Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.

This landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves.

This book presents a review of theoretical and experimental work on the problem of the interplay of Anderson localization and superconductivity in strongly disordered systems. Superconductivity persists close to disorder-induced metal-insulator transition in a number of real systems, e.g. amorphous metals and compounds, systems disordered by fast neutron irradiation, systems with impurities, etc. High temperature superconductors are especially interesting from this point of view, as the experiments with controllable disordering may provide important clues to the nature of electronic states in these systems.The book starts with a brief discussion on modern aspects of localization theory, including the basic concept of scaling, self-consistent theory of localization and interaction effects. After that it analyzes disorder effects on Cooper pairing and superconductivity transition temperature as well as Ginzburg-Landau equations for superconductors that are close to the Anderson transition. A necessary generalization of the usual theory of dirty superconductors is formulated which allows one to analyze anomalies of the main superconducting properties close to disorder-induced metal-insulator transition. Finally, the book reviews a number of experiments demonstrating superconductivity close to the Anderson transition, in both traditional and high c superconductors."

Focuses on an important aspect of this highly diversified area of condensed state physics: the one-body approximation in the theory of disordered systems. It describes the scope of problems within the framework of this approximation, its use in formulating several basic concepts, and its value in revealing many characteristic features of disordered systems. The book's main focus is on the density of states and the space-time correlation functions, and on their basic thermodynamic and kinetic characteristics. Among the many areas explored are the general properties of the one-body models frequently used and descriptions of selected one-dimensional problems, including closed dynamical equations; these are then used to thoroughly explore the density of states for several systems. In addition, some of the more complex characteristics of one-dimensional disordered systems are examined using the Fokkerr-Planck equations developed earlier in the text. Also includes a description of the general structure of concentration expansions, giving examples of simple applications.

This thesis is a contribution at the intersection of a number of active fields in theoretical and experimental condensed matter, particularly those concerned with disordered systems, integrable models, lattice gauge theories, and non-equilibrium quantum dynamics. It contributes an important new facet to our understanding of relaxation in isolated quantum systems by conclusively demonstrating localization without disorder for the first time, answering a long-standing question in this field. This is achieved by introducing a family of models – intimately related to paradigmatic condensed matter models – and studying their non-equilibrium dynamics through a combination of exact analytical mappings and an array of numerical techniques. This thesis also makes contributions relevant to the theory of quantum chaotic behaviour by calculating novel, and often intractable, entanglement measures and out-of-time-ordered correlators. A concrete and feasible proposal is also made for the experimental realization and dynamical study of the family of models, based on currently available technologies.

``Electron-Electron Interactions in Disordered Systems'' deals with the interplay of disorder and the Coulomb interaction. Prominent experts give state-of-the-art reviews of the theoretical and experimental work in this field and make it clear that the interplay of the two effects is essential, especially in low-dimensional systems.

Confirming the fact that optics continues to be a highly active field of research where many interesting developments are currently taking place, the latest volume in this renowned series presents five review articles by well-known experts, on topics of current interest in optics. The first article concerns quantum fluctuations, a phenomenon encountered directly or indirectly in all optical measurements. Such fluctuations set limits to attainable accuracy with which measurements can be made. In recent years theoretical as well as experimental research has demonstrated that limitations arising from quantum fluctuations can sometimes be circumvented to some extent. These developments are of importance from the standpoint of basic physics as well as in connection with technological applications, such as noise reduction in communication systems. The second article deals with correlation holographic interferometry and speckle photography, paying special attention to the effects of random variation of surface microstructure on the contrast of interference fringes. The article which follows covers an important subject in the broad area of wave propagation in random media, namely wave localization. This phenomenon is a subtle manifestation of interference of multiply scattered waves and provides information about important properties of disordered systems. The article considers mainly localization in one-dimensional systems, which elucidate some of the underlying physics. The fourth article discusses an important nonlinear phenomenon, namely soliton propagation in fibres. Solitons are pulses which can propagate over long distances without change in shape. Because of their considerable stability, they are of particular interest for communication systems. The concluding article presents the theory and describes experiments on elementary quantum systems in the context of cavity quantum optics. Such experiments are providing deeper understanding of the interaction of light with matter and give new insights into the foundations of quantum mechanics.