Professor Dmitry A. Ryndyk is an expert on quantum transport theory and has taught classes on this subject at the University of Regensberg and Technische Universität Dresden. This book has been developed from his course notes and is aimed at being a suitable advanced-level textbook for master’s- and PhD-level students, with the further intent that it be useful for experts working in the fields of quantum transport theory and nanoscience. Topics that the author says are not discussed include quantum interference of the Aharonov–Bohm type, weak localization, universal conductance fluctuations, random matrix theory, the quantum Hall effect, and quasiclassical and semiclassical transport. There are nine chapters split in two parts.
Chapter 1 is a brief introduction that outlines the excluded subjects listed previously, and provides an overview of the rest of the book. Part I, covering basic concepts, then follows. Chapter 2 explores the Landauer–Büttiker method with sections on quantum junctions, a formulation and derivation of the Landauer formula, multichannel scattering and transport, and a consideration of multi-terminal systems. Chapter 3 discusses Green functions with sections on the scattering problem, matrix Green functions, recursive methods, semi-infinite electrodes, and resonant transport. Chapter 4 explores tunneling with sections on the Hamiltonian method and sequential tunneling. Chapter 5 explores electron–electron interactions and the Coulomb blockade, including sections on the electron–electron interaction, single-electron box, single-electron transistor, Coulomb blockade in quantum dots, and co-tunneling. Chapter 6 explores vibrons and polarons, including sections on electron–vibron interactions, inelastic electron tunneling spectroscopy, local polarons, inelastic tunneling in the single-particle approximation, and sequential inelastic tunneling.
Part II considers advanced methods. Chapter 7 explores nonequilibrium Green functions (NGFs), including retarded and advanced Green functions, the fluctuation-dissipation theorem, free fermions, free bosons, Green functions for vibrons, the Schwinger–Keldysh time contour, the nonequilibrium equation of motion method, and the Kadanoff–Baym–Keldysh method. Chapter 8 discusses NGF methods for transport through nanosystems. Chapter 9 explores nonequilibrium problems involving vibronic effects as well as Coulomb blockade effects. There is a two-page index, and most of the book’s 77 illustrations add value.
The author has done an excellent job of citing the original research literature; however, there are only a few reference citations for 2010, and none beyond that date. The book is heavily mathematical, and (as the author notes) requires some prior understanding of theoretical physics, including quantum mechanics. Although the scientific problems discussed above are worked through in detail, no homework problems are provided. However, the book is useful for a graduate-level seminar class on nanoscale quantum transport and for self-study for experts working in this field. For those interested in nanoscale quantum transport, I recommend this book.
Reviewer: Steven C. Moss is a senior scientist in the Electronics and Photonics Laboratory at The Aerospace Corporation in El Segundo, Calif., USA.
