Topological quantum numbers in nonrelativistic physics

Topological quantum numbers are distinguimelted from quantum numbers based upon symmeattempt because they are insensitive to the imperfections of the devices in which they are oboffered.

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They have come to be incredibly important in precision measurements in recent years, and carry out the ideal measurements of voltage and also electric resistance. This book defines the theory of such quantum numbers, founding through Dirac"s discussion for the quantization of electric charge, and also continuing via discussions on the helium superfluids, flux quantization and also the Josephboy impact in superconductors, the quantum Hall effect, solids and also liquid crystals, and topological phase transitions. The accompanying reprints incorporate some of the timeless speculative and theoretical records in this location.Physicists — both experimental and theoretical — that are interested in the topic will discover this book an inhelpful recommendation.

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Table of Contents

Preconfront v1 Introduction 11.1 Whole numbers in physics 11.2 Quantum numbers due to symmetry and also topological quantum numbers 31.3 Topics spanned in this book 41.4 Order parameters and also broken symmetry 61.5 Homotopy classes 101.6 Defects 142 Quantization of Electric Charge 162.1 Magnetic monopoles and electrical charge 162.2 Gauge invariance and also the Aharonov-Bohm result 183 Circulation and also Vortices in Superfluid 4He 213.1 Theory of Bose superfluids 213.2 Vortex lines 263.3 Detection of quantized circulation and vortices 293.4 The Magnus pressure 324 Superconductivity and also Flux Quantization 354.1 Superfluids and also superconductors 354.2 Order parameter for superconductors 364.3 London"s equation and flux quantization 374.4 Types I and II superconductors 394.5 Ginzburg-Landau concept 414.6 Flux-line lattice 445 Josephson Effects 465.1 Josephboy junctions and also SQUIDs 465.2 Voltage-frequency relation 526 Superfluid 3He 556.1 The nature of the order parameter 556.2 Vortices and also circulation in superfluid 3He 586.3 Defects and textures 646.4 Superliquid 3He in thin films and also narrowhead channel 667 The Quantum Hall Effect 687.1 Review 687.2 Proportionality of current density and also electrical field 697.3 Bloch"s theorem and also the Laughlin discussion 717.4 Chern numbers 747.5 Long range order in quantum Hall units 777.6 Edge states in the integer quantum Hall result 797.7 Fractional quantum Hall result 807.8 Fractional quantization and degeneprice ground claims 827.9 Topology of fractional quantum Hall fluids 837.10 Coupled quantum Hall systems 858 Solids and Liquid Crystals 898.1 Dislocations in solids 898.2 Order in liquid crystals 928.3 Defects and also textures 949 Topological Phase Transitions 1029.1 Overview 1029.2 The vortex induced shift in superliquid helium movies 1039.3 Two-dimensional magnetic units 1089.4 Topological order in solids 1109.6 Superconducting movies and also layered materials 1129.6 Josephson junction arrays 113References 116Reprinted Papers1 Summary 1371.1 G. Toulousage and also M. Kléguy, "Principles of a Group of Defects in Ordered Media", J. Phys. Lett. (Paris) 37(1976)L149-51 1381.2 G.E. Volovik and also VP. Mineev, "Investigation of Singularities in Superfluid He and also Liquid Crystals by Homotopic Topology Methods", Zhur. Eksp. Teor. Fiz. 72, 2256 1412 Quantization of Electric Charge 1532.1 A.M. Dirac, "Quantised Singularities in the Electromagnetic Field", Proc. Roy. Soc. London 133(1931)60-72 1542.2 Aharonov and D. Bohm, "Significance of Electromagnetic Potentials in the Quantum Theory", Phys. Rev. 115(1959)485-91 1673 Circulation and also Vortices in Superliquid 4He 1753.1 L. Onsager. Nuovo Cimento 6, Suppl. 2(1949)249-50 1773.2 W.F. Vinen, "The Detection of Single Quanta of Circulation in Liquid Helium II", Proc. Roy. Soc. London A260(1961)218-36 1793.3 G.W. Rayfield and F. Reif, "Evidence for the Creation and Motion of Quantized Vortex Rings in Superliquid Helium", Phys. Rev. Lett. 11(1963)305-8 1993.4 E.J. Yarmchuk, M.J.V. Gordan and R.E. Packard, "Observation of Stationary Vortex Arrays in Rotating Superfluid Helium", Phys. Rev. Lett. 43(1979)214-7 2033.5 D.J. Thoumuch less, P. Ao and also Q. Niu, "Transverse Force on a Quantized Vortex in a Superfluid", Phys. Rev. Lett. 76(1996)3758-61 2074 Superconductivity and Flux Quantization 2114.1 N. Byers and also C.N. Yang, "Theoretical Considerations Worrying Quantized Magnetic Flux in Superconducting Cylinders", Phys. Rev. Lett. 7(1961)46-9 2124.2 B.S. Deaver, Jr. and also W.M. Fairbank, "Experipsychological Evidence for Quantized Flux in Superconducting Cylinders", Phys. Rev. Lett. 7(1961)43-6 2164.3 R. Doll and also M. Näbauer, "Experimental Proof of Magnetic Flux Quantization in a Superconducting Ring", Phys. Rev. Lett. 7(1961)51-2 2204.4 C.E. Gough, M.S. Colclough, E.M. Fbody organ, R.G. Jordan, M. Keene, CM. Muirhead, A.I.M. Rae, N. Thomas, J.S. Abell, and also S. Sutton, "Flux Quantization in a High-Tc Superconductor", Nature 326(1987)855 2225 Josephson Effects 2235.1 B.D. Josephchild, "Possible New Effects in Superconductive Tunnelling", Phy. Lett. 1(1962)251-3 2255.2 R.C Jaklevic, J.J. Lambe, A.H. Silver, and also J.E. Mercereau, "Quantum Interference from a Static Vector Potential in a Field-Free Region", Phys. Rev. Lett. 12(1964)274-5 2285.3 S. Shapiro, "Josephkid Curleas in Superconducting Tunnelling: The Effect of Microwaves and also Other Observations", Phys. Rev. Lett. 11(1963)80-2 2305.4 D.N. Langenberg and also J.R. Schrieffer, "Comments on Quantum-Electrodynamic Correction to the Electron Charge in Metals", Phys. Rev. B3(1971)1776 8 2335.5 J. S. Tsai, A.K. Jain, and also J.E. Lukens, "High-Precision Test of the Universality of the Josephboy Voltage-Frequency Relation", Phys. Rev. Lett. 51(1983)316-9 2366 Superfluid 3He 2416.1 P.W. Anderson and G. Toulousage, "Phase Slipweb page without Vortex Cores: Vortex Textures in Superliquid 3He", Phys. Rev. Lett. 38(1977)508-11 2426.2 V.M.H. Ruutu, Ü. Parts, and also M.

