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

Paperback | September 15, 2010

byPier A. Mello, Narendra Kumar

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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 onmesoscopic 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 thepowerful, 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 severalco-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 quantumelectronic 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 problemof 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 generallyin the subject of quantum transport through disordered and chaotic systems in their preparation for it, and beyond.

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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 onmesoscopic fluctuations.The universal character...

Pier Mello is Distinguished Professor at the Universidad Nacional Autonoma de Mexico (UNAM). He took his B.S. degree in Physics at UNAM in 1962, and his PhD there in 1965. he was a member of the Institute for Advanced Study, Princeton, 1965-67, and has been Full Professor of Physics at the Instituto de Fisica, UNAM, Mexico, since 1974...

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Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy…
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Hardcover|May 26 2004

$269.10 online$337.50list price(save 20%)
Format:PaperbackDimensions:416 pages, 9.21 × 6.14 × 0.68 inPublished:September 15, 2010Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198525834

ISBN - 13:9780198525837

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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

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