Microscopic Aspects Of Nonlinearity In Condensed Matter

Proceedings of a NATO ARW held in Florence, Italy, June 7--13, 1990

In the history of physics and science, quantum mechanics has served as the foundation of modern science. This book discusses the properties of microscopic particles in nonlinear systems, principles of the nonlinear quantum mechanical theory, and its applications in condensed matter, polymers and biological systems.The book is essentially composed of three parts. The first part presents a review of linear quantum mechanics, as well as theoretical and experimental fundamentals that establish the nonlinear quantum mechanical theory. The theory itself and its essential features are covered in the second part. In the final part, extensive applications of this theory in physics, biology and polymer are introduced. The whole volume forms a complete system of nonlinear quantum mechanics.The book is intended for researchers, graduate students as well as upper-level undergraduates.

The Sixth Annual Conference of the Center for Nonlinear Studies at the Los Alamos National Laboratory was held May 5-9, 1986, on the topic "Nonlinearity in Condensed Matter: Lessons from the Past and Prospects for the Future. " As conference organizers, we felt that the study of non linear phenomena in condensed matter had matured to the point where it made sense to take stock of the numerous lessons to be learned from a variety of contexts where nonlinearity plays a fundamental role and to evaluate the prospects for the growth of this general discipline. The successful 1978 Oxford Symposium on nonlinear (soliton) struc ture and dynamics in condensed matter (Springer Ser. Solid-State Sci. , Vol. 8) was held at a time when the ubiquity of solitons was just begin ning to be appreciated by the condensed matter community; in subsequent years the soliton paradigm has provided a rather useful framework for in vestigating a large number of phenomena, particularly in low-dimensional systems. Nevertheless, we felt that the importance of nonlinearity in wider arenas than "solitonics" merited a significant expansion in the scope of the conference over that of the 1978 symposium. Indeed, many of the lessons are quite general and their potential for cross-fertilization of otherwise poorly connected disciplines was certainly one of the prime motivations for this conference. Thus, while these proceedings contain many contribu tions pertaining to soliton behavior in different contexts, the reader will find much more as well, particularly in the later chapters.

In the past three decades there has been enormous progress in identifying the essential role that nonlinearity plays in physical systems, including supporting soliton-like solutions and self-trapped sxcitations such as polarons. during the same period, similarly impressive progress has occurred in understanding the effects of disorder in linear quantum problems, especially regarding Anderson localization arising from impurities, random spatial structures, stochastic applied fields, and so forth. These striking consequences of disorder, noise and nonlinearity frequently occur together in physical systems. Yet there have been only limited attempts to develop systematic techniques which can include all of these ingredients, which may reinforce, complement or frustrate each other. This book contains a range of articles which provide important steps toward the goal of systematic understanding and classification of phenomenology. Experts from Australia, Europe, Japan, USA, and the USSR describe both mathematical and numerical techniques - especially from soliton and statistical physics disciplines - and applicaations to a number of important physical systems and devices, including optical and electronic transmission lines, liquid crystals, biophysics and magnetism.

Present day heterogeneous catalysis is rapidly being transformed from a technical art into a science-based technology. A major contribution to this important change is the advance of surface spectroscopic techniques able to characterize the complex surfaces of the heterogeneous catalytic system. The Advanced Study Institute (on which the current proceedings is based) has as its primary aim the bringing together of a variety of lecturers, outstanding in those fields of experience, to enable a broad coverage of different relevant approaches. Not only catalyst characterization but also catalytic reactivity had to be covered in order to relate catalyst properties with catalyst performance. Since modern catalysis relates catalytic performance to microscopic molecular catalyst features, theoretical electronic aspects also had to be included. The Advanced Study Institute had a unique feature in that it brought together physicists, catalytic chemists and chemical engineers whom rarely directly interact. From physics especially new experimental possibilities of beams were emphasized. At present it is possible to obtain very detailed information on model catalysts, whilst the applications to practical catalysts are gaining rapidly in sophistication. Apart from the plenary lectures, the Institute included "hot topics" to highlight special developments and offered participants the opportunity to present contributed papers (either orally or as a poster). These contributions formed an integral part of the summer school and significantly enhanced the interaction between participants. Inclusion of the hot topics and contributed papers in these proceedings give them an added topical value.

Singularities in Fluids, Plasmas and Optics, which contains the proceedings of a NATO Workshop held in Heraklion, Greece, in July 1992, provides a survey of the state of the art in the analysis and computation of singularities in physical problems drawn from fluid mechanics, plasma physics and nonlinear optics. The singularities include curvature singularities on fluid interfaces, the onset of turbulence in 3-D inviscid flows, focusing singularities for laser beams, and magnetic reconnection. The highlights of the book include the nonlinear Schrödinger equation for describing laser beam focusing, the method of complex variables for the analysis and computation of singularities on fluid interfaces, and studies of singularities for the 3-D Euler equations. The book is suitable for graduate students and researchers in these areas.

The phase transformation from liquid to solid is a phenomenon central to a wide range of manufacturing and natural processes. The presence of phase transformation can drive convection in the melt through the liberation of latent heat, the rejection of solute, and the change of density upon freezing. The fluid mechanics itself can playa central role; the phase transformation can be strongly altered by convective transport in the liquid through the modification of the thermal and solutal environment of the solid-liquid interface; these local fields control the freezing characteristics at the interface. The convection can be generated naturally by buoyancy forces arising from gradients of temperature and concentration in the liquid, by density changes upon freezing, and by thermocapillary and solutocapillary forces on liquid-solid interfaces. The interactive coupling between solidification and convection forms the subject of this volume. Such coupled processes are significant on a large range of scales. Among the applications of interest are the manufacture of single crystals, the processing of surfaces using laser or molecular beams, and the processes of soldering and welding. One wants to understand and predict macrosegregation in castings, transport and fractionation in geological and geophysical systems, and heat accumulation in energy redistribution and storage systems. This volume contains papers presented at the NATO Advanced Research Workshop on "Interactive Dynamics of Convection and Solidification" held in Chamonix, France, March 8-13, 1992.

Recent innovations in experimental techniques such as molecular and cluster beam epitaxy, supersonic jet expansion, matrix isolation and chemical synthesis are increasingly enabling researchers to produce materials by design and with atomic dimension. These materials constrained by sire, shape, and symmetry range from clusters containing as few as two atoms to nanoscale materials consisting of thousands of atoms. They possess unique structuraI, electronic, magnetic and optical properties that depend strongly on their size and geometry. The availability of these materials raises many fundamental questions as weIl as technological possibilities. From the academic viewpoint, the most pertinent question concerns the evolution of the atomic and electronic structure of the system as it grows from micro clusters to crystals. At what stage, for example, does the cluster look as if it is a fragment of the corresponding crystal. How do electrons forming bonds in micro-clusters transform to bands in solids? How do the size dependent properties change from discrete quantum conditions, as in clusters, to boundary constrained bulk conditions, as in nanoscale materials, to bulk conditions insensitive to boundaries? How do the criteria of classification have to be changed as one goes from one size domain to another? Potential for high technological applications also seem to be endless. Clusters of otherwise non-magnetic materials exhibit magnetic behavior when constrained by size, shape, and dimension. NanoscaIe metal particles exhibit non-linear opticaI properties and increased mechanical strength. SimiIarly, materials made from nanoscale ceramic particIes possess plastic behavior.