## Topological Quantum Numbers In Nonrelativistic PhysicsTopological 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. |

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### Contents

1 | |

2 Quantization of Electric Charge | 16 |

3 Circulation and Vortices in Superfluid 4He | 21 |

4 Superconductivity and Flux Quantization | 35 |

5 Josephson Effects | 46 |

6 Superfluid 3He | 55 |

7 The Quantum Hall Effect | 68 |

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### Common terms and phrases

argument atoms axis boundary Burgers vector charge circulation closed component configuration constant core corresponding critical curve cylinder defects defined direction disclination discussed dislocation edge electron equation equilibrium experimental Fermi Fermi energy films finite fluid free vortex frequency gauge given gives Hall conductance Hamiltonian He-A helium homotopy integral interaction JETP Josephson Josephson effect Kosterlitz Landau level lattice Lett linear liquid crystals loop low temperatures magnetic field magnetic flux matrix measured nematic normal obtained order parameter pairs particles path phase transition Phys physical plane quantized quantum Hall effect quasiparticles region result rotation sample shown in Fig singularities solid space sphere spin superconducting superfluid superfluid density surface symmetry texture theoretical theory Thouless tion topologically stable torus two-dimensional velocity Vinen Volovik voltage vortex lines vortices wave function wire xy model zero