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Symmetry Breaking and Defects

  • T. W. B. Kibble
Conference paper
Part of the NATO Science Series book series (NAII, volume 127)

Abstract

Symmetry-breaking phase transitions are ubiquitous in condensed matter systems and in quantum field theories. There is also good reason to believe that they feature in the very early history of the Universe. At many such transitions topological defects of one kind or another are formed. Because of their inherent stability, they can have important effects on the subsequent behaviour of the system.

Keywords

Gauge Theory Domain Wall Symmetry Breaking Defect Formation Homotopy Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Yeomans, J.M. (1992) Statistical Mechanics of Phase Transitions, Clarendon, Oxford.Google Scholar
  2. [2]
    Martin, P.A. and Rothen, F. (2002) Many-body Problems and Quantum Field Theory: An Introduction, Springer, Berlin.zbMATHGoogle Scholar
  3. [3]
    Anderson, M.H., Ensher J.R., Matthews, M.R., Wieman, C.E. and Cornell, E.A. (1995) Observation of Bose-Einstein condensation in a dilute atomic vapor, Science 269, 198–201.ADSCrossRefGoogle Scholar
  4. [4]
    Tilley, D.R. and Tilley, J. (1990) Superfluidity and Superconductivity, 3rd ed., IoP Publishing, Bristol.Google Scholar
  5. [5]
    Elitzur, S. (1975) Impossibility of spontaneously breaking local symmetries, Phys. Rev. D 12, 3978–3982.ADSCrossRefGoogle Scholar
  6. [6]
    Itzykson, C. and Drouffe, J.-M. (1989) Statistical Field Theory, vol. 1, 3rd. ed., p. 341, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
  7. [7]
    De Gennes, P.G. and Prost, J. (1993) The Physics of Liquid Crystals, Oxford University Press, Oxford.Google Scholar
  8. [8]
    Kibble, T.W.B. (2000) Classification of topological defects and their relevance to cosmology and elsewhere, in Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions, ed. Y.M. Bunkov and H. Godfrin, NATO Science Series C 549, 7–31, Kluwer Academic Publishers, Dordrecht.CrossRefGoogle Scholar
  9. [9]
    Vollhardt, D. and Welfle, P. (1990) The Superfluid Phases of Helium-3, Taylor and Francis, London.Google Scholar
  10. [10]
    Volovik, G.E. (1992) Exotic Properties of Superfluid 3 He, World Scientific, Singapore.Google Scholar
  11. [11]
    Amaldi, U., de Boer, W. and Furstenau, H. (1991) Comparison of grand unified theories with electroweak and strong coupling-constants measured at LEP, Phys. Lett. B260, 447–455.ADSGoogle Scholar
  12. [12]
    Amaldi, U., de Boer, W., Frampton, P.H., Furstenau, H. and Liu, J.T. (1992) Consistency checks of grand unified theories, Phys. Lett. B281, 374–382.ADSGoogle Scholar
  13. [13]
    Haber, H.E. (1998) The status of the minimal supersymmetric standard model and beyond, Nuc. Phys. Proc. Supp. B62, 469–484.ADSCrossRefGoogle Scholar
  14. [14]
    Hu, S.-T. (1959) Homotopy Theory, Academic Press, New York.zbMATHGoogle Scholar
  15. [15]
    Kajantie, K., Laine, M., Rummukainen, K. and Shaposhnikov, M. (1996) Is there a hot electroweak phase transition at m(H) greater than or similar to m(W)?, Phys. Rev. Lett. 77, 2887–2890.ADSCrossRefGoogle Scholar
  16. [16]
    Contaldi, C, Hindmarsh, M.B. and Magueijo, J. (1999) Cosmic microwave background and density fluctuations from strings plus inflation, Phys. Rev. Lett. 82, 2034–2037.ADSCrossRefGoogle Scholar
