Introduction to Wave Scattering, Localization and Mesoscopic Phenomena

Waves are everywhere around us. We rely on light and sound to sense our immediate surroundings. Radio waves and microwaves are indispensable means of communication. Water waves are responsible for the ocean's perpetually dynamic image. Quantum waves associated with electrons and atoms, while not directly visible, are important in maintaining the structure and stability of solids. With such a ubiquitous presence, wave phenomena naturally occupy a central position in our study of the physical world. Indeed, for waves in simple systems and ordered structures, an extensive literature already exists. However, for the more difficult problem of waves in disordered media, i.e., multiply scattered waves, a coherent (but by no means complete) understanding has only recently emerged, and from what is already known the picture is very different from that we normally associate with waves. In particular, the possibility that a wave can become localized in a random medium is especially intriguing because localization involves a change in the basic wave character. A localized wave has no spatial periodicity or possibility for transport and thus requires a new theoretical framework for its description and understanding. The purposes of this volume are to delineate the main features of this emerging picture of wave behavior in disordered media and to introduce the theoretical techniques for describing these features. Mesoscopic phenomena, which are the natural manifestations of wave scattering and interference effects, are also treated. A brief sketch below of the prominent random-wave characteristics serves as both an introduction to the subject and a map to what follows.