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Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint

Online ISBN:
9780191712234
Print ISBN:
9780198525820
Publisher:
Oxford University Press
Book

Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint

Pier A. Mello,
Pier A. Mello
Instituto de Fisica, UNAM, Mexico City, Mexico
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Narendra Kumar
Narendra Kumar
Director, Raman Research Institute, Bangalore, India
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Published online:
1 September 2007
Published in print:
20 May 2004
Online ISBN:
9780191712234
Print ISBN:
9780198525820
Publisher:
Oxford University Press

Abstract

This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities and quantum dots) or possessing quenched randomness (e.g., disordered conductors). The emphasis here is on mesoscopic fluctuations of the sample-specific transport. The universal character of the statistical behaviour of these phenomena is revealed in a natural way through a novel maximum-entropy approach (MEA). The latter leads to the most probable distribution for the set of random matrices that describe the ensemble of disordered/chaotic samples, which are macroscopically identical but differ in microscopic details. Here, the Shannon information entropy associated with these random matrices is maximized subject to the symmetries and the constraints which are physically relevant. This non-perturbative information-theoretic approach is reminiscent of, but distinct from, the standard random-matrix theory, and indeed forms the most distinctive feature of the book.

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