Quantum Transport in Mesoscopic Systems Complexity and Statistical Fluctuations

This book presents the statistical theory of wave scattering and quantumtransport in complex systems - systems which have chaotic classical dynamics, asin the case of microwave cavities and quantum dots, or which possess quenchedrandomness, as in the case of disordered conductors - with an emphasis onmesoscopic fluctuations. The universal character of the statistical behaviour ofthese phenomena is revealed in a natural way by adopting a novel maximum-entropyapproach. Shannon's information entropy is maximised, subject to the symmetriesand constraints which are physically relevant, within the powerful andnon-perturbative theory of random matrices; this is a most distinctive featureof the book.Aiming for a self-contained presentation, the quantum theory of scattering, setin the context of quasi-one-dimensional, multichannel systems, and relateddirectly to scattering problems in mesoscopic physics, is introduced in chapterstwo and three. The linear-response theory of quantum electronic transport,adapted to the context of mesoscopic systems, is discussed in chapter four.These chapters, together with chapter five on the maximum-entropy approach andchapter eight on weak localization, have been written in a most pedagogicalstyle, suitable for use on graduate courses. In chapters six and seven, theproblem of electronic transport through classically chaotic cavities andquasi-one-dimensional disordered systems, is discussed. Many exercises areincluded, most of which are worked through in detail, aiding graduate students,teachers, and research scholars interested in the subject of quantum transportthrough disordered and chaotic systems.

Narendra Kumar is Professor of Physics and Director of the Raman Research Institute in India.