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Cover Art
PRINTED BOOKS
Author Thouless, D. J.

Title Topological quantum numbers in nonrelativistic physics / David J. Thouless.

Published Singapore ; River Edge, N.J. : World Scientific, [1998]
©1998

Copies

Location Call No. Status
 UniM ERC  530.143 THOU    AVAILABLE
Physical description xii, 426 pages : illustrations ; 27 cm
Bibliography Includes bibliographical references and index.
Contents 1 Introduction 1 -- 1.1 Whole numbers in physics 1 -- 1.2 Quantum numbers due to symmetry and topological quantum numbers 3 -- 1.3 Topics covered in this book 4 -- 1.4 Order parameters and broken symmetry 6 -- 1.5 Homotopy classes 10 -- 1.6 Defects 14 -- 2 Quantization of Electric Charge 16 -- 2.1 Magnetic monopoles and electric charge 16 -- 2.2 Gauge invariance and the Aharonov-Bohm effect 18 -- 3 Circulation and Vortices in Superfluid ⁴He 21 -- 3.1 Theory of Bose superfluids 21 -- 3.2 Vortex lines 26 -- 3.3 Detection of quantized circulation and vortices 29 -- 3.4 Magnus force 32 -- 4 Superconductivity and Flux Quantization 35 -- 4.1 Superfluids and superconductors 35 -- 4.2 Order parameter for superconductors 36 -- 4.3 London's equation and flux quantization 37 -- 4.4 Types I and II superconductors 39 -- 4.5 Ginzburg-Landau theory 41 -- 4.6 Flux-line lattice 44 -- 5 Josephson Effects 46 -- 5.1 Josephson junctions and SQUIDs 46 -- 5.2 Voltage-frequency relation 52 -- 6 Superfluid ³He 55 -- 6.1 Nature of the order parameter 55 -- 6.2 Vortices and circulation in superfluid ³He 58 -- 6.3 Defects and textures 64 -- 6.4 Superfluid ³He in thin films and narrow channel 66 -- 7 Quantum Hall Effect 68 -- 7.1 Introduction 68 -- 7.2 Proportionality of current density and electric field 69 -- 7.3 Bloch's theorem and the Laughlin argument 71 -- 7.4 Chern numbers 74 -- 7.5 Long range order in quantum Hall systems 77 -- 7.6 Edge states in the integer quantum Hall effect 79 -- 7.7 Fractional quantum Hall effect 80 -- 7.8 Fractional quantization and degenerate ground states 82 -- 7.9 Topology of fractional quantum Hall fluids 83 -- 7.10 Coupled quantum Hall systems 85 -- 8 Solids and Liquid Crystals 89 -- 8.1 Dislocations in solids 89 -- 8.2 Order in liquid crystals 92 -- 8.3 Defects and textures 94 -- 9 Topological Phase Transitions 102 -- 9.1 Introduction 102 -- 9.2 Vortex induced transition in superfluid helium films 103 -- 9.3 Two-dimensional magnetic systems 108 -- 9.4 Topological order in solids 110 -- 9.6 Superconducting films and layered materials 112 -- 9.6 Josephson junction arrays 113.
Summary Describes the theory of topological quantum numbers, starting with Dirac's argument for the quantization of electric charge, and continuing with discussions on the helium superfluids, flux quantization, the quantum Hall effect, solids and liquid crystals, and the importance of topological concepts in the theory of phase transitions in two dimensions. Material is accessible to those with background in quantum mechanics and statistical mechanics. The bulk of the book consists of reprints of classic experimental and theoretical papers, written from the 1930s to the 1990s. Annotation copyrighted by Book News, Inc., Portland, OR
Subject Quantum field theory.
Mathematical physics.
ISBN 9810229003
9810230257 (paperback)