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Symmetry Breaking and Defects

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Part of the book series: NATO Science 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.

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References

  1. Yeomans, J.M. (1992) Statistical Mechanics of Phase Transitions, Clarendon, Oxford.

    Google Scholar 

  2. Martin, P.A. and Rothen, F. (2002) Many-body Problems and Quantum Field Theory: An Introduction, Springer, Berlin.

    MATH  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  4. Tilley, D.R. and Tilley, J. (1990) Superfluidity and Superconductivity, 3rd ed., IoP Publishing, Bristol.

    Google Scholar 

  5. Elitzur, S. (1975) Impossibility of spontaneously breaking local symmetries, Phys. Rev. D 12, 3978–3982.

    Article  ADS  Google Scholar 

  6. Itzykson, C. and Drouffe, J.-M. (1989) Statistical Field Theory, vol. 1, 3rd. ed., p. 341, Cambridge University Press, Cambridge.

    Book  Google Scholar 

  7. De Gennes, P.G. and Prost, J. (1993) The Physics of Liquid Crystals, Oxford University Press, Oxford.

    Google Scholar 

  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.

    Chapter  Google Scholar 

  9. Vollhardt, D. and Welfle, P. (1990) The Superfluid Phases of Helium-3, Taylor and Francis, London.

    Google Scholar 

  10. Volovik, G.E. (1992) Exotic Properties of Superfluid 3 He, World Scientific, Singapore.

    Google Scholar 

  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.

    ADS  Google Scholar 

  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.

    ADS  Google Scholar 

  13. Haber, H.E. (1998) The status of the minimal supersymmetric standard model and beyond, Nuc. Phys. Proc. Supp. B62, 469–484.

    Article  ADS  Google Scholar 

  14. Hu, S.-T. (1959) Homotopy Theory, Academic Press, New York.

    MATH  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  17. Durrer, R., Kunz, M. and Melchiorri, A. (2002) Cosmic structure formation with topological defects, Phys. Rep. 364, 1–81.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Vachaspati, T. and Vilenkin, A. (1991) Large-scale structure from wiggly cosmic strings, Phys. Rev. Lett. 57, 4629–41.

    Google Scholar 

  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.

    Article  ADS  Google Scholar 

  20. Dimpoloulos, K. (1998) Primordial magnetic fields from superconducting string net-works, Phys. Rev. D 57, 4629–41.

    Article  ADS  Google Scholar 

  21. Bonazzola, S. and Peter, P. (1997) Can high energy cosmic rays be vortons?, Astropart. Phys. 7, 161–172.

    Article  ADS  Google Scholar 

  22. Bhattacharjee, P. and Sigl, G. (2000) Origin and propagation of extremely high energy cosmic rays, Phys. Rep. 327, 109–247.

    Article  ADS  Google Scholar 

  23. Davis, A.C. and Perkins, W.B. (1997) Dissipating cosmic vortons and baryogenesis, Phys. Lett. B392, 46–50.

    ADS  Google Scholar 

  24. Dimpoloulos, K. and Davis, A.C. (1999) Cosmological consequences of superconducting string networks, Phys. Lett. B446, 238–246.

    ADS  Google Scholar 

  25. Chuang, I., Durrer, R., Turok, N. and Yurke, B. (1991) Cosmology in the laboratory — defect dynamics in liquid crystals, Science 251, 1336–42.

    Article  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  27. Srivastava, A.M. (1992) Numerical simulation of dynamical production of vortices by critical and subcritical bubbles, Phys. Rev. D 46, 1353–67.

    Article  ADS  Google Scholar 

  28. Pogosian, L. and Vachaspati, T. (1998) Relaxing the geodesic rule in defect formation algorithms, Phys. Lett. 423B, 45–48.

    ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  30. Zurek, W.H. (1985) Cosmological experiments in superfluid helium, Nature 317, 505–508.

    Article  ADS  Google Scholar 

  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. Zurek, W.H. (1996) Cosmological experiments in condensed matter systems, Phys. Rep. 276, 177–221.

    Article  ADS  Google Scholar 

  33. Kibble, T.W.B. (1980) Some implications of a cosmological phase transition, Phys. Rep. 67C, 183–199.

    Article  MathSciNet  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  38. Rivers, R.J. (2000) Slow 4 He quenches produce fuzzy, transient vortices, Phys. Rev. Lett. 84, 1248–51.

    Article  ADS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  45. Copeland, E.J. and Saffin, P. (1996) Bubble collisions in Abelian gauge theories and the geodesic rule, Phys. Rev. D 54, 6088–94.

    Article  ADS  Google Scholar 

  46. Hindmarsh, M.B. and Rajantie, A. (2000) Defect formation and local gauge invariance, Phys. Rev. Lett. 85, 4660–63.

    Article  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  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. Karra, G. and Rivers, R.J. (1997) Initial vortex densities after a temperature quench, Phys. Lett. 414B, 28–33.

    ADS  Google Scholar 

  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 

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Kibble, T.W.B. (2003). Symmetry Breaking and Defects. In: Arodz, H., Dziarmaga, J., Zurek, W.H. (eds) Patterns of Symmetry Breaking. NATO Science Series, vol 127. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1029-0_1

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  • DOI: https://doi.org/10.1007/978-94-007-1029-0_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1745-2

  • Online ISBN: 978-94-007-1029-0

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