The investigation of the properties of nonlinear systems is one of the fast deve­ loping areas of physics. In condensed matter physics this 'terra incognita' is approached from various starting points such as phase transitions and renormali­ zation group theory, nonlinear models, statistical mechanics and others. The study of the mutual interrelations of these disciplines is important in developing uni­ fying methods and models towards a better understanding of nonlinear systems. The present book collects the lectures and seminars delivered at the workshop on "Statics and Dynamics of Nonlinear Systems" held at the Centre for SCientific Culture "Ettore Majorana·" in Erice;· Italy, July 1 to 11, 1983, in the framework of the International School of Materials Science and Technology. Experts and young researchers came together to discuss nonlinear phenomena in condensed matter physics. The book is divided into five parts, each part containing a few general artic­ les introducing the subject, followed by related specialized papers. The first part deals with basic properties of nonlinear systems including an introduction to the general theoretical methods. Contrfbutions to the nonlinear aspects of phase transitions are collected in the second part. In the third part properties of incommensurate systems are discussed. Here, competing interactions lead to charge-density waves, soliton lattices and other complex structures. Another point of special interest, illustrated in the fourth part, is the 'chaotic' be­ havior of various systems such as Josephson junctions and discrete lattices.

Inhalt

1 Basic Aspects of Nonlinear Systems.- 1.1 Introduction.- 1.2 Spectral Transform and Solitons.- 1.3 Linear and Nonlinear Aspects in Lattice Dynamics.- 1.4 The Thermoelastic-Plastic Transition in Metals: Thermal Emission as a Probe to Identify the Yield Point.- 1.5 Solvable Many-Body Problems.- 1.6 Stability of Hydrated M1+-DNAs: A Challenge in the Theory of Nonlinear Systems.- 2 Phase Transitions.- 2.1 Anharmonic Properties Near Structural Phase Transitions: An Update.- 2.2 Critical Phenomena from Wilson's Exact Renormalization-Group Equation.- 2.3 Quantum Fluctuations of a 3-Dimensional ?4 Model-Quantum Ferroelectrics.- 2.4 Stochastic Quantization and Critical Dynamics.- 3 Incommensurate Phases and Charge-Density Waves.- 3.1 The Physical Mechanisms Leading to Incommensurate Phases.- 3.2 Excitations and Chaotic States in Incommensurate Multi-Soliton Lattices: Experiments.- 3.3 The Transition by Breaking of Analyticity in Incommensurate Structures and the Devil's Staircase; Application to Metal-Insulator Transitions in Peierls Chains.- 3.4 Non-Linearity Induced by Charge-Density Wave Motion.- 3.5 Low-Frequency Dynamics of Soliton Lattices.- 4 Chaos in Condensed Matter.- 4.1 Universality and Fractal Dimension of Mode-Locking Structure in Systems with Competing Periodicities.- 4.2 Chaos and Solitons in Josephson Junctions.- 4.3 Transition to Deterministic Chaos in a Hydrodynamic System.- 4.4 Chaos and Solitons in Dissipative Nonlinear Systems.- 4.5 Chaos-Induced Diffusion.- 5 Solitons and Other Exact Solutions of Nonlinear Equations.- 5.1 Classical Statistical Mechanics of Lattice Dynamic Model Systems: Transfer Integral and Molecular-Dynamics Studies.- 5.2 The Spectral Transform: Methods for the Fourier Analysis of Nonlinear Wave Data.- 5.3 Kink- and Polaron-Solitons in Models of Polyacetylene and Other Peierls-Distorted Materials.- 5.4 Counting Solitons and Phonons in the Toda Lattice.- 5.5 Structure of Interfaces.- 5.6 Commensurate Structures in Solids.- 5.7 Periodon Solutions in Two- and Three-Dimensional Lattices.- 5.8 Intrinsic Non-Linearity (in Phonon Numbers) of the Response Functions of Elastic Systems: A Proposal of Quantum Acoustics.- Index of Contributors.