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Krusius, "NMR Signatures of Topological Objects in Rotating Superliquid 3He-A", J. Low. Temp. Phys. 103(1996)331 43 2466.3 N.D. Mermin, "Surconfront Singularities and Supercirculation in 3He-A", in Quantum Fluids and Solids, edited by S.M. Triccrucial, E.D. Adams, and J.W. Dufty (Plenum, New York, 1977), pp. 3-22 2597 The Quantum Hall Effect 2797.1 K.v. Klitzing, G. Dorda and also M Pepper, "New Method for High-Accuracy Determicountry of the Fine-Structure Constant Based on Quantized Hall Resistance", Phys. Rev. Lett. 45(1980)494-7 2817.2 A Hurtland also, K. Jones, J. M. Williams, B.L. Gallagher, and T. Gallomeans, "Direct Comparikid of the Quantized Hall Resistance in Gallium Arsenide and Silicon", Phys. Rev. Lett. 66(1991)969-73 2857.3 R.B. Laughlin, "Quantized Hall Conductivity in Two Dimensions", Phy. Rev. B23(1981)5632-3 2907.4 J.E. Avron and also R. Seiler, "Quantization of the Hall Conductance for General, Multippost Schrödinger Hamiltonians", Phys. Rev. Lett. 54(1985)259-62 2927.5 M. Kohmoto, "Topological Invariant and also the Quantization of the Hall Conductance", Ann. Phys. (NY) 160(1985)343-54 2967.6 R.B. Laughlin, "Anomalous Quantum Hall Efffect: An Incompressible Quantum Fluid through Fractionally Charged Excitations", Phys. Rev. Lett. 50(1983)1395-8 3087.7 D.J. Thoumuch less and Y.Gefen, "Fractional Quantum Hall Effect and Multiple Aharonov-Bohm Periods", Phys. Rev. Lett. 66(1991)806-9 3127.8 X.G. Wen and A. Zee, "Category of Abelian Quantum Hall States and also Matrix Formulation of Topological Fluids", Phys. Rev. B46(1992)2290-301 3168 Solids and Liquid Crystals 3298.1 M. Klémale, "Relationship between Burgers Circuit, Volterra Process and also Homotopy Groups", J. Phys. Lett. (Paris) 38(l977)L199-202 3308.2 M. Kléman and L. Michel, "Spontaneous Breaking of Euclidean Invariance and Group of Topologically Stable Defects and also Configurations of Crystals and Liquid Crystals", Phys. Rev. Lett. 40(1978)1387-90 3348.3 V. Poénaru and also G. Toulouse, "The Crossing of Defects in Ordered Media and the Topology of 3-Manifolds", J. Phys. 38(1977)887-95 3389 Topological Phase Transitions 3479.1 J.M. Kosterlitz and D.J. Thouless, "Ordering, Metastcapacity and also Phase Transitions in Two-Dimensional Systems", J. Phys. C6(1973)1181-203 3499.2 D.R. Nelboy and J.M. Kosterlitz, "Universal Jump in the Superliquid Density of Two-Dimensional Superfluids", Phys. Rev. Lett. 39(1977)1201-5 3729.3 J.M. Kosterlitz. "The Critical Properties of the Two-Dimensional xy Model", J. Phys. C7(1974)1046-60 3779.4 D.J. Bishop and J.D. Reppy, "Study of the Superliquid Transition in Two-Dimensional 4He Films", Phys. Rev. Lett. 40(1978)1727-30 3929.5 B.I. Halperin and D.R. Nelchild, "Theory of Two-Dimensional Melting", Phys. Rev. Lett. 41(1978)121-4; Errata, Phys. Rev. Lett. 41(1978)519 3969.6 M.R. Beasley, J.E. Mooij, and T.P. Orlanexecute, "Possibility of Vortex-AntiVortex Pair Dissociation in Two-Dimensional Superconductors", Phys. Rev. Lett. 42(1979)1165-8 4019.7 S. Doniach and B.A. Huberguy, "Topological Excitations in Two-Dimensional Superconductors", Phys. Rev. Lett. 42(1979)1169-72 4059.8 A.F. Hebard and also A.T. Fiory, "Critical-Exponent Measurements of a Two-Dimensional Superconductor", Phys. Rev. Lett. 50(1983)1603-6 4099.9 B.A. Hubermale and also S. Doniach, "Melting of Two-Dimensional Vortex Lattices", Phys. Rev. Lett. 43(1979)950-2 413Index 417