By G. E. Volovik (auth.), Yuriy M. Bunkov, Henri Godfrin (eds.)
Topological defects shaped at symmetry-breaking part transitions play a massive function in lots of diverse fields of physics. they seem in lots of condensed-matter platforms at low temperature; examples contain vortices in superfluid helium-4, a wealthy number of defects in helium-3, quantized magazine netic flux tubes in type-II superconductors, and disclination strains and different defects in liquid crystals. In cosmology, unified gauge theories of particle interactions recommend a chain of part transitions within the very early uni verse a few of that could result in illness formation. In astrophysics, defects play an immense position within the dynamics of neutron stars. In 1997 the eu technological know-how starting place began the medical community "Topological defects" headed via Tom Kibble. This community has supplied us with a different chance of building a collaboration among the representatives of those very various branches of contemporary physics. The NATO-ASI (Advanced learn Institute), held in Les Houches in February 1999 due to the help of the medical department of NATO, the eu technological know-how starting place and the CNRS, represents a key occasion of this ESF community. It introduced jointly individuals from largely diversified fields, with diversified services and vocabulary, fostering the alternate of principles. The lectures given by way of particle physicists, cosmologists and condensed topic physicists are the results of the fruitful collaborations proven considering 1997 among teams in numerous eu nations and within the U.S.A.
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Extra info for Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions
Exactly as in the case of a composite defect, what happens is that the string becomes the boundary of a domain wall. 3. THE A PHASE If normal 3He is cooled at pressures above about 21 bar, it makes a transition to a different superfluid phase, the A phase. The form of that minimizes the free energy in this region is quite different from (20), namely (30) Here d, e and f are unit vectors with e . f = 0; d is the spin anisotropy axis: the state is one in which the component of S along the direction d is zero.
And Schwesinger, B. (1986) Baryons in the Skyrme model, Rep. Prog. Phys. 49, 825-872. 28. Manton, N. (1987) Geometry of Skyrmions, Comm. Math. Phys. 111,469-478. 29. H. (1993) Cosmic strings in laboratory superfluids and topological remnants of other phase transitions, Acta Phys. Polon. B24, 1301-1311. 30. H. (1996) Cosmological experiments in condensed matter systems, Phys. Rep. 276, 177-221. 31. H. (1985) Cosmological experiments in superfluid helium, Nature 317, 505-508. 32. E. H. (1994) Generation of defects in superfluid He-4 as an analog of the formation of cosmic strings, Nature 368, 315-317.
To find out what happens at large distances to the defects present at short distances, we can again examine the relative homotopy groups 7rn (M A, M A). In this case, one finds: 7r3(MA, M A) = Z, 7r2(MA, M A) = Z, 7rl (MA' M A) = Z2. (37) ... ... ... " ... • ... + + + + ~~ ... ... ... K ...... ... ...... K ~ II ~ Figure 6. II ~ II ~ II ~ ....... ~ ....... Small monopole attached to a fat string. So large-scale monopoles, strings and domain walls are generated by the 'second transition'. We then have to examine the effect of the maps from one homotopy group to another on the homotopy classes of the defects.