Topological quantum numbers are distinguished from quantum numbers based on symmetry because they are insensitive to the imperfections of the systems in which they are observed. They have become very important in precision measurements in recent years, and provide the best measurements of voltage and electrical resistance. This book describes the theory of such quantum numbers, starting with Dirac's argument for the quantization of electric charge, and continuing with discussions on the helium superfluids, flux quantization and the Josephson effect in superconductors, the quantum Hall effect, solids and liquid crystals, and topological phase transitions. The accompanying reprints include some of the classic experimental and theoretical papers in this area.
Physicists — both experimental and theoretical — who are interested in the topic will find this book an invaluable reference.
Contents:
- Quantization of Electric Charge
- Circulation and Vortices in Superfluid 4He
- Superconductivity and Flux Quantization
- Josephson Effects
- Superfluid 3He
- The Quantum Hall Effect
- Solids and Liquid Crystals
- Topological Phase Transitions
Readership: Researchers and graduate students in condensed matter physics and quantum mechanics.
"This book is a collection, with commentary, of papers which over the last three decades of the last century pioneered some of the topological considerations which are today recognized as fundamental in many-body physics. As recognized by the award of the 2016 physics Nobel prize, David Thouless has been the dominant figure in this development, and his lucid and magisterial survey of the field is as useful today as when the book was first published. This is "must-read" for anyone starting research in the area of topological insulators or superconductors, the quantum Hall effect or indeed much of modern condensed matter physics."
Anthony J Leggett
Nobel laureate in Physics, 2003
"This excellent book, just now reprinted, is written with the typical clarity for which the author, David Thouless, is well known. It is surely to be welcomed, especially in light of the Nobel Prize awarded this year, 2016, to Thouless together with Michael Kosterlitz and Duncan Haldane.
Starting with a systematic overview of the complexity of the topological aspects in so many different contexts, Thouless provides more detailed accounts in eight subsequent chapters. This well-presented material is, in turn, supplemented, one must say exceptionally, by over 250 references!"Read Full Review
Michael E Fisher
Distinguished University Professor, University of Maryland
"The lectures in this book contain interesting remarks on ‘whole numbers in physics’, and it is indeed interesting and thought-provoking that both quantum theory and topology can lead to similar situations. This well-produced book provides a most welcome introductory survey of the many areas of condensed matter physics in which topological ideas have played a significant role."
Contemporary Physics
David Thouless is Emeritus Professor of Physics at the University of Washington, Seattle. He was a student of Hans Bethe and wrote an early book on "The Quantum Mechanics of Many-Particle Systems". His best-known work, on topological phase transitions, was done at Birmingham University in collaboration with Michael Kosterlitz. He has worked on the theory of nuclear matter, collective motion in nuclei, superconductivity and superfluidity, magnetism, electrons in disordered systems, and on the quantum Hall effect. He is a Fellow of the Royal Society and a Member of the US National Academy of Sciences. He received the Fritz London Memorial Prize for Low-temperature Physics (1984), the Wolf Prize in Physics (1990), and the Nobel Prize in Physics (2016).
