## Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase TransitionsTopological defects formed at symmetry-breaking phase transitions play an important role in many different fields of physics. They appear in many condensed-matter systems at low temperature; examples include vortices in superfluid helium-4, a rich variety of defects in helium-3, quantized mag netic flux tubes in type-II superconductors, and disclination lines and other defects in liquid crystals. In cosmology, unified gauge theories of particle interactions suggest a sequence of phase transitions in the very early uni verse some of which may lead to defect formation. In astrophysics, defects play an important role in the dynamics of neutron stars. In 1997 the European Science Foundation started the scientific network "Topological defects" headed by Tom Kibble. This network has provided us with a unique opportunity of establishing a collaboration between the representatives of these very different branches of modern physics. The NATO-ASI (Advanced Study Institute), held in Les Houches in February 1999 thanks to the support of the Scientific Division of NATO, the European Science Foundation and the CNRS, represents a key event of this ESF network. It brought together participants from widely different fields, with diverse expertise and vocabulary, fostering the exchange of ideas. The lectures given by particle physicists, cosmologists and condensed matter physicists are the result of the fruitful collaborations established since 1997 between groups in several European countries and in the U.S.A. |

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3He-A level anisotropy atoms axis BCS theory Breaking Phase Transitions Bunkov composite defects condensed matter configuration Cooper pairs correlation length corresponding coset cosmic strings cosmology defect formation define density domain walls Dynamics of Symmetry effect electroweak elements exact sequence factor Fermi gas Fermi system fermions free energy gauge geodesic rule Ginzburg-Landau groundstate helium-3 homotopy classes homotopy groups infinite strings interaction invariant Kibble Kluwer Academic Publishers Landau lattice Lett loop in G maps molecular field Non-Equilibrium Dynamics non-trivial nuclear order parameter pair radius pair wave function particle Phys physics potential quantity quasiparticles quench relative result rotation scalar field second transition simulations skyrmion space spin and orbital stable monopoles subgroup superconductors superfluid 3He superfluid phases Symmetry Breaking Phase symmetry group TDGL temperature textures topological defects topologically stable trivial vacuum manifold vector Volovik vortex in 3He-A vortices wave function winding number zero Zurek

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