Heterogeneous dynamics in liquids: fluctuations in space and time

The disordered nature of glass-forming melts gives rise to non-Arrhenius and non-exponential behaviour of their dynamics. With respect to the microscopic details involved in the structural relaxation, these materials have remained an unsolved puzzle for over a century. The observation of spatial heterogeneity regarding the dynamics provides an important step towards understanding the relation between the macroscopic properties of soft condensed matter and the molecular mechanisms involved. On the other hand, dynamic heterogeneity is the source of several new questions: What is the length scale and persistence time associated with such clusters of relaxation time? What is the signature of heterogeneity at high temperatures and in the glassy state? How do these features depend on the particular material and on the correlation function used for probing these heterogeneities? This work attempts to review the various approaches to heterogeneous dynamics and the generally accepted results, as well as some controversial issues. Undoubtedly, heterogeneity has provoked a number of novel experimental techniques targeted at studying glass-forming liquids at the molecular level. It will be emphasized that the picture of heterogeneity is a requirement for rationalizing an increasing number of experimental observations rather than just an alternative model for the dynamics of molecules.