistical Mechanics of Assemblies of Coupled Oscillators, Pages 524-535
Dynamics of a Simple Many-Body System of Hard Rods, Pages 536-544
Equipartition of Energy for Nonlinear Systems, Pages 545-551
Computer Studies of Energy Sharing and Ergodicity for Nonlinear Oscillator Systems, Pages 552-565