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The aim of this book is to present a statistical theory of certain complex wave-interference phenomena of considerable interest in mesoscopic physics, namely the statistical fluctuations of transmission and reflection of waves. The complexity here may derive from the chaotic nature of the underlying classical dynamics, as in the case of chaotic microwave cavities and quantum dots, or from the quenched randomness of scattering potentials, as in the case of disordered conductors. A theme that recurs throughout this book is that of universality of the statistical behavior, in the sense that it involves a relatively small number of relevant physical parameters, while the rest of the system details serves as mere scaffolding. Admittedly, there is an extensive literature on the subject of statistical wave scattering in physical systems such as atomic nuclei, disordered conductors and chaotic cavities; a powerful, non-perturbative approach is that of random-matrix theory. The treatment developed in this book is also frankly statistical; we follow a maximum-entropy approach, where the Shannon information entropy is maximized, subject to the symmetries and constraints that are physically relevant. We believe, however, that the present route to random-matrix theory is refreshingly novel. Indeed, this distinctive feature provides a partial justification for writing this book. Another, rather compelling, reason is that it collects and organizes in one place the material and notions which are scattered through an extensive literature on the subject. Much of the material presented here is derived from the published work of the authors in collaboration with several co-workers, and also from the work of others.
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