The dynamical properties of solids have recently attracted renewed interest in connection with the increasing understanding of phase transitions and re lated phenomena. In particular, soft modes or, more generally, phonon 'anom alies' seem to play an important role in structural and electronic phase tran sitions, such as ferroelectric or superconducting transitions. The understanding of the mechanisms responsible for the occurrence of unusually low frequencies in phonon spectra requires a detailed analysis of the microscopic forces governing the lattice vibrations. Of particular importance is the influence of the electron lattice interaction in the adiabatic approximation which in many cases is the origin of peculiarities in the phonon self-energy. In this work the vibrational spectra of pure non-metals and of those con taining point defects are investigated. ' In these materials the interrelation be tween the pseudo-harmonic forces (determining the phonon dispersion re lations) and the non-linear anharmonic and electron-phonon forces (as they act in infrared and Raman spectra) is most obvious and can be quantitatively analysed in terms of appropriate models. The main task is to arrive at a physically correct treatment of electronic degrees of freedom, as for example in an electronic 'shell' model, which leads to the description of phonon spectra in terms of long-range polarizabilities and short-range deformabilities. The pur pose of our review is to stimulate further investigations which, we hope, will result in explicit relations between the parameters of the semi-microscopic models and the matrix elements from the electronic band structure."

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."

This phonon atlas presents a collection of phonon-dispersion and density-of states curves of more than a hundred insulating crystals. It grew out of an appendix to a handbook article on phonon spectra 2.1J from which it was fin ally separated mainly because this phonon atlas provides a rather self-con tained tool for every scientist who is working in the field of dynamical properties of solids. He often may find it' useful to have a handy documen tation of the experimental phonon dispersion curves which have been measured so far, together with information on calculated dispersion relations and densities of states. The book will be found to be incomplete by readers who are interested not only in phonon frequencies of a specific crystal but would also like to know about related properties such as elastic and dielectric constants. This is, at the present time, beyond the scope of this volume, but the authors would welcome all suggestions and criticism which could be considered for a forth coming edition. Furthermore, we would be pleased to provide interested readers with information about phonon spectra which came to our knowledge after completion of the manuscript. On the other hand, we will be most grateful for all information about phonon dispersion curves which is missing in our collection or new data for further editions."