Kibble-Zurek mechanism and infinitely slow annealing through critical points
Biroli G. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France) Gugliandolo L.F. (LPTHE UMR 7589, Université Pierre et Marie Curie–Paris VI, 4 Place Jussieu, 75252 Paris Cedex 05, France) Sicilia A. (Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW Cambridge, United Kingdom)
Abstract: We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phase ordering systems during an infinitely slow annealing across a second order phase transition. We elucidate the time and cooling rate dependence of the typical growing length and we use it to predict the number of topological defects left over in the symmetry broken phase as a function of time, both close and far from the critical region. Our results extend the Kibble-Zurek mechanism and reveal its limitations.