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Non-linear effects are basically manifested in a variety of physical phenomena such as defect mediated transitions, pattern formation, growth of aggregates, turbulence, chemical reactions, diffusion in porous media, biological information processing, etc. Many non-linear dynamical systems are extremely sensitive to small changes in the initial conditions. Different routes to chaos have been established and a new geometry, called fractal geometry, has been developed. The aim of this School is to review the main achievements of the modern theory of irregular structures and to discuss the exciting new trends in non-linear phenomena.
In recent years one has witnessed in physics a substantial increase in interest in carrying out fundamental studies in the nonlinear optics of condensed matter. At the Danish universities, this increase has been especially pronounced at the Institute of Physics at the University of Aalborg, where the main activities are centered around fundamental research within the domains of nonlinear quantum optics, nonlinear optics of metals and superconductors, and nonlinear surface optics. In recognition of this it was decided to arrange the first international summer school on nonlinear optics in Denmark at the Institute of Physics at the University of Aalborg. This book is based on the lectures and contributed papers presented at this international summer school, which was held in the period 31 July-4 Au gust 1989. About 60 experienced and younger scientists from 12 different countries participated. Twenty-eight lectures were given by 14 distinguished scientists from the United States, Italy, France, Germany, Scotland, England, and Denmark. In addition to the lectures given by the invited speakers, 11 contributed papers were presented. The programme of the summer school em phasized a treatment of basic physical properties of the nonlinear interaction of light and condensed matter and both theoretical and experimental aspects were covered. Furthermore, general principles as well as topics of current interest in the research literature were discussed.
ill the past three decades there has been enonnous progress in identifying the es sential role that "nonlinearity" plays in physical systems. Classical nonlinear wave equations can support localized, stable "soliton" solutions, and nonlinearities in quantum systems can lead to self-trapped excitations, such as polarons. Since these nonlinear excitations often dominate the transport and response properties of the systems in which they exist, accurate modeling of their effects is essential to interpreting a wide range of physical phenomena. Further, the dramatic de velopments in "deterministic chaos", including the recognition that even simple nonlinear dynamical systems can produce seemingly random temporal evolution, have similarly demonstrated that an understanding of chaotic dynamics is vital to an accurate interpretation of the behavior of many physical systems. As a conse quence of these two developments, the study of nonlinear phenomena has emerged as a subject in its own right. During these same three decades, similar progress has occurred in understand ing the effects of "disorder". Stimulated by Anderson's pioneering work on "dis ordered" quantum solid state materials, this effort has also grown into a field that now includes a variety of classical and quantum systems and treats "disorder" arising from many sources, including impurities, random spatial structures, and stochastic applied fields. Significantly, these two developments have occurred rather independently, with relatively little overlapping research.
This proceedings feature lectures and contributions identifying and exploring major new trends in contemporary materials science, in particular electronic and optoelectronic materials. Various aspects of the preparative technology, characterisation techniques, physical and physicochemical properties and device applications of new electronic and optoelectronic materials (amorphous, polycrystalline, crystalline semiconductors, magnetic media, high Tc superconductors, polymeric thin films, ferroelectrics, etc.) are treated via in depth reviews.
This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.