  The Kibble-Zurek mechanism describes the evolution of topological defect
structures like domain walls, strings, and monopoles when a system is driven
through a second order phase transition. The model is used on very different
scales like the Higgs field in the early universe or quantum fluids in
condensed matter systems. A defect structure naturally arises during cooling if
separated regions are too far apart to `communicate' (e.g. about their
orientation or phase) due to finite signal velocity. This results in separated
domains with different (degenerated) locally broken symmetry. Within this
picture we investigate the non-equilibrium dynamics in a condensed matter
analogue, a two-dimensional ensemble of colloidal particles. In equilibrium it
obeys the so called Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) melting
scenario with continuous (second-order like) phase transitions. The ensemble is
exposed to a set of finite cooling rates covering roughly three orders of
magnitude. Along this process, we analyze the defect and domain structure
quantitatively via video microscopy and determine the scaling of the
corresponding length scales as a function of the cooling rate. We indeed
observe the scaling predicted by the Kibble-Zurek mechanism for the KTHNY
universality class.