  17. [17]
    Durrer, R., Kunz, M. and Melchiorri, A. (2002) Cosmic structure formation with topological defects, Phys. Rep. 364, 1–81.MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. [18]
    Vachaspati, T. and Vilenkin, A. (1991) Large-scale structure from wiggly cosmic strings, Phys. Rev. Lett. 57, 4629–41.Google Scholar
  19. [19]
    Avelino, P.P. and Shellard, E.P.S. (1995) Dynamical friction on cosmic string motion and magnetic field generation, Phys. Rev. D 51, 5946–49.ADSCrossRefGoogle Scholar
  20. [20]
    Dimpoloulos, K. (1998) Primordial magnetic fields from superconducting string net-works, Phys. Rev. D 57, 4629–41.ADSCrossRefGoogle Scholar
  21. [21]
    Bonazzola, S. and Peter, P. (1997) Can high energy cosmic rays be vortons?, Astropart. Phys. 7, 161–172.ADSCrossRefGoogle Scholar
  22. [22]
    Bhattacharjee, P. and Sigl, G. (2000) Origin and propagation of extremely high energy cosmic rays, Phys. Rep. 327, 109–247.ADSCrossRefGoogle Scholar
  23. [23]
    Davis, A.C. and Perkins, W.B. (1997) Dissipating cosmic vortons and baryogenesis, Phys. Lett. B392, 46–50.ADSGoogle Scholar
  24. [24]
    Dimpoloulos, K. and Davis, A.C. (1999) Cosmological consequences of superconducting string networks, Phys. Lett. B446, 238–246.ADSGoogle Scholar
  25. [25]
    Chuang, I., Durrer, R., Turok, N. and Yurke, B. (1991) Cosmology in the laboratory — defect dynamics in liquid crystals, Science 251, 1336–42.ADSCrossRefGoogle Scholar
  26. [26]
    Bowick, M.J., Chandar, L., Schiff, E.A. and Srivastava, A.M. (1994) The cosmological Kibble mechanism in the laboratory — string formation in liquid crystals, Science 263, 943–5.ADSCrossRefGoogle Scholar
  27. [27]
    Srivastava, A.M. (1992) Numerical simulation of dynamical production of vortices by critical and subcritical bubbles, Phys. Rev. D 46, 1353–67.ADSCrossRefGoogle Scholar
  28. [28]
    Pogosian, L. and Vachaspati, T. (1998) Relaxing the geodesic rule in defect formation algorithms, Phys. Lett. 423B, 45–48.ADSGoogle Scholar
  29. [29]
    Digal, S., Ray, R. and Srivastava, A.M. (1999) Observing correlated production of defects-antidefects in liquid crystals, Phys. Rev. Lett. 83, 5030–33.ADSCrossRefGoogle Scholar
  30. [30]
    Zurek, W.H. (1985) Cosmological experiments in superfluid helium, Nature 317, 505–508.ADSCrossRefGoogle Scholar
  31. [31]
    Zurek, W.H. (1993) Cosmic strings in laboratory superfluids and topological remnants of other phase transitions, Acta Phys. Polon. B24, 1301–11.Google Scholar
  32. [32]
    Zurek, W.H. (1996) Cosmological experiments in condensed matter systems, Phys. Rep. 276, 177–221.ADSCrossRefGoogle Scholar
  33. [33]
    Kibble, T.W.B. (1980) Some implications of a cosmological phase transition, Phys. Rep. 67C, 183–199.MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    Laguna, P. and Zurek, W.H. (1997) Density of kinks after a quench: When symmetry breaks, how big are the pieces?, Phys. Rev. Lett. 78, 2519–2522.ADSCrossRefGoogle Scholar
  35. [35]
    Yates, A. and Zurek, W.H. (1998) Vortex formation in two dimensions: When symmetry breaks, how big are the pieces?, Phys. Rev. Lett. 80, 5477–5480.ADSCrossRefGoogle Scholar
  36. [36]
    Hendry, P.C., Lawson, N.S., Lee, R.A.M., McClintock, P.V.E. and Williams, C.D.H. (1994) Generation of defects in superfluid He-4 as an analog of the formation of cosmic strings, Nature 368, 315–317.ADSCrossRefGoogle Scholar
