Mathematical Physics In One Dimension: Exactly Soluble Models Of Interacting Particles (perspectives In Physics : A Series Of Reprint Collections)

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 Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles covers problems of mathematical physics with one-dimensional analogs. The book discusses classical statistical mechanics and phase transitions; the disordered chain of harmonic oscillators; and electron energy bands in ordered and disordered crystals. The text also describes the many-fermion problem; the theory of the interacting boson gas; the theory of the antiferromagnetic linear chains; and the time-dependent phenomena of many-body systems (i.e., classical or quantum-mechanical dynamics). Physicists and mathematicians will find the book invaluable.