In 1966, E.H. Lieb and D.C. r1attis published a book on "Mathematical Physics in One Dimension" [Academic Press, New York and London] which is much more than just a collection of reprints and which in fact marked the beginnings of the rapidly growing interest in one-dimensional problems and materials in the 1970's. In their Foreword, Lieb and r~attis made the observation that " ... there now exists a vast literature on this subject, albeit one which is not indexed under the topic "one dimension" in standard indexing journals and which is therefore hard to research ... ". Today, the situation is even worse, and we hope that these Proceedings will be a valuable guide to some of the main current areas of one-dimensional physics. From a theoretical point of view, one-dimensional problems have always been very attractive. Many non-trivial models are soluble in one dimension, while they are only approximately understood in three dimensions. Therefore, the corresponding exact solutions serve as a useful test of approximate ma thematical methods, and certain features of the one-dimensional solution re main relevant in higher dimensions. On the other hand, many important phe nomena are strongly enhanced, and many concepts show up especially clearly in one-dimensional or quasi -one-dimensional systems. Among them are the ef fects of fluctuations, of randomness, and of nonlinearity; a number of in teresting consequences are specific to one dimension.
Author(s): Daniel C. Mattis (auth.), Dr. Jakob Bernasconi, Dr. Toni Schneider (eds.)
Series: Springer Series in Solid-State Sciences 23
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1981
Language: English
Pages: 370
Tags: Condensed Matter Physics
Front Matter....Pages I-IX
Front Matter....Pages 1-1
How to Reduce Practically Any Problem to One Dimension....Pages 3-10
Front Matter....Pages 11-11
An Overview of Soliton Mathematics....Pages 13-26
Statistical Mechanics of Solitons....Pages 27-46
The Quantum Inverse Scattering Method and Applications to Spin Chains....Pages 47-58
Bethe Ansatz, Connection Between One-Dimensional Models and Their Classification....Pages 59-62
Quantum Statistics of Solitons....Pages 63-74
Classical Statistical Mechanics of Soliton-Bearing Systems....Pages 75-86
Multistable Driven Systems....Pages 87-99
Inherent Effects of Discretization in an Interacting Kink-Phonon System....Pages 100-103
Ising Models, Solitons, and the Devil’s Staircase....Pages 104-112
Front Matter....Pages 113-113
Quantum Spin Chains....Pages 115-128
Dynamic Correlations in Classical Heisenberg Chains....Pages 129-139
Dynamics of One-Dimensional Magnets: Neutron Scattering Studies....Pages 140-152
Solitons in One-Dimensional Magnets with Various Symmetries....Pages 153-156
A Comparison of Static and Dynamic Properties of One-Dimensional Magnets and Corresponding sG Systems....Pages 157-160
Evidence for Soliton Excitations in the One-Dimensional Antiferromagnet TMMC....Pages 161-164
Quantum Effects in the Dynamics of the One-Dimensional Planar Antiferromagnet....Pages 165-168
Ground-State and Local Excitations in Co(PYR) 2 Cl 2 ....Pages 169-172
New High-Field Phenomena in Spin-Peierls Systems....Pages 173-176
Front Matter....Pages 177-177
Solitons in Polyacetylene: A Summary of Experimental Results....Pages 179-193
Front Matter....Pages 177-177
Magnetic Resonance Studies of Soliton Diffusion in Polyacetylene....Pages 194-200
Theory of Polymers Having Broken Symmetry Ground States....Pages 201-211
Attracting Solitons and a first Order Lock-In Transition: Metallic Polyacetylene and the Spin-Peierls System....Pages 212-213
Polyacetylene Revisited....Pages 214-217
Magnetic Behavior of Polyacetylene, Polyparaphenylene and Polypyrrole....Pages 218-220
Static and Dynamic Susceptibilities of Magnetic Polymers....Pages 221-224
Front Matter....Pages 225-225
Structural Ordering in Quasi-One-Dimensional Systems....Pages 227-228
One-Dimensional Metals: Theory versus Experiment....Pages 229-238
Electronic Instabilities in Quasi-One-Dimensional Conductors: Insulator or Superconductor?....Pages 239-252
Non-linear Transport in the Fröhlich Mode Conductor, NbSe 3 ....Pages 253-262
Front Matter....Pages 263-263
Lattice Dynamics and Spectral Properties of Disordered Chains....Pages 265-276
Excitation Dynamics in Random One-Dimensional Systems....Pages 277-288
Random Exchange Spin Chains....Pages 289-301
Universality in Quantum Random Magnetic Chains....Pages 302-305
Localization in One Dimension....Pages 306-309
Localization in Thin Wires....Pages 310-316
Transport Quantities in One-Dimensional Disordered Systems....Pages 317-320
Front Matter....Pages 321-321
One-Dimensional Superionic Conductors....Pages 323-334
One-Dimensional Coulomb Systems....Pages 335-350
Exciton Dynamics in Quasi-One-Dimensional Molecular Systems....Pages 351-362
Front Matter....Pages 321-321
Critical Phenomena and Fractals with Dimensionality Near 1....Pages 363-365
Back Matter....Pages 367-370
