Dynamics of Symmetry Breaking out of Equilibrium: from Condensed Matter to Qcd and the Early Universe∗

The dynamics of symmetry breaking during out of equilibrium phase transitions is a topic of great importance in many disciplines, from condensed matter to particle physics and early Universe cosmology with definite experimental impact. In these notes we provide a summary of the relevant aspects of the dynamics of symmetry breaking in many different fields with emphasis on the experimental realizations. In condensed matter we address the dynamics of phase ordering, the emergence of condensates, coarsening and dynamical scaling. In QCD the possibility of disoriented chiral condensates of pions emerging during a strongly out of equilibrium phase transition is discussed. We elaborate on the dynamics of phase ordering in phase transitions in the Early Universe, in particular the emergence of condensates and scaling in FRW cosmologies. We mention some experimental efforts in different fields that study this wide ranging phenomena and offer a quantitative theoretical description both at the phenomenological level in condensed matter, introducing the scaling hypothesis as well as at a microscopic level in quantum field theories. The emergence of semiclassical condensates and a dynamical length scale is shown in detail, in quantum field theory this length scale is constrained by causality. The large N limit provides a natural bridge to compare the solutions in different settings and to establish similarities and differences. Invited by the National Academy of Sciences of India, to appear in ANSI-2000, and in the Proceedings of the VIème Colloque Cosmologie, Paris, 16-18 JUNE 1999 Laboratoire Associé au CNRS UMR 7589.