  37. [37]
    Dodd, M.E., Hendry, P.C., Lawson, N.S., McClintock, P.V.E. and Williams, C.D.H. (1998) Nonappearance of vortices in fast mechanical expansions of liquid He-4 through the lambda transition, Phys. Rev. Lett. 81, 3703–3706.ADSCrossRefGoogle Scholar
  38. [38]
    Rivers, R.J. (2000) Slow 4 He quenches produce fuzzy, transient vortices, Phys. Rev. Lett. 84, 1248–51.ADSCrossRefGoogle Scholar
  39. [39]
    Rivers, R.J. (2001) Zurek-Kibble causality bounds in time-dependent Ginzburg-Landau theory and quantum field theory, J. Low Temp. Phys. 124, 41–83.CrossRefGoogle Scholar
  40. [40]
    Hendry, P.C., Lawson, N.S. and McClintock, P.V.E. (2000) Does the Kibble mechanism operate in liquid He-4? J. Low Temp. Phys. 119, 249–256.CrossRefGoogle Scholar
  41. [41]
    Bauerle, C, Bunkov, Yu.M., Fisher, S.N., Godfrin, H. and Pickett, G.R. (1996) Laboratory Simulation of cosmic string formation in the early Universe using superfluid He-3, Nature 382, 332–334.ADSCrossRefGoogle Scholar
  42. [42]
    Ruutu, V.M.H., Eltsov, V.B., Gill, A.J., Kibble, T.W.B., Krusius, M., Makhlin, Yu.G., Placais, B., Volovik, G.E. and Xu, W. (1996) Vortex formation in neutron-irradiated superfluid He-3 as an analogue of cosmological defect formation, Nature 382, 334–336.ADSCrossRefGoogle Scholar
  43. [43]
    Carmi, R. and Polturak, E. (1999) Search for spontaneous nucleation of magnetic flux during rapid cooling of YBa2 Cu3 O7-δ films through T c, Phys. Rev. B 60, 7595–7600.ADSCrossRefGoogle Scholar
  44. [44]
    Rudaz, S. and Srivastava, A.M. (1993) On the production of lfux vortices and magnetic monopoles in phase transitions, Mod. Phys. Lett. A 8, 1443–50.ADSCrossRefGoogle Scholar
  45. [45]
    Copeland, E.J. and Saffin, P. (1996) Bubble collisions in Abelian gauge theories and the geodesic rule, Phys. Rev. D 54, 6088–94.ADSCrossRefGoogle Scholar
  46. [46]
    Hindmarsh, M.B. and Rajantie, A. (2000) Defect formation and local gauge invariance, Phys. Rev. Lett. 85, 4660–63.ADSCrossRefGoogle Scholar
  47. [47]
    Carmi, R., Polturak, E. and Koren, G. (2000) Observation of spontaneous flux generation in a multi-Josephson-junction loop, Phys. Rev. Lett. 84, 4966–69.ADSCrossRefGoogle Scholar
  48. [48]
    Kavoussanaki, E., Monaco, R. and Rivers, R.J. (2000) Testing the Kibble-Zurek scenario with annular Josephson tunneling junctions, Phys. Rev. Lett. 85, 3452–5.ADSCrossRefGoogle Scholar
  49. [49]
    Monaco, R., Mygind, J. and Rivers, R.J. (2002) Zurek-Kibble domain structures: The dynamics of spontaneous vortex formation in annular Josephson tunneling junctions, Phys. Rev. Lett. 89,080603.Google Scholar
  50. [50]
    Karra, G. and Rivers, R.J. (1997) Initial vortex densities after a temperature quench, Phys. Lett. 414B, 28–33.ADSGoogle Scholar
  51. [51]
    See for instance ref. [4], p. 347; but see also Kleinert, H. and Schulte-Frohlinde, V. (2001), Critical properties of φ4-theories, World Scientific Publishing Co., Singapore, p. 18.Google Scholar
  52. [52] Hindmarsh, M.B. and Rajantie, A. (2001) Phase transition dynamics in the hot Abelian Higgs model, Phys. Rev. D 64, 065016.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • T. W. B. Kibble
    • 1
  1. 1.Blackett LaboratoryImperial CollegeLondonUK

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