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

Hardcover | May 26, 2004

byPier A. Mello, Narendra Kumar

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This book presents the statistical theory of complex wave scattering and quantum transport in physical systems which have chaotic classical dynamics, as in the case of microwave cavities and quantum dots, or which possess quenched randomness, as in the case of disordered conductors - with anemphasis on mesoscopic fluctuations. The statistical regularity of the phenomena is revealed in a natural way by adopting a novel maximum-entropy approach. Shannon's information entropy is maximised, subject to the symmetries and constraints which are physically relevant, within the powerful andnon-perturbative theory of random matrices; this is a most distinctive feature of the book. Aiming for a self-contained presentation, the quantum theory of scattering, set in the context of quasi-one-dimensional, multichannel systems, and related directly to scattering problems in mesoscopic physics, is introduced in chapters two and three. The linear-response theory of quantum electronictransport, adapted to the context of mesoscopic systems, is discussed in chapter four. These chapters, together with chapter five on the maximum-entropy approach and chapter eight on weak localization, have been written in a most pedagogical style, suitable for use on graduate courses. In chapterssix and seven, the problem of electronic transport through classically chaotic cavities and quasi-one-dimensional disordered systems is discussed. Many exercises are included, most of which are worked through in detail, aiding graduate students, teachers, and research scholars interested in thesubject of quantum transport through disordered and chaotic systems.

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This book presents the statistical theory of complex wave scattering and quantum transport in physical systems which have chaotic classical dynamics, as in the case of microwave cavities and quantum dots, or which possess quenched randomness, as in the case of disordered conductors - with anemphasis on mesoscopic fluctuations. The stat...

Pier A. Mello, Instituto de Fisica, U.N.A.M., Apartado Postal 20-364, Delegacion A. Obregon, 01000 Mexico D.F., Mexico. Tel: +52 55 5622 5142, Fax: +52 55 5622 5015, Email: mello@fisica.unam.mx Present position: Distinguished Professor of Physics at Instituto de Fisica, U.N.A.M., Mexico Narendra Kumar, Raman Research Institute, C.V. R...

other books by Pier A. Mello

Format:HardcoverDimensions:414 pages, 9.21 × 6.14 × 0.84 inPublished:May 26, 2004Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198525826

ISBN - 13:9780198525820

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Table of Contents

1. Introduction2. Quantum Mechanical Time Independent Scattering Theory I3. Quantum Mechanical Time Independent Scattering Theory II4. Linear Response Theory of Quantum Electronic Transport5. The Maximum Entropy Approach6. Electronic Transport through Open Chaotic Cavities7. Electronic Transport through Quasi One-Dimensional Disordered Systems8. An Introduction to Localization TheoryA. The Theorem of Kane-Serota-LeeB. The Conductivity Tensor in RPAC. The Conductance in Terms of the Transmission Coefficient of the SampleD. Evaluation of the Invariant Measure

Editorial Reviews

`...a most important and timely topic. [...] There are other books, but not at the same level of depth.'John Spence, Arizona State University