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Quantum Transport in Mesoscopic Systems - Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint (Paperback)
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Quantum Transport in Mesoscopic Systems - Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint (Paperback)
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The aim of this book is to present a statistical theory of wave
scattering by complex systems -systems which have a chaotic
classical dynamics, as in the case of microwave cavities and
quantum dots, or possess quenched randomness, as in the case of
disordered conductors- with emphasis on mesoscopic fluctuations.
The universal character of the statistical behavior of these
phenomena is incorporated in a natural way by approaching the
problem from a Maximum-Entropy viewpoint -Shannon's information
entropy is maximized, subject to the symmetries and constraints
that are physically relevant- within the powerful, non-perturbative
Theory of Random Matrices. This is a distinctive feature of the
present book that greatly motivated our writing it. Another reason
is that it collects in one place the material and notions -derived
from the published work of the authors in collaboration with
several co-workers, as well as from the work of others- which are
scattered through research journals and textbooks on the subject.
To make the book self-contained, we present in Chapters 2 and 3 the
quantum theory of scattering, set in the context of
quasi-one-dimensional, multichannel systems, thus related directly
to scattering problems in mesoscopic physics. Chapter 4 discusses
the linear-response theory of quantum electronic transport, adapted
to the context of mesoscopic systems. These chapters, together with
Chapter 5 on the Maximum-Entropy Approach and Chapter 8 on weak
localization, have been written in a pedagogical style, and can be
used as part of a graduate course. Chapters 6 and 7 discuss the
problem of electronic transport through classically chaotic
cavities and quasi-one-dimensional disordered systems. There are
many exercises, most of them worked out in detail, distributed
throughout the book. This should help graduate students, their
teachers and the research scholars interested generally in the
subject of quantum transport through disordered and chaotic systems
in their preparation for it, and beyond.
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