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.
Author(s): A. Bishop (auth.), Professor Dr. Giorgio Benedek, Professor Dr. Heinz Bilz, Dr. Roland Zeyher (eds.)
Series: Springer Series in Solid-State Sciences 47
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1983
Language: English
Pages: 314
Tags: Theoretical, Mathematical and Computational Physics;Condensed Matter Physics
Front Matter....Pages I-VIII
Front Matter....Pages 1-1
Introduction....Pages 3-6
Spectral Transform and Solitons....Pages 7-17
Linear and Nonlinear Aspects in Lattice Dynamics....Pages 18-27
The Thermoelastic-Plastic Transition in Metals Thermal Emission as a Probe to Identify the Yield Point....Pages 28-34
Solvable Many-Body Problems....Pages 35-36
Front Matter....Pages 37-66
Anharmonic Properties Near Structural Phase Transitions: An Update....Pages 67-67
Critical Phenomena from Wilson’s Exact Renormalization-Group Equation....Pages 68-79
Quantum Fluctuations of a 3-Dimensional φ 4 Model-Quantum Ferroelectrics....Pages 80-84
Stochastic Quantization and Critical Dynamics....Pages 85-89
Front Matter....Pages 90-96
The Physical Mechanisms Leading to Incommensurate Phases....Pages 97-97
Excitations and Chaotic States in Incommensurate Multi-Soliton Lattices: Experiments....Pages 98-112
The Transition by Breaking of Analyticity in Incommensurate Structures and the Devil’s Staircase; Application to Metal-Insulator Transitions in Peierls Chains....Pages 113-125
Non-Linearity Induced by Charge-Density Wave Motion....Pages 126-143
Low-Frequency Dynamics of Soliton Lattices....Pages 144-152
Front Matter....Pages 153-157
Universality and Fractal Dimension of Mode-Locking Structure in Systems with Competing Periodicities....Pages 159-159
Chaos and Solitons in Josephson Junctions....Pages 160-169
Transition to Deterministic Chaos in a Hydrodynamic System....Pages 170-188
Chaos and Solitons in Dissipative Nonlinear Systems....Pages 189-196
Chaos-Induced Diffusion....Pages 197-203
Front Matter....Pages 204-210
Classical Statistical Mechanics of Lattice Dynamic Model Systems: Transfer Integral and Molecular-Dynamics Studies....Pages 211-211
The Spectral Transform: Methods for the Fourier Analysis of Nonlinear Wave Data....Pages 212-241
Kink- and Polaron-Solitons in Models of Polyacetylene and Other Peierls-Distorted Materials....Pages 242-261
Counting Solitons and Phonons in the Toda Lattice....Pages 263-270
Structure of Interfaces....Pages 271-277
Commensurate Structures in Solids....Pages 278-280
Periodon Solutions in Two- and Three-Dimensional Lattices....Pages 281-293
Intrinsic Non-Linearity (in Phonon Numbers) of the Response Functions of Elastic Systems: A Proposal of Quantum Acoustics....Pages 294-299
Back Matter....Pages 300-310
....Pages 311-314
