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Topological Quantum Numbers in Nonrelativistic Physics - David Thouless

Topological Quantum Numbers in Nonrelativistic Physics

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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 measurement of voltage and electrical resistance. This text 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.

Preface
Introductionp. 1
Quantization of Electric Chargep. 16
Circulation and Vortices in Superfluid [superscript 4]Hep. 21
Superconductivity and Flux Quantizationp. 35
Josephson Effectsp. 46
Superfluid [superscript 3]Hep. 55
The Quantum Hall Effectp. 68
Solids and Liquid Crystalsp. 89
Topological Phase Transitionsp. 102
Referencesp. 116
Principles of a Classification of Defects in Ordered Mediap. 138
Investigation of Singularities in Superfluid He and Liquid Crystals by Homotopic Topology Methodsp. 141
Quantization of Electric Chargep. 153
Quantised Singularities in the Electromagnetic Fieldp. 154
Significance of Electromagnetic Potentials in the Quantum Theoryp. 167
Circulation and Vortices in Superfluid [superscript 4]Hep. 175
Nuovo Cimento 6p. 177
The Detection of Single Quanta of Circulation in Liquid Helium IIp. 179
Evidence for the Creation and Motion of Quantized Vortex Rings in Superfluid Heliump. 199
Observation of Stationary Vortex Arrays in Rotating Superfluid Heliump. 203
Transverse Force on a Quantized Vortex in a Superfluidp. 207
Superconductivity and Flux Quantizationp. 211
Theoretical Considerations Concerning Quantized Magnetic Flux in Superconducting Cylindersp. 212
Experimental Evidence for Quantized Flux in Superconducting Cylindersp. 216
Experimental Proof of Magnetic Flux Quantization in a Superconducting Ringp. 220
Flux Quantization in a High-T[subscript c] Superconductorp. 222
Josephson Effectsp. 223
Possible New Effects in Superconductive Tunnellingp. 225
Quantum Interference from a Static Vector Potential in a Field-Free Regionp. 228
Josephson Currents in Superconducting Tunnelling: The Effect of Microwaves and Other Observationsp. 230
Comments on Quantum-Electrodynamic Corrections to the Electron Charge in Metalsp. 233
High-Precision Test of the Universality of the Josephson Voltage-Frequency Relationp. 236
Superfluid [superscript 3]Hep. 241
Phase Slippage without Vortex Cores: Vortex Textures in Superfluid [superscript 3]Hep. 242
NMR Signatures of Topological Objects in Rotating Superfluid [superscript 3]He-Ap. 246
Surface Singularities and Superflow in [superscript 3]He-Ap. 259
The Quantum Hall Effectp. 279
New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistancep. 281
Direct Comparison of the Quantized Hall Resistance in Gallium Arsenide and Siliconp. 285
Quantized Hall Conductivity in Two Dimensionsp. 290
Quantization of the Hall Conductance for General, Multiparticle Schrodinger Hamiltoniansp. 292
Topological Invariant and the Quantization of the Hall Conductancep. 296
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitationsp. 308
Fractional Quantum Hall Effect and Multiple Aharonov-Bohm Periodsp. 312
Classification of Abelian Quantum Hall States and Matrix Formulation of Topological Fluidsp. 316
Solids and Liquid Crystalsp. 329
Relationship between Burgers Circuit, Volterra Process and Homotopy Groupsp. 330
Spontaneous Breaking of Euclidean Invariance and Classification of Topologically Stable Defects and Configurations of Crystals and Liquid Crystalsp. 334
The Crossing of Defects in Ordered Media and the Topology of 3-Manifoldsp. 338
Topological Phase Transitionsp. 347
Ordering, Metastability and Phase Transitions in Two-Dimensional Systemsp. 349
Universal Jump in the Superfluid Density of Two-Dimensional Superfluidsp. 372
The Critical Properties of the Two-Dimensional xy Modelp. 377
Study of the Superfluid Transition in Two-Dimensional [superscript 4]He Filmsp. 392
Theory of Two-Dimensional Meltingp. 396
Possibility of Vortex-AntiVortex Pair Dissociation in Two-Dimensional Superconductorsp. 401
Topological Excitations in Two-Dimensional Superconductorsp. 405
Critical-Exponent Measurements of a Two-Dimensional Superconductorp. 409
Melting of Two-Dimensional Vortex Latticesp. 413
Indexp. 417
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9789810229009
ISBN-10: 9810229003
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 440
Published: 1997
Country of Publication: SG
Dimensions (cm): 27.31 x 20.32  x 3.18
Weight (kg): 1